wenzelm@44163
|
1 |
(* Title: HOL/Tools/ATP/atp_translate.ML
|
blanchet@38506
|
2 |
Author: Fabian Immler, TU Muenchen
|
blanchet@38506
|
3 |
Author: Makarius
|
blanchet@38506
|
4 |
Author: Jasmin Blanchette, TU Muenchen
|
blanchet@38506
|
5 |
|
blanchet@44734
|
6 |
Translation of HOL to FOL for Metis and Sledgehammer.
|
blanchet@38506
|
7 |
*)
|
blanchet@38506
|
8 |
|
blanchet@43926
|
9 |
signature ATP_TRANSLATE =
|
blanchet@38506
|
10 |
sig
|
nik@44535
|
11 |
type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
|
blanchet@43977
|
12 |
type connective = ATP_Problem.connective
|
blanchet@43977
|
13 |
type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
|
blanchet@43780
|
14 |
type format = ATP_Problem.format
|
blanchet@43580
|
15 |
type formula_kind = ATP_Problem.formula_kind
|
blanchet@38506
|
16 |
type 'a problem = 'a ATP_Problem.problem
|
blanchet@43926
|
17 |
|
blanchet@44282
|
18 |
datatype locality =
|
nik@45449
|
19 |
General | Helper | Induction | Extensionality | Intro | Elim | Simp |
|
nik@45449
|
20 |
Local | Assum | Chained
|
blanchet@43484
|
21 |
|
blanchet@44491
|
22 |
datatype order = First_Order | Higher_Order
|
blanchet@45349
|
23 |
datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
|
blanchet@45256
|
24 |
datatype soundness = Unsound | Sound_Modulo_Infiniteness | Sound
|
blanchet@43484
|
25 |
datatype type_level =
|
blanchet@45256
|
26 |
All_Types |
|
blanchet@45256
|
27 |
Noninf_Nonmono_Types of soundness |
|
blanchet@45256
|
28 |
Fin_Nonmono_Types |
|
blanchet@45256
|
29 |
Const_Arg_Types |
|
blanchet@44233
|
30 |
No_Types
|
blanchet@45261
|
31 |
datatype type_uniformity = Uniform | Nonuniform
|
blanchet@43484
|
32 |
|
blanchet@44493
|
33 |
datatype type_enc =
|
blanchet@45455
|
34 |
Simple_Types of order * polymorphism * type_level |
|
blanchet@45261
|
35 |
Guards of polymorphism * type_level * type_uniformity |
|
blanchet@45261
|
36 |
Tags of polymorphism * type_level * type_uniformity
|
blanchet@43484
|
37 |
|
blanchet@45351
|
38 |
val type_tag_idempotence : bool Config.T
|
blanchet@45351
|
39 |
val type_tag_arguments : bool Config.T
|
blanchet@44959
|
40 |
val no_lambdasN : string
|
blanchet@44959
|
41 |
val concealedN : string
|
blanchet@44959
|
42 |
val liftingN : string
|
blanchet@44959
|
43 |
val combinatorsN : string
|
blanchet@44959
|
44 |
val hybridN : string
|
blanchet@44959
|
45 |
val lambdasN : string
|
blanchet@44959
|
46 |
val smartN : string
|
blanchet@44367
|
47 |
val schematic_var_prefix : string
|
blanchet@44367
|
48 |
val fixed_var_prefix : string
|
blanchet@44367
|
49 |
val tvar_prefix : string
|
blanchet@44367
|
50 |
val tfree_prefix : string
|
blanchet@44367
|
51 |
val const_prefix : string
|
blanchet@44367
|
52 |
val type_const_prefix : string
|
blanchet@44367
|
53 |
val class_prefix : string
|
blanchet@44807
|
54 |
val polymorphic_free_prefix : string
|
blanchet@43926
|
55 |
val skolem_const_prefix : string
|
blanchet@43926
|
56 |
val old_skolem_const_prefix : string
|
blanchet@43926
|
57 |
val new_skolem_const_prefix : string
|
blanchet@43966
|
58 |
val type_decl_prefix : string
|
blanchet@43966
|
59 |
val sym_decl_prefix : string
|
blanchet@44860
|
60 |
val guards_sym_formula_prefix : string
|
blanchet@45255
|
61 |
val tags_sym_formula_prefix : string
|
blanchet@40445
|
62 |
val fact_prefix : string
|
blanchet@38506
|
63 |
val conjecture_prefix : string
|
blanchet@43750
|
64 |
val helper_prefix : string
|
blanchet@43966
|
65 |
val class_rel_clause_prefix : string
|
blanchet@43966
|
66 |
val arity_clause_prefix : string
|
blanchet@43966
|
67 |
val tfree_clause_prefix : string
|
blanchet@43750
|
68 |
val typed_helper_suffix : string
|
blanchet@43966
|
69 |
val untyped_helper_suffix : string
|
blanchet@44000
|
70 |
val type_tag_idempotence_helper_name : string
|
blanchet@43807
|
71 |
val predicator_name : string
|
blanchet@43807
|
72 |
val app_op_name : string
|
blanchet@45255
|
73 |
val type_guard_name : string
|
blanchet@43945
|
74 |
val type_tag_name : string
|
blanchet@43803
|
75 |
val simple_type_prefix : string
|
blanchet@44015
|
76 |
val prefixed_predicator_name : string
|
blanchet@43971
|
77 |
val prefixed_app_op_name : string
|
blanchet@43971
|
78 |
val prefixed_type_tag_name : string
|
blanchet@44367
|
79 |
val ascii_of : string -> string
|
blanchet@44367
|
80 |
val unascii_of : string -> string
|
blanchet@43926
|
81 |
val strip_prefix_and_unascii : string -> string -> string option
|
blanchet@44000
|
82 |
val proxy_table : (string * (string * (thm * (string * string)))) list
|
blanchet@44000
|
83 |
val proxify_const : string -> (string * string) option
|
blanchet@44367
|
84 |
val invert_const : string -> string
|
blanchet@44367
|
85 |
val unproxify_const : string -> string
|
blanchet@43934
|
86 |
val new_skolem_var_name_from_const : string -> string
|
blanchet@44089
|
87 |
val atp_irrelevant_consts : string list
|
blanchet@44089
|
88 |
val atp_schematic_consts_of : term -> typ list Symtab.table
|
blanchet@45256
|
89 |
val type_enc_from_string : soundness -> string -> type_enc
|
blanchet@44692
|
90 |
val is_type_enc_higher_order : type_enc -> bool
|
blanchet@44493
|
91 |
val polymorphism_of_type_enc : type_enc -> polymorphism
|
blanchet@44493
|
92 |
val level_of_type_enc : type_enc -> type_level
|
blanchet@45256
|
93 |
val is_type_enc_quasi_sound : type_enc -> bool
|
blanchet@44493
|
94 |
val is_type_enc_fairly_sound : type_enc -> bool
|
blanchet@45275
|
95 |
val adjust_type_enc : format -> type_enc -> type_enc
|
blanchet@43977
|
96 |
val mk_aconns :
|
blanchet@43977
|
97 |
connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
|
nik@44535
|
98 |
val unmangled_const : string -> string * (string, 'b) ho_term list
|
blanchet@43971
|
99 |
val unmangled_const_name : string -> string
|
blanchet@44035
|
100 |
val helper_table : ((string * bool) * thm list) list
|
blanchet@44372
|
101 |
val factsN : string
|
blanchet@40240
|
102 |
val prepare_atp_problem :
|
blanchet@45253
|
103 |
Proof.context -> format -> formula_kind -> formula_kind -> type_enc
|
blanchet@45256
|
104 |
-> bool -> string -> bool -> bool -> term list -> term
|
blanchet@44959
|
105 |
-> ((string * locality) * term) list
|
blanchet@43412
|
106 |
-> string problem * string Symtab.table * int * int
|
blanchet@44055
|
107 |
* (string * locality) list vector * int list * int Symtab.table
|
blanchet@41561
|
108 |
val atp_problem_weights : string problem -> (string * real) list
|
blanchet@38506
|
109 |
end;
|
blanchet@38506
|
110 |
|
blanchet@43926
|
111 |
structure ATP_Translate : ATP_TRANSLATE =
|
blanchet@38506
|
112 |
struct
|
blanchet@38506
|
113 |
|
blanchet@43926
|
114 |
open ATP_Util
|
blanchet@38506
|
115 |
open ATP_Problem
|
blanchet@43926
|
116 |
|
blanchet@43926
|
117 |
type name = string * string
|
blanchet@43926
|
118 |
|
blanchet@45351
|
119 |
val type_tag_idempotence =
|
blanchet@45411
|
120 |
Attrib.setup_config_bool @{binding atp_type_tag_idempotence} (K false)
|
blanchet@45351
|
121 |
val type_tag_arguments =
|
blanchet@45411
|
122 |
Attrib.setup_config_bool @{binding atp_type_tag_arguments} (K false)
|
blanchet@45351
|
123 |
|
blanchet@44959
|
124 |
val no_lambdasN = "no_lambdas"
|
blanchet@44959
|
125 |
val concealedN = "concealed"
|
blanchet@44959
|
126 |
val liftingN = "lifting"
|
blanchet@44959
|
127 |
val combinatorsN = "combinators"
|
blanchet@44959
|
128 |
val hybridN = "hybrid"
|
blanchet@44959
|
129 |
val lambdasN = "lambdas"
|
blanchet@44959
|
130 |
val smartN = "smart"
|
blanchet@44959
|
131 |
|
blanchet@44692
|
132 |
val generate_info = false (* experimental *)
|
blanchet@38506
|
133 |
|
blanchet@44559
|
134 |
fun isabelle_info s =
|
blanchet@44559
|
135 |
if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
|
blanchet@44559
|
136 |
else NONE
|
blanchet@43748
|
137 |
|
blanchet@44559
|
138 |
val introN = "intro"
|
blanchet@44559
|
139 |
val elimN = "elim"
|
blanchet@44559
|
140 |
val simpN = "simp"
|
blanchet@43748
|
141 |
|
blanchet@45480
|
142 |
(* TFF1 is still in development, and it is still unclear whether symbols will be
|
blanchet@45480
|
143 |
allowed to have types like "$tType > $o" (i.e., "![A : $tType] : $o"), with
|
blanchet@45480
|
144 |
"dummy" type variables. *)
|
blanchet@45480
|
145 |
val exploit_tff1_dummy_type_vars = false
|
blanchet@45480
|
146 |
|
blanchet@43926
|
147 |
val bound_var_prefix = "B_"
|
blanchet@45262
|
148 |
val all_bound_var_prefix = "BA_"
|
blanchet@45262
|
149 |
val exist_bound_var_prefix = "BE_"
|
blanchet@43926
|
150 |
val schematic_var_prefix = "V_"
|
blanchet@43926
|
151 |
val fixed_var_prefix = "v_"
|
blanchet@43926
|
152 |
val tvar_prefix = "T_"
|
blanchet@43926
|
153 |
val tfree_prefix = "t_"
|
blanchet@43926
|
154 |
val const_prefix = "c_"
|
blanchet@43926
|
155 |
val type_const_prefix = "tc_"
|
blanchet@45346
|
156 |
val simple_type_prefix = "s_"
|
blanchet@43926
|
157 |
val class_prefix = "cl_"
|
blanchet@43926
|
158 |
|
blanchet@44807
|
159 |
val polymorphic_free_prefix = "poly_free"
|
blanchet@44778
|
160 |
|
blanchet@44734
|
161 |
val skolem_const_prefix = "ATP" ^ Long_Name.separator ^ "Sko"
|
blanchet@43926
|
162 |
val old_skolem_const_prefix = skolem_const_prefix ^ "o"
|
blanchet@43926
|
163 |
val new_skolem_const_prefix = skolem_const_prefix ^ "n"
|
blanchet@43926
|
164 |
|
blanchet@43839
|
165 |
val type_decl_prefix = "ty_"
|
blanchet@43839
|
166 |
val sym_decl_prefix = "sy_"
|
blanchet@44860
|
167 |
val guards_sym_formula_prefix = "gsy_"
|
blanchet@45255
|
168 |
val tags_sym_formula_prefix = "tsy_"
|
blanchet@40445
|
169 |
val fact_prefix = "fact_"
|
blanchet@38506
|
170 |
val conjecture_prefix = "conj_"
|
blanchet@38506
|
171 |
val helper_prefix = "help_"
|
blanchet@44000
|
172 |
val class_rel_clause_prefix = "clar_"
|
blanchet@38506
|
173 |
val arity_clause_prefix = "arity_"
|
blanchet@43926
|
174 |
val tfree_clause_prefix = "tfree_"
|
blanchet@38506
|
175 |
|
blanchet@44734
|
176 |
val lambda_fact_prefix = "ATP.lambda_"
|
blanchet@43750
|
177 |
val typed_helper_suffix = "_T"
|
blanchet@43750
|
178 |
val untyped_helper_suffix = "_U"
|
blanchet@44000
|
179 |
val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
|
blanchet@43750
|
180 |
|
blanchet@45346
|
181 |
val predicator_name = "pp"
|
blanchet@45346
|
182 |
val app_op_name = "aa"
|
blanchet@45346
|
183 |
val type_guard_name = "gg"
|
blanchet@45346
|
184 |
val type_tag_name = "tt"
|
blanchet@43402
|
185 |
|
blanchet@44015
|
186 |
val prefixed_predicator_name = const_prefix ^ predicator_name
|
blanchet@43971
|
187 |
val prefixed_app_op_name = const_prefix ^ app_op_name
|
blanchet@43971
|
188 |
val prefixed_type_tag_name = const_prefix ^ type_tag_name
|
blanchet@43971
|
189 |
|
blanchet@38506
|
190 |
(* Freshness almost guaranteed! *)
|
blanchet@44734
|
191 |
val atp_weak_prefix = "ATP:"
|
blanchet@38506
|
192 |
|
blanchet@43926
|
193 |
(*Escaping of special characters.
|
blanchet@43926
|
194 |
Alphanumeric characters are left unchanged.
|
blanchet@43926
|
195 |
The character _ goes to __
|
blanchet@43926
|
196 |
Characters in the range ASCII space to / go to _A to _P, respectively.
|
blanchet@43926
|
197 |
Other characters go to _nnn where nnn is the decimal ASCII code.*)
|
blanchet@43934
|
198 |
val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
|
blanchet@43926
|
199 |
|
blanchet@43926
|
200 |
fun stringN_of_int 0 _ = ""
|
blanchet@43926
|
201 |
| stringN_of_int k n =
|
blanchet@43926
|
202 |
stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
|
blanchet@43926
|
203 |
|
blanchet@43926
|
204 |
fun ascii_of_char c =
|
blanchet@43926
|
205 |
if Char.isAlphaNum c then
|
blanchet@43926
|
206 |
String.str c
|
blanchet@43926
|
207 |
else if c = #"_" then
|
blanchet@43926
|
208 |
"__"
|
blanchet@43926
|
209 |
else if #" " <= c andalso c <= #"/" then
|
blanchet@43926
|
210 |
"_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
|
blanchet@43926
|
211 |
else
|
blanchet@43926
|
212 |
(* fixed width, in case more digits follow *)
|
blanchet@43926
|
213 |
"_" ^ stringN_of_int 3 (Char.ord c)
|
blanchet@43926
|
214 |
|
blanchet@43926
|
215 |
val ascii_of = String.translate ascii_of_char
|
blanchet@43926
|
216 |
|
blanchet@43926
|
217 |
(** Remove ASCII armoring from names in proof files **)
|
blanchet@43926
|
218 |
|
blanchet@43926
|
219 |
(* We don't raise error exceptions because this code can run inside a worker
|
blanchet@43926
|
220 |
thread. Also, the errors are impossible. *)
|
blanchet@43926
|
221 |
val unascii_of =
|
blanchet@43926
|
222 |
let
|
blanchet@43926
|
223 |
fun un rcs [] = String.implode(rev rcs)
|
blanchet@43926
|
224 |
| un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
|
blanchet@43926
|
225 |
(* Three types of _ escapes: __, _A to _P, _nnn *)
|
blanchet@44367
|
226 |
| un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
|
blanchet@43926
|
227 |
| un rcs (#"_" :: c :: cs) =
|
blanchet@43926
|
228 |
if #"A" <= c andalso c<= #"P" then
|
blanchet@43926
|
229 |
(* translation of #" " to #"/" *)
|
blanchet@43926
|
230 |
un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
|
blanchet@43926
|
231 |
else
|
blanchet@44367
|
232 |
let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
|
blanchet@43926
|
233 |
case Int.fromString (String.implode digits) of
|
blanchet@43926
|
234 |
SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
|
blanchet@44367
|
235 |
| NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
|
blanchet@43926
|
236 |
end
|
blanchet@43926
|
237 |
| un rcs (c :: cs) = un (c :: rcs) cs
|
blanchet@43926
|
238 |
in un [] o String.explode end
|
blanchet@43926
|
239 |
|
blanchet@43926
|
240 |
(* If string s has the prefix s1, return the result of deleting it,
|
blanchet@43926
|
241 |
un-ASCII'd. *)
|
blanchet@43926
|
242 |
fun strip_prefix_and_unascii s1 s =
|
blanchet@43926
|
243 |
if String.isPrefix s1 s then
|
blanchet@43926
|
244 |
SOME (unascii_of (String.extract (s, size s1, NONE)))
|
blanchet@43926
|
245 |
else
|
blanchet@43926
|
246 |
NONE
|
blanchet@43926
|
247 |
|
blanchet@44000
|
248 |
val proxy_table =
|
blanchet@44000
|
249 |
[("c_False", (@{const_name False}, (@{thm fFalse_def},
|
blanchet@44000
|
250 |
("fFalse", @{const_name ATP.fFalse})))),
|
blanchet@44000
|
251 |
("c_True", (@{const_name True}, (@{thm fTrue_def},
|
blanchet@44000
|
252 |
("fTrue", @{const_name ATP.fTrue})))),
|
blanchet@44000
|
253 |
("c_Not", (@{const_name Not}, (@{thm fNot_def},
|
blanchet@44000
|
254 |
("fNot", @{const_name ATP.fNot})))),
|
blanchet@44000
|
255 |
("c_conj", (@{const_name conj}, (@{thm fconj_def},
|
blanchet@44000
|
256 |
("fconj", @{const_name ATP.fconj})))),
|
blanchet@44000
|
257 |
("c_disj", (@{const_name disj}, (@{thm fdisj_def},
|
blanchet@44000
|
258 |
("fdisj", @{const_name ATP.fdisj})))),
|
blanchet@44000
|
259 |
("c_implies", (@{const_name implies}, (@{thm fimplies_def},
|
blanchet@44000
|
260 |
("fimplies", @{const_name ATP.fimplies})))),
|
blanchet@44000
|
261 |
("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
|
nik@44537
|
262 |
("fequal", @{const_name ATP.fequal})))),
|
nik@44537
|
263 |
("c_All", (@{const_name All}, (@{thm fAll_def},
|
nik@44537
|
264 |
("fAll", @{const_name ATP.fAll})))),
|
nik@44537
|
265 |
("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
|
nik@44537
|
266 |
("fEx", @{const_name ATP.fEx}))))]
|
blanchet@43926
|
267 |
|
blanchet@44000
|
268 |
val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
|
blanchet@43926
|
269 |
|
blanchet@43926
|
270 |
(* Readable names for the more common symbolic functions. Do not mess with the
|
blanchet@43926
|
271 |
table unless you know what you are doing. *)
|
blanchet@43926
|
272 |
val const_trans_table =
|
blanchet@43926
|
273 |
[(@{type_name Product_Type.prod}, "prod"),
|
blanchet@43926
|
274 |
(@{type_name Sum_Type.sum}, "sum"),
|
blanchet@43926
|
275 |
(@{const_name False}, "False"),
|
blanchet@43926
|
276 |
(@{const_name True}, "True"),
|
blanchet@43926
|
277 |
(@{const_name Not}, "Not"),
|
blanchet@43926
|
278 |
(@{const_name conj}, "conj"),
|
blanchet@43926
|
279 |
(@{const_name disj}, "disj"),
|
blanchet@43926
|
280 |
(@{const_name implies}, "implies"),
|
blanchet@43926
|
281 |
(@{const_name HOL.eq}, "equal"),
|
nik@44537
|
282 |
(@{const_name All}, "All"),
|
nik@44537
|
283 |
(@{const_name Ex}, "Ex"),
|
blanchet@43926
|
284 |
(@{const_name If}, "If"),
|
blanchet@43926
|
285 |
(@{const_name Set.member}, "member"),
|
blanchet@43926
|
286 |
(@{const_name Meson.COMBI}, "COMBI"),
|
blanchet@43926
|
287 |
(@{const_name Meson.COMBK}, "COMBK"),
|
blanchet@43926
|
288 |
(@{const_name Meson.COMBB}, "COMBB"),
|
blanchet@43926
|
289 |
(@{const_name Meson.COMBC}, "COMBC"),
|
blanchet@43926
|
290 |
(@{const_name Meson.COMBS}, "COMBS")]
|
blanchet@43926
|
291 |
|> Symtab.make
|
blanchet@44000
|
292 |
|> fold (Symtab.update o swap o snd o snd o snd) proxy_table
|
blanchet@43926
|
293 |
|
blanchet@43926
|
294 |
(* Invert the table of translations between Isabelle and ATPs. *)
|
blanchet@43926
|
295 |
val const_trans_table_inv =
|
blanchet@43926
|
296 |
const_trans_table |> Symtab.dest |> map swap |> Symtab.make
|
blanchet@43926
|
297 |
val const_trans_table_unprox =
|
blanchet@43926
|
298 |
Symtab.empty
|
blanchet@44000
|
299 |
|> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
|
blanchet@43926
|
300 |
|
blanchet@43926
|
301 |
val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
|
blanchet@43926
|
302 |
val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
|
blanchet@43926
|
303 |
|
blanchet@43926
|
304 |
fun lookup_const c =
|
blanchet@43926
|
305 |
case Symtab.lookup const_trans_table c of
|
blanchet@43926
|
306 |
SOME c' => c'
|
blanchet@43926
|
307 |
| NONE => ascii_of c
|
blanchet@43926
|
308 |
|
blanchet@44489
|
309 |
fun ascii_of_indexname (v, 0) = ascii_of v
|
blanchet@44489
|
310 |
| ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
|
blanchet@43926
|
311 |
|
blanchet@43926
|
312 |
fun make_bound_var x = bound_var_prefix ^ ascii_of x
|
blanchet@45262
|
313 |
fun make_all_bound_var x = all_bound_var_prefix ^ ascii_of x
|
blanchet@45262
|
314 |
fun make_exist_bound_var x = exist_bound_var_prefix ^ ascii_of x
|
blanchet@43926
|
315 |
fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
|
blanchet@43926
|
316 |
fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
|
blanchet@43926
|
317 |
|
blanchet@44489
|
318 |
fun make_schematic_type_var (x, i) =
|
blanchet@45459
|
319 |
tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
|
blanchet@44489
|
320 |
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
|
blanchet@43926
|
321 |
|
nik@45451
|
322 |
(* "HOL.eq" and Choice are mapped to the ATP's equivalents *)
|
nik@45451
|
323 |
local
|
nik@45451
|
324 |
val choice_const = (fst o dest_Const o HOLogic.choice_const) Term.dummyT
|
nik@45451
|
325 |
fun default c = const_prefix ^ lookup_const c
|
nik@45451
|
326 |
in
|
nik@45451
|
327 |
fun make_fixed_const _ @{const_name HOL.eq} = tptp_old_equal
|
blanchet@45453
|
328 |
| make_fixed_const (SOME (THF0 THF_With_Choice)) c =
|
nik@45451
|
329 |
if c = choice_const then tptp_choice else default c
|
nik@45451
|
330 |
| make_fixed_const _ c = default c
|
nik@45451
|
331 |
end
|
blanchet@43926
|
332 |
|
blanchet@43926
|
333 |
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
|
blanchet@43926
|
334 |
|
blanchet@43926
|
335 |
fun make_type_class clas = class_prefix ^ ascii_of clas
|
blanchet@43926
|
336 |
|
blanchet@43934
|
337 |
fun new_skolem_var_name_from_const s =
|
blanchet@43934
|
338 |
let val ss = s |> space_explode Long_Name.separator in
|
blanchet@43934
|
339 |
nth ss (length ss - 2)
|
blanchet@43934
|
340 |
end
|
blanchet@43934
|
341 |
|
blanchet@44089
|
342 |
(* These are either simplified away by "Meson.presimplify" (most of the time) or
|
blanchet@44089
|
343 |
handled specially via "fFalse", "fTrue", ..., "fequal". *)
|
blanchet@44089
|
344 |
val atp_irrelevant_consts =
|
blanchet@44089
|
345 |
[@{const_name False}, @{const_name True}, @{const_name Not},
|
blanchet@44089
|
346 |
@{const_name conj}, @{const_name disj}, @{const_name implies},
|
blanchet@44089
|
347 |
@{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
|
blanchet@44089
|
348 |
|
blanchet@44089
|
349 |
val atp_monomorph_bad_consts =
|
blanchet@44089
|
350 |
atp_irrelevant_consts @
|
blanchet@44089
|
351 |
(* These are ignored anyway by the relevance filter (unless they appear in
|
blanchet@44089
|
352 |
higher-order places) but not by the monomorphizer. *)
|
blanchet@44089
|
353 |
[@{const_name all}, @{const_name "==>"}, @{const_name "=="},
|
blanchet@44089
|
354 |
@{const_name Trueprop}, @{const_name All}, @{const_name Ex},
|
blanchet@44089
|
355 |
@{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
|
blanchet@44089
|
356 |
|
blanchet@44099
|
357 |
fun add_schematic_const (x as (_, T)) =
|
blanchet@44099
|
358 |
Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
|
blanchet@44099
|
359 |
val add_schematic_consts_of =
|
blanchet@44099
|
360 |
Term.fold_aterms (fn Const (x as (s, _)) =>
|
blanchet@44099
|
361 |
not (member (op =) atp_monomorph_bad_consts s)
|
blanchet@44099
|
362 |
? add_schematic_const x
|
blanchet@44099
|
363 |
| _ => I)
|
blanchet@44099
|
364 |
fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
|
blanchet@44089
|
365 |
|
blanchet@43926
|
366 |
(** Definitions and functions for FOL clauses and formulas for TPTP **)
|
blanchet@43926
|
367 |
|
blanchet@43926
|
368 |
(** Isabelle arities **)
|
blanchet@43926
|
369 |
|
blanchet@45483
|
370 |
type arity_atom = name * name * name list
|
blanchet@43926
|
371 |
|
blanchet@44104
|
372 |
val type_class = the_single @{sort type}
|
blanchet@44104
|
373 |
|
blanchet@43927
|
374 |
type arity_clause =
|
blanchet@44367
|
375 |
{name : string,
|
blanchet@45483
|
376 |
prem_atoms : arity_atom list,
|
blanchet@45483
|
377 |
concl_atom : arity_atom}
|
blanchet@45483
|
378 |
|
blanchet@45483
|
379 |
fun add_prem_atom tvar =
|
blanchet@45483
|
380 |
fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar, []))
|
blanchet@43926
|
381 |
|
blanchet@43926
|
382 |
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
|
blanchet@43926
|
383 |
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
|
blanchet@43926
|
384 |
let
|
blanchet@45459
|
385 |
val tvars = map (prefix tvar_prefix o string_of_int) (1 upto length args)
|
blanchet@43926
|
386 |
val tvars_srts = ListPair.zip (tvars, args)
|
blanchet@43926
|
387 |
in
|
blanchet@43927
|
388 |
{name = name,
|
blanchet@45483
|
389 |
prem_atoms = [] |> fold (uncurry add_prem_atom) tvars_srts,
|
blanchet@45483
|
390 |
concl_atom = (`make_type_class cls, `make_fixed_type_const tcons,
|
blanchet@45483
|
391 |
tvars ~~ tvars)}
|
blanchet@43926
|
392 |
end
|
blanchet@43926
|
393 |
|
blanchet@43926
|
394 |
fun arity_clause _ _ (_, []) = []
|
blanchet@44366
|
395 |
| arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
|
blanchet@44366
|
396 |
arity_clause seen n (tcons, ars)
|
blanchet@44366
|
397 |
| arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
|
blanchet@44366
|
398 |
if member (op =) seen class then
|
blanchet@44366
|
399 |
(* multiple arities for the same (tycon, class) pair *)
|
blanchet@44366
|
400 |
make_axiom_arity_clause (tcons,
|
blanchet@44366
|
401 |
lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
|
blanchet@44366
|
402 |
ar) ::
|
blanchet@44366
|
403 |
arity_clause seen (n + 1) (tcons, ars)
|
blanchet@44366
|
404 |
else
|
blanchet@44366
|
405 |
make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
|
blanchet@44366
|
406 |
ascii_of class, ar) ::
|
blanchet@44366
|
407 |
arity_clause (class :: seen) n (tcons, ars)
|
blanchet@43926
|
408 |
|
blanchet@43926
|
409 |
fun multi_arity_clause [] = []
|
blanchet@43926
|
410 |
| multi_arity_clause ((tcons, ars) :: tc_arlists) =
|
blanchet@43926
|
411 |
arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
|
blanchet@43926
|
412 |
|
blanchet@44489
|
413 |
(* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
|
blanchet@44489
|
414 |
theory thy provided its arguments have the corresponding sorts. *)
|
blanchet@43926
|
415 |
fun type_class_pairs thy tycons classes =
|
blanchet@43934
|
416 |
let
|
blanchet@43934
|
417 |
val alg = Sign.classes_of thy
|
blanchet@43934
|
418 |
fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
|
blanchet@43934
|
419 |
fun add_class tycon class =
|
blanchet@43934
|
420 |
cons (class, domain_sorts tycon class)
|
blanchet@43934
|
421 |
handle Sorts.CLASS_ERROR _ => I
|
blanchet@43934
|
422 |
fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
|
blanchet@43934
|
423 |
in map try_classes tycons end
|
blanchet@43926
|
424 |
|
blanchet@43926
|
425 |
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
|
blanchet@43926
|
426 |
fun iter_type_class_pairs _ _ [] = ([], [])
|
blanchet@43926
|
427 |
| iter_type_class_pairs thy tycons classes =
|
blanchet@44104
|
428 |
let
|
blanchet@44104
|
429 |
fun maybe_insert_class s =
|
blanchet@44104
|
430 |
(s <> type_class andalso not (member (op =) classes s))
|
blanchet@44104
|
431 |
? insert (op =) s
|
blanchet@44104
|
432 |
val cpairs = type_class_pairs thy tycons classes
|
blanchet@44104
|
433 |
val newclasses =
|
blanchet@44104
|
434 |
[] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
|
blanchet@44104
|
435 |
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
|
blanchet@44107
|
436 |
in (classes' @ classes, union (op =) cpairs' cpairs) end
|
blanchet@43926
|
437 |
|
blanchet@43926
|
438 |
fun make_arity_clauses thy tycons =
|
blanchet@43926
|
439 |
iter_type_class_pairs thy tycons ##> multi_arity_clause
|
blanchet@43926
|
440 |
|
blanchet@43926
|
441 |
|
blanchet@43926
|
442 |
(** Isabelle class relations **)
|
blanchet@43926
|
443 |
|
blanchet@43927
|
444 |
type class_rel_clause =
|
blanchet@44367
|
445 |
{name : string,
|
blanchet@44367
|
446 |
subclass : name,
|
blanchet@44367
|
447 |
superclass : name}
|
blanchet@43926
|
448 |
|
blanchet@44489
|
449 |
(* Generate all pairs (sub, super) such that sub is a proper subclass of super
|
blanchet@44489
|
450 |
in theory "thy". *)
|
blanchet@43926
|
451 |
fun class_pairs _ [] _ = []
|
blanchet@43926
|
452 |
| class_pairs thy subs supers =
|
blanchet@43926
|
453 |
let
|
blanchet@43926
|
454 |
val class_less = Sorts.class_less (Sign.classes_of thy)
|
blanchet@43926
|
455 |
fun add_super sub super = class_less (sub, super) ? cons (sub, super)
|
blanchet@43926
|
456 |
fun add_supers sub = fold (add_super sub) supers
|
blanchet@43926
|
457 |
in fold add_supers subs [] end
|
blanchet@43926
|
458 |
|
blanchet@44489
|
459 |
fun make_class_rel_clause (sub, super) =
|
blanchet@44489
|
460 |
{name = sub ^ "_" ^ super, subclass = `make_type_class sub,
|
blanchet@43927
|
461 |
superclass = `make_type_class super}
|
blanchet@43926
|
462 |
|
blanchet@43926
|
463 |
fun make_class_rel_clauses thy subs supers =
|
blanchet@43934
|
464 |
map make_class_rel_clause (class_pairs thy subs supers)
|
blanchet@43926
|
465 |
|
blanchet@44730
|
466 |
(* intermediate terms *)
|
blanchet@44730
|
467 |
datatype iterm =
|
blanchet@44730
|
468 |
IConst of name * typ * typ list |
|
blanchet@44730
|
469 |
IVar of name * typ |
|
blanchet@44730
|
470 |
IApp of iterm * iterm |
|
blanchet@44730
|
471 |
IAbs of (name * typ) * iterm
|
blanchet@43926
|
472 |
|
blanchet@44730
|
473 |
fun ityp_of (IConst (_, T, _)) = T
|
blanchet@44730
|
474 |
| ityp_of (IVar (_, T)) = T
|
blanchet@44730
|
475 |
| ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
|
blanchet@44730
|
476 |
| ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
|
blanchet@43926
|
477 |
|
blanchet@43926
|
478 |
(*gets the head of a combinator application, along with the list of arguments*)
|
blanchet@44730
|
479 |
fun strip_iterm_comb u =
|
blanchet@44367
|
480 |
let
|
blanchet@44730
|
481 |
fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
|
blanchet@44367
|
482 |
| stripc x = x
|
blanchet@44367
|
483 |
in stripc (u, []) end
|
blanchet@43926
|
484 |
|
blanchet@43926
|
485 |
fun atyps_of T = fold_atyps (insert (op =)) T []
|
blanchet@43926
|
486 |
|
blanchet@43926
|
487 |
fun new_skolem_const_name s num_T_args =
|
blanchet@43926
|
488 |
[new_skolem_const_prefix, s, string_of_int num_T_args]
|
blanchet@43926
|
489 |
|> space_implode Long_Name.separator
|
blanchet@43926
|
490 |
|
blanchet@45458
|
491 |
fun robust_const_type thy s =
|
blanchet@45458
|
492 |
if s = app_op_name then Logic.varifyT_global @{typ "('a => 'b) => 'a => 'b"}
|
blanchet@45458
|
493 |
else s |> Sign.the_const_type thy
|
blanchet@45458
|
494 |
|
blanchet@45458
|
495 |
(* This function only makes sense if "T" is as general as possible. *)
|
blanchet@45458
|
496 |
fun robust_const_typargs thy (s, T) =
|
blanchet@45458
|
497 |
(s, T) |> Sign.const_typargs thy
|
blanchet@45458
|
498 |
handle TYPE _ => [] |> Term.add_tvarsT T |> rev |> map TVar
|
blanchet@45458
|
499 |
|
blanchet@44730
|
500 |
(* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
|
blanchet@44730
|
501 |
Also accumulates sort infomation. *)
|
nik@45350
|
502 |
fun iterm_from_term thy format bs (P $ Q) =
|
blanchet@43926
|
503 |
let
|
nik@45350
|
504 |
val (P', P_atomics_Ts) = iterm_from_term thy format bs P
|
nik@45350
|
505 |
val (Q', Q_atomics_Ts) = iterm_from_term thy format bs Q
|
blanchet@44730
|
506 |
in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
|
nik@45350
|
507 |
| iterm_from_term thy format _ (Const (c, T)) =
|
nik@45350
|
508 |
(IConst (`(make_fixed_const (SOME format)) c, T,
|
blanchet@45458
|
509 |
robust_const_typargs thy (c, T)),
|
blanchet@44778
|
510 |
atyps_of T)
|
nik@45350
|
511 |
| iterm_from_term _ _ _ (Free (s, T)) =
|
blanchet@44778
|
512 |
(IConst (`make_fixed_var s, T,
|
blanchet@44807
|
513 |
if String.isPrefix polymorphic_free_prefix s then [T] else []),
|
blanchet@44778
|
514 |
atyps_of T)
|
nik@45350
|
515 |
| iterm_from_term _ format _ (Var (v as (s, _), T)) =
|
blanchet@43926
|
516 |
(if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
|
blanchet@43926
|
517 |
let
|
blanchet@43926
|
518 |
val Ts = T |> strip_type |> swap |> op ::
|
blanchet@43926
|
519 |
val s' = new_skolem_const_name s (length Ts)
|
nik@45350
|
520 |
in IConst (`(make_fixed_const (SOME format)) s', T, Ts) end
|
blanchet@43926
|
521 |
else
|
blanchet@44730
|
522 |
IVar ((make_schematic_var v, s), T), atyps_of T)
|
nik@45350
|
523 |
| iterm_from_term _ _ bs (Bound j) =
|
blanchet@45262
|
524 |
nth bs j |> (fn (_, (name, T)) => (IConst (name, T, []), atyps_of T))
|
nik@45350
|
525 |
| iterm_from_term thy format bs (Abs (s, T, t)) =
|
nik@44537
|
526 |
let
|
nik@44537
|
527 |
fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
|
nik@44537
|
528 |
val s = vary s
|
blanchet@45262
|
529 |
val name = `make_bound_var s
|
nik@45350
|
530 |
val (tm, atomic_Ts) = iterm_from_term thy format ((s, (name, T)) :: bs) t
|
blanchet@45262
|
531 |
in (IAbs ((name, T), tm), union (op =) atomic_Ts (atyps_of T)) end
|
blanchet@43926
|
532 |
|
blanchet@44282
|
533 |
datatype locality =
|
nik@45449
|
534 |
General | Helper | Induction | Extensionality | Intro | Elim | Simp |
|
nik@45449
|
535 |
Local | Assum | Chained
|
blanchet@43926
|
536 |
|
blanchet@44491
|
537 |
datatype order = First_Order | Higher_Order
|
blanchet@45349
|
538 |
datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
|
blanchet@45256
|
539 |
datatype soundness = Unsound | Sound_Modulo_Infiniteness | Sound
|
blanchet@43484
|
540 |
datatype type_level =
|
blanchet@45256
|
541 |
All_Types |
|
blanchet@45256
|
542 |
Noninf_Nonmono_Types of soundness |
|
blanchet@45256
|
543 |
Fin_Nonmono_Types |
|
blanchet@45256
|
544 |
Const_Arg_Types |
|
blanchet@44233
|
545 |
No_Types
|
blanchet@45261
|
546 |
datatype type_uniformity = Uniform | Nonuniform
|
blanchet@43484
|
547 |
|
blanchet@44493
|
548 |
datatype type_enc =
|
blanchet@45455
|
549 |
Simple_Types of order * polymorphism * type_level |
|
blanchet@45261
|
550 |
Guards of polymorphism * type_level * type_uniformity |
|
blanchet@45261
|
551 |
Tags of polymorphism * type_level * type_uniformity
|
blanchet@43484
|
552 |
|
blanchet@43559
|
553 |
fun try_unsuffixes ss s =
|
blanchet@43559
|
554 |
fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
|
blanchet@43559
|
555 |
|
blanchet@45256
|
556 |
fun type_enc_from_string soundness s =
|
blanchet@43587
|
557 |
(case try (unprefix "poly_") s of
|
blanchet@43587
|
558 |
SOME s => (SOME Polymorphic, s)
|
blanchet@43484
|
559 |
| NONE =>
|
blanchet@45349
|
560 |
case try (unprefix "raw_mono_") s of
|
blanchet@45349
|
561 |
SOME s => (SOME Raw_Monomorphic, s)
|
blanchet@43587
|
562 |
| NONE =>
|
blanchet@45349
|
563 |
case try (unprefix "mono_") s of
|
blanchet@43587
|
564 |
SOME s => (SOME Mangled_Monomorphic, s)
|
blanchet@43587
|
565 |
| NONE => (NONE, s))
|
blanchet@43484
|
566 |
||> (fn s =>
|
blanchet@44491
|
567 |
(* "_query" and "_bang" are for the ASCII-challenged Metis and
|
blanchet@44491
|
568 |
Mirabelle. *)
|
blanchet@43559
|
569 |
case try_unsuffixes ["?", "_query"] s of
|
blanchet@45256
|
570 |
SOME s => (Noninf_Nonmono_Types soundness, s)
|
blanchet@43484
|
571 |
| NONE =>
|
blanchet@43559
|
572 |
case try_unsuffixes ["!", "_bang"] s of
|
blanchet@44233
|
573 |
SOME s => (Fin_Nonmono_Types, s)
|
blanchet@43484
|
574 |
| NONE => (All_Types, s))
|
blanchet@43699
|
575 |
||> apsnd (fn s =>
|
blanchet@45261
|
576 |
case try (unsuffix "_uniform") s of
|
blanchet@45261
|
577 |
SOME s => (Uniform, s)
|
blanchet@45261
|
578 |
| NONE => (Nonuniform, s))
|
blanchet@45261
|
579 |
|> (fn (poly, (level, (uniformity, core))) =>
|
blanchet@45261
|
580 |
case (core, (poly, level, uniformity)) of
|
blanchet@45455
|
581 |
("simple", (SOME poly, _, Nonuniform)) =>
|
blanchet@45455
|
582 |
(case poly of
|
blanchet@45455
|
583 |
Raw_Monomorphic => raise Same.SAME
|
blanchet@45455
|
584 |
| _ => Simple_Types (First_Order, poly, level))
|
blanchet@45455
|
585 |
| ("simple_higher", (SOME poly, _, Nonuniform)) =>
|
blanchet@45455
|
586 |
(case (poly, level) of
|
blanchet@45455
|
587 |
(Raw_Monomorphic, _) => raise Same.SAME
|
blanchet@45455
|
588 |
| (_, Noninf_Nonmono_Types _) => raise Same.SAME
|
blanchet@45455
|
589 |
| _ => Simple_Types (Higher_Order, poly, level))
|
blanchet@45261
|
590 |
| ("guards", (SOME poly, _, _)) => Guards (poly, level, uniformity)
|
blanchet@43755
|
591 |
| ("tags", (SOME Polymorphic, _, _)) =>
|
blanchet@45261
|
592 |
Tags (Polymorphic, level, uniformity)
|
blanchet@45261
|
593 |
| ("tags", (SOME poly, _, _)) => Tags (poly, level, uniformity)
|
blanchet@45261
|
594 |
| ("args", (SOME poly, All_Types (* naja *), Nonuniform)) =>
|
blanchet@45261
|
595 |
Guards (poly, Const_Arg_Types, Nonuniform)
|
blanchet@45261
|
596 |
| ("erased", (NONE, All_Types (* naja *), Nonuniform)) =>
|
blanchet@45261
|
597 |
Guards (Polymorphic, No_Types, Nonuniform)
|
blanchet@43618
|
598 |
| _ => raise Same.SAME)
|
blanchet@43618
|
599 |
handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
|
blanchet@43484
|
600 |
|
blanchet@45455
|
601 |
fun is_type_enc_higher_order (Simple_Types (Higher_Order, _, _)) = true
|
blanchet@44493
|
602 |
| is_type_enc_higher_order _ = false
|
blanchet@44491
|
603 |
|
blanchet@45455
|
604 |
fun polymorphism_of_type_enc (Simple_Types (_, poly, _)) = poly
|
blanchet@44860
|
605 |
| polymorphism_of_type_enc (Guards (poly, _, _)) = poly
|
blanchet@44493
|
606 |
| polymorphism_of_type_enc (Tags (poly, _, _)) = poly
|
blanchet@43484
|
607 |
|
blanchet@45455
|
608 |
fun level_of_type_enc (Simple_Types (_, _, level)) = level
|
blanchet@44860
|
609 |
| level_of_type_enc (Guards (_, level, _)) = level
|
blanchet@44493
|
610 |
| level_of_type_enc (Tags (_, level, _)) = level
|
blanchet@43699
|
611 |
|
blanchet@45261
|
612 |
fun uniformity_of_type_enc (Simple_Types _) = Uniform
|
blanchet@45261
|
613 |
| uniformity_of_type_enc (Guards (_, _, uniformity)) = uniformity
|
blanchet@45261
|
614 |
| uniformity_of_type_enc (Tags (_, _, uniformity)) = uniformity
|
blanchet@43702
|
615 |
|
blanchet@45256
|
616 |
fun is_type_level_quasi_sound All_Types = true
|
blanchet@45256
|
617 |
| is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true
|
blanchet@45256
|
618 |
| is_type_level_quasi_sound _ = false
|
blanchet@45256
|
619 |
val is_type_enc_quasi_sound =
|
blanchet@45256
|
620 |
is_type_level_quasi_sound o level_of_type_enc
|
blanchet@43484
|
621 |
|
blanchet@43484
|
622 |
fun is_type_level_fairly_sound level =
|
blanchet@45256
|
623 |
is_type_level_quasi_sound level orelse level = Fin_Nonmono_Types
|
blanchet@44493
|
624 |
val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
|
blanchet@43484
|
625 |
|
blanchet@45256
|
626 |
fun is_type_level_monotonicity_based (Noninf_Nonmono_Types _) = true
|
blanchet@45256
|
627 |
| is_type_level_monotonicity_based Fin_Nonmono_Types = true
|
blanchet@45256
|
628 |
| is_type_level_monotonicity_based _ = false
|
blanchet@45256
|
629 |
|
blanchet@45455
|
630 |
fun adjust_type_enc (THF0 _) (Simple_Types (order, Polymorphic, level)) =
|
blanchet@45455
|
631 |
Simple_Types (order, Mangled_Monomorphic, level)
|
blanchet@45455
|
632 |
| adjust_type_enc (THF0 _) type_enc = type_enc
|
blanchet@45455
|
633 |
| adjust_type_enc (TFF (TFF_Monomorphic, _)) (Simple_Types (_, _, level)) =
|
blanchet@45455
|
634 |
Simple_Types (First_Order, Mangled_Monomorphic, level)
|
blanchet@45455
|
635 |
| adjust_type_enc (TFF (_, _)) (Simple_Types (_, poly, level)) =
|
blanchet@45455
|
636 |
Simple_Types (First_Order, poly, level)
|
blanchet@45455
|
637 |
| adjust_type_enc format (Simple_Types (_, poly, level)) =
|
blanchet@45455
|
638 |
adjust_type_enc format (Guards (poly, level, Uniform))
|
blanchet@45275
|
639 |
| adjust_type_enc CNF_UEQ (type_enc as Guards stuff) =
|
blanchet@45275
|
640 |
(if is_type_enc_fairly_sound type_enc then Tags else Guards) stuff
|
blanchet@45275
|
641 |
| adjust_type_enc _ type_enc = type_enc
|
blanchet@43942
|
642 |
|
blanchet@44959
|
643 |
fun lift_lambdas ctxt type_enc =
|
blanchet@44959
|
644 |
map (close_form o Envir.eta_contract) #> rpair ctxt
|
blanchet@44959
|
645 |
#-> Lambda_Lifting.lift_lambdas
|
blanchet@44959
|
646 |
(if polymorphism_of_type_enc type_enc = Polymorphic then
|
blanchet@44959
|
647 |
SOME polymorphic_free_prefix
|
blanchet@44959
|
648 |
else
|
blanchet@44959
|
649 |
NONE)
|
blanchet@44959
|
650 |
Lambda_Lifting.is_quantifier
|
blanchet@44959
|
651 |
#> fst
|
blanchet@44959
|
652 |
|
blanchet@44959
|
653 |
fun intentionalize_def (Const (@{const_name All}, _) $ Abs (_, _, t)) =
|
blanchet@44959
|
654 |
intentionalize_def t
|
blanchet@44959
|
655 |
| intentionalize_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
|
blanchet@44959
|
656 |
let
|
blanchet@44959
|
657 |
fun lam T t = Abs (Name.uu, T, t)
|
blanchet@44959
|
658 |
val (head, args) = strip_comb t ||> rev
|
blanchet@44959
|
659 |
val head_T = fastype_of head
|
blanchet@44959
|
660 |
val n = length args
|
blanchet@44959
|
661 |
val arg_Ts = head_T |> binder_types |> take n |> rev
|
blanchet@44959
|
662 |
val u = u |> subst_atomic (args ~~ map Bound (0 upto n - 1))
|
blanchet@44959
|
663 |
in HOLogic.eq_const head_T $ head $ fold lam arg_Ts u end
|
blanchet@44959
|
664 |
| intentionalize_def t = t
|
blanchet@44959
|
665 |
|
blanchet@40358
|
666 |
type translated_formula =
|
blanchet@44367
|
667 |
{name : string,
|
blanchet@44367
|
668 |
locality : locality,
|
blanchet@44367
|
669 |
kind : formula_kind,
|
blanchet@44730
|
670 |
iformula : (name, typ, iterm) formula,
|
blanchet@44367
|
671 |
atomic_types : typ list}
|
blanchet@38506
|
672 |
|
blanchet@44730
|
673 |
fun update_iformula f ({name, locality, kind, iformula, atomic_types}
|
blanchet@44730
|
674 |
: translated_formula) =
|
blanchet@44730
|
675 |
{name = name, locality = locality, kind = kind, iformula = f iformula,
|
blanchet@43433
|
676 |
atomic_types = atomic_types} : translated_formula
|
blanchet@43413
|
677 |
|
blanchet@44730
|
678 |
fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
|
blanchet@43429
|
679 |
|
blanchet@43905
|
680 |
fun insert_type ctxt get_T x xs =
|
blanchet@43905
|
681 |
let val T = get_T x in
|
blanchet@45258
|
682 |
if exists (type_instance ctxt T o get_T) xs then xs
|
blanchet@45258
|
683 |
else x :: filter_out (type_generalization ctxt T o get_T) xs
|
blanchet@43905
|
684 |
end
|
blanchet@43547
|
685 |
|
blanchet@43618
|
686 |
(* The Booleans indicate whether all type arguments should be kept. *)
|
blanchet@43618
|
687 |
datatype type_arg_policy =
|
blanchet@43618
|
688 |
Explicit_Type_Args of bool |
|
blanchet@43618
|
689 |
Mangled_Type_Args of bool |
|
blanchet@43618
|
690 |
No_Type_Args
|
blanchet@41384
|
691 |
|
blanchet@45458
|
692 |
fun should_drop_arg_type_args (Simple_Types _) = false
|
blanchet@44493
|
693 |
| should_drop_arg_type_args type_enc =
|
blanchet@44493
|
694 |
level_of_type_enc type_enc = All_Types andalso
|
blanchet@45261
|
695 |
uniformity_of_type_enc type_enc = Uniform
|
blanchet@43702
|
696 |
|
blanchet@44493
|
697 |
fun type_arg_policy type_enc s =
|
blanchet@44495
|
698 |
if s = type_tag_name then
|
blanchet@44493
|
699 |
(if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
|
blanchet@44490
|
700 |
Mangled_Type_Args
|
blanchet@44490
|
701 |
else
|
blanchet@44490
|
702 |
Explicit_Type_Args) false
|
blanchet@44495
|
703 |
else case type_enc of
|
blanchet@45261
|
704 |
Tags (_, All_Types, Uniform) => No_Type_Args
|
blanchet@44495
|
705 |
| _ =>
|
blanchet@45257
|
706 |
let val level = level_of_type_enc type_enc in
|
blanchet@45257
|
707 |
if level = No_Types orelse s = @{const_name HOL.eq} orelse
|
blanchet@45257
|
708 |
(s = app_op_name andalso level = Const_Arg_Types) then
|
blanchet@45257
|
709 |
No_Type_Args
|
blanchet@45257
|
710 |
else
|
blanchet@45257
|
711 |
should_drop_arg_type_args type_enc
|
blanchet@45257
|
712 |
|> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
|
blanchet@45257
|
713 |
Mangled_Type_Args
|
blanchet@45257
|
714 |
else
|
blanchet@45257
|
715 |
Explicit_Type_Args)
|
blanchet@45257
|
716 |
end
|
blanchet@43088
|
717 |
|
blanchet@45483
|
718 |
(* Make atoms for sorted type variables. *)
|
blanchet@44104
|
719 |
fun generic_add_sorts_on_type (_, []) = I
|
blanchet@44104
|
720 |
| generic_add_sorts_on_type ((x, i), s :: ss) =
|
blanchet@44104
|
721 |
generic_add_sorts_on_type ((x, i), ss)
|
blanchet@44104
|
722 |
#> (if s = the_single @{sort HOL.type} then
|
blanchet@43934
|
723 |
I
|
blanchet@43934
|
724 |
else if i = ~1 then
|
blanchet@45481
|
725 |
insert (op =) (`make_type_class s, `make_fixed_type_var x)
|
blanchet@43934
|
726 |
else
|
blanchet@45481
|
727 |
insert (op =) (`make_type_class s,
|
blanchet@45481
|
728 |
(make_schematic_type_var (x, i), x)))
|
blanchet@44104
|
729 |
fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
|
blanchet@44104
|
730 |
| add_sorts_on_tfree _ = I
|
blanchet@44104
|
731 |
fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
|
blanchet@44104
|
732 |
| add_sorts_on_tvar _ = I
|
blanchet@43926
|
733 |
|
blanchet@45483
|
734 |
val tvar_a_str = "'a"
|
blanchet@45483
|
735 |
val tvar_a = TVar ((tvar_a_str, 0), HOLogic.typeS)
|
blanchet@45483
|
736 |
val tvar_a_name = (make_schematic_type_var (tvar_a_str, 0), tvar_a_str)
|
blanchet@45483
|
737 |
val itself_name = `make_fixed_type_const @{type_name itself}
|
blanchet@45483
|
738 |
val TYPE_name = `(make_fixed_const NONE) @{const_name TYPE}
|
blanchet@45483
|
739 |
val tvar_a_atype = AType (tvar_a_name, [])
|
blanchet@45483
|
740 |
val a_itself_atype = AType (itself_name, [tvar_a_atype])
|
blanchet@45483
|
741 |
|
blanchet@45483
|
742 |
fun type_class_formula type_enc class arg =
|
blanchet@45483
|
743 |
AAtom (ATerm (class, arg ::
|
blanchet@45483
|
744 |
(case type_enc of
|
blanchet@45483
|
745 |
Simple_Types (_, Polymorphic, _) =>
|
blanchet@45483
|
746 |
if exploit_tff1_dummy_type_vars then [] else [ATerm (TYPE_name, [arg])]
|
blanchet@45483
|
747 |
| _ => [])))
|
blanchet@45483
|
748 |
fun formulas_for_types type_enc add_sorts_on_typ Ts =
|
blanchet@44493
|
749 |
[] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
|
blanchet@45483
|
750 |
|> map (fn (class, name) =>
|
blanchet@45483
|
751 |
type_class_formula type_enc class (ATerm (name, [])))
|
blanchet@41385
|
752 |
|
blanchet@43405
|
753 |
fun mk_aconns c phis =
|
blanchet@43405
|
754 |
let val (phis', phi') = split_last phis in
|
blanchet@43405
|
755 |
fold_rev (mk_aconn c) phis' phi'
|
blanchet@43405
|
756 |
end
|
blanchet@38506
|
757 |
fun mk_ahorn [] phi = phi
|
blanchet@43405
|
758 |
| mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
|
blanchet@43393
|
759 |
fun mk_aquant _ [] phi = phi
|
blanchet@43393
|
760 |
| mk_aquant q xs (phi as AQuant (q', xs', phi')) =
|
blanchet@43393
|
761 |
if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
|
blanchet@43393
|
762 |
| mk_aquant q xs phi = AQuant (q, xs, phi)
|
blanchet@38506
|
763 |
|
blanchet@43393
|
764 |
fun close_universally atom_vars phi =
|
blanchet@41393
|
765 |
let
|
blanchet@41393
|
766 |
fun formula_vars bounds (AQuant (_, xs, phi)) =
|
blanchet@43397
|
767 |
formula_vars (map fst xs @ bounds) phi
|
blanchet@41393
|
768 |
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
|
blanchet@43393
|
769 |
| formula_vars bounds (AAtom tm) =
|
blanchet@43397
|
770 |
union (op =) (atom_vars tm []
|
blanchet@43397
|
771 |
|> filter_out (member (op =) bounds o fst))
|
blanchet@43393
|
772 |
in mk_aquant AForall (formula_vars [] phi []) phi end
|
blanchet@43393
|
773 |
|
blanchet@44730
|
774 |
fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
|
blanchet@44730
|
775 |
| iterm_vars (IConst _) = I
|
blanchet@44730
|
776 |
| iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
|
blanchet@44730
|
777 |
| iterm_vars (IAbs (_, tm)) = iterm_vars tm
|
blanchet@44730
|
778 |
fun close_iformula_universally phi = close_universally iterm_vars phi
|
blanchet@43393
|
779 |
|
blanchet@45457
|
780 |
fun term_vars type_enc =
|
blanchet@45457
|
781 |
let
|
blanchet@45457
|
782 |
fun vars bounds (ATerm (name as (s, _), tms)) =
|
blanchet@45457
|
783 |
(if is_tptp_variable s andalso not (member (op =) bounds name) then
|
blanchet@45457
|
784 |
(case type_enc of
|
blanchet@45457
|
785 |
Simple_Types (_, Polymorphic, _) =>
|
blanchet@45459
|
786 |
if String.isPrefix tvar_prefix s then SOME atype_of_types
|
blanchet@45459
|
787 |
else NONE
|
blanchet@45457
|
788 |
| _ => NONE)
|
blanchet@45457
|
789 |
|> pair name |> insert (op =)
|
blanchet@45457
|
790 |
else
|
blanchet@45457
|
791 |
I)
|
blanchet@45457
|
792 |
#> fold (vars bounds) tms
|
blanchet@45457
|
793 |
| vars bounds (AAbs ((name, _), tm)) = vars (name :: bounds) tm
|
blanchet@45457
|
794 |
in vars end
|
blanchet@45457
|
795 |
fun close_formula_universally type_enc =
|
blanchet@45457
|
796 |
close_universally (term_vars type_enc [])
|
blanchet@41393
|
797 |
|
blanchet@45458
|
798 |
val fused_infinite_type_name = @{type_name ind} (* any infinite type *)
|
blanchet@45458
|
799 |
val fused_infinite_type = Type (fused_infinite_type_name, [])
|
blanchet@45458
|
800 |
|
blanchet@45458
|
801 |
fun tvar_name (x as (s, _)) = (make_schematic_type_var x, s)
|
blanchet@43835
|
802 |
|
nik@44535
|
803 |
fun ho_term_from_typ format type_enc =
|
blanchet@43835
|
804 |
let
|
blanchet@43835
|
805 |
fun term (Type (s, Ts)) =
|
blanchet@44493
|
806 |
ATerm (case (is_type_enc_higher_order type_enc, s) of
|
blanchet@43835
|
807 |
(true, @{type_name bool}) => `I tptp_bool_type
|
blanchet@43835
|
808 |
| (true, @{type_name fun}) => `I tptp_fun_type
|
blanchet@45458
|
809 |
| _ => if s = fused_infinite_type_name andalso
|
blanchet@45106
|
810 |
is_format_typed format then
|
blanchet@44019
|
811 |
`I tptp_individual_type
|
blanchet@44019
|
812 |
else
|
blanchet@44019
|
813 |
`make_fixed_type_const s,
|
blanchet@43835
|
814 |
map term Ts)
|
blanchet@43835
|
815 |
| term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
|
blanchet@45458
|
816 |
| term (TVar (x, _)) = ATerm (tvar_name x, [])
|
blanchet@43835
|
817 |
in term end
|
blanchet@43433
|
818 |
|
nik@44535
|
819 |
fun ho_term_for_type_arg format type_enc T =
|
nik@44535
|
820 |
if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
|
blanchet@44264
|
821 |
|
blanchet@43433
|
822 |
(* This shouldn't clash with anything else. *)
|
blanchet@43413
|
823 |
val mangled_type_sep = "\000"
|
blanchet@43413
|
824 |
|
blanchet@43433
|
825 |
fun generic_mangled_type_name f (ATerm (name, [])) = f name
|
blanchet@43433
|
826 |
| generic_mangled_type_name f (ATerm (name, tys)) =
|
blanchet@43626
|
827 |
f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
|
blanchet@43626
|
828 |
^ ")"
|
blanchet@44558
|
829 |
| generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
|
blanchet@43413
|
830 |
|
blanchet@45255
|
831 |
fun mangled_type format type_enc =
|
blanchet@45255
|
832 |
generic_mangled_type_name fst o ho_term_from_typ format type_enc
|
blanchet@45255
|
833 |
|
blanchet@43926
|
834 |
fun make_simple_type s =
|
blanchet@43926
|
835 |
if s = tptp_bool_type orelse s = tptp_fun_type orelse
|
blanchet@43926
|
836 |
s = tptp_individual_type then
|
blanchet@43926
|
837 |
s
|
blanchet@43926
|
838 |
else
|
blanchet@43926
|
839 |
simple_type_prefix ^ ascii_of s
|
blanchet@43926
|
840 |
|
nik@44535
|
841 |
fun ho_type_from_ho_term type_enc pred_sym ary =
|
blanchet@43804
|
842 |
let
|
blanchet@45457
|
843 |
fun to_mangled_atype ty =
|
blanchet@43804
|
844 |
AType ((make_simple_type (generic_mangled_type_name fst ty),
|
blanchet@45457
|
845 |
generic_mangled_type_name snd ty), [])
|
blanchet@45457
|
846 |
fun to_poly_atype (ATerm (name, tys)) = AType (name, map to_poly_atype tys)
|
blanchet@45457
|
847 |
| to_poly_atype _ = raise Fail "unexpected type abstraction"
|
blanchet@45457
|
848 |
val to_atype =
|
blanchet@45457
|
849 |
if polymorphism_of_type_enc type_enc = Polymorphic then to_poly_atype
|
blanchet@45457
|
850 |
else to_mangled_atype
|
blanchet@43804
|
851 |
fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
|
blanchet@43839
|
852 |
fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
|
blanchet@43835
|
853 |
| to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
|
blanchet@44558
|
854 |
| to_fo _ _ = raise Fail "unexpected type abstraction"
|
blanchet@43835
|
855 |
fun to_ho (ty as ATerm ((s, _), tys)) =
|
nik@44535
|
856 |
if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
|
nik@44535
|
857 |
| to_ho _ = raise Fail "unexpected type abstraction"
|
blanchet@44493
|
858 |
in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
|
blanchet@43804
|
859 |
|
nik@44536
|
860 |
fun ho_type_from_typ format type_enc pred_sym ary =
|
nik@44535
|
861 |
ho_type_from_ho_term type_enc pred_sym ary
|
nik@44535
|
862 |
o ho_term_from_typ format type_enc
|
blanchet@43804
|
863 |
|
blanchet@44493
|
864 |
fun mangled_const_name format type_enc T_args (s, s') =
|
blanchet@43804
|
865 |
let
|
nik@44535
|
866 |
val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
|
blanchet@43804
|
867 |
fun type_suffix f g =
|
blanchet@43804
|
868 |
fold_rev (curry (op ^) o g o prefix mangled_type_sep
|
blanchet@43804
|
869 |
o generic_mangled_type_name f) ty_args ""
|
blanchet@43804
|
870 |
in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
|
blanchet@43413
|
871 |
|
blanchet@43413
|
872 |
val parse_mangled_ident =
|
blanchet@43413
|
873 |
Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
|
blanchet@43413
|
874 |
|
blanchet@43413
|
875 |
fun parse_mangled_type x =
|
blanchet@43413
|
876 |
(parse_mangled_ident
|
blanchet@43413
|
877 |
-- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
|
blanchet@43413
|
878 |
[] >> ATerm) x
|
blanchet@43413
|
879 |
and parse_mangled_types x =
|
blanchet@43413
|
880 |
(parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
|
blanchet@43413
|
881 |
|
blanchet@43413
|
882 |
fun unmangled_type s =
|
blanchet@43413
|
883 |
s |> suffix ")" |> raw_explode
|
blanchet@43413
|
884 |
|> Scan.finite Symbol.stopper
|
blanchet@43413
|
885 |
(Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
|
blanchet@43413
|
886 |
quote s)) parse_mangled_type))
|
blanchet@43413
|
887 |
|> fst
|
blanchet@43413
|
888 |
|
blanchet@43432
|
889 |
val unmangled_const_name = space_explode mangled_type_sep #> hd
|
blanchet@43413
|
890 |
fun unmangled_const s =
|
blanchet@43413
|
891 |
let val ss = space_explode mangled_type_sep s in
|
blanchet@43413
|
892 |
(hd ss, map unmangled_type (tl ss))
|
blanchet@43413
|
893 |
end
|
blanchet@43413
|
894 |
|
blanchet@44493
|
895 |
fun introduce_proxies type_enc =
|
blanchet@43439
|
896 |
let
|
blanchet@44858
|
897 |
fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, [])
|
blanchet@44858
|
898 |
| tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _]))
|
blanchet@44858
|
899 |
_ =
|
blanchet@44858
|
900 |
(* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser
|
blanchet@44858
|
901 |
limitation. This works in conjuction with special code in
|
blanchet@44858
|
902 |
"ATP_Problem" that uses the syntactic sugar "!" and "?" whenever
|
blanchet@44858
|
903 |
possible. *)
|
blanchet@44858
|
904 |
IAbs ((`I "P", p_T),
|
blanchet@44858
|
905 |
IApp (IConst (`I ho_quant, T, []),
|
blanchet@44858
|
906 |
IAbs ((`I "X", x_T),
|
blanchet@44858
|
907 |
IApp (IConst (`I "P", p_T, []),
|
blanchet@44858
|
908 |
IConst (`I "X", x_T, [])))))
|
blanchet@44858
|
909 |
| tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier"
|
blanchet@44858
|
910 |
fun intro top_level args (IApp (tm1, tm2)) =
|
blanchet@44858
|
911 |
IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2)
|
blanchet@44858
|
912 |
| intro top_level args (IConst (name as (s, _), T, T_args)) =
|
blanchet@43441
|
913 |
(case proxify_const s of
|
blanchet@44000
|
914 |
SOME proxy_base =>
|
blanchet@44493
|
915 |
if top_level orelse is_type_enc_higher_order type_enc then
|
blanchet@43841
|
916 |
case (top_level, s) of
|
blanchet@44858
|
917 |
(_, "c_False") => IConst (`I tptp_false, T, [])
|
blanchet@44858
|
918 |
| (_, "c_True") => IConst (`I tptp_true, T, [])
|
blanchet@44858
|
919 |
| (false, "c_Not") => IConst (`I tptp_not, T, [])
|
blanchet@44858
|
920 |
| (false, "c_conj") => IConst (`I tptp_and, T, [])
|
blanchet@44858
|
921 |
| (false, "c_disj") => IConst (`I tptp_or, T, [])
|
blanchet@44858
|
922 |
| (false, "c_implies") => IConst (`I tptp_implies, T, [])
|
blanchet@44858
|
923 |
| (false, "c_All") => tweak_ho_quant tptp_ho_forall T args
|
blanchet@44858
|
924 |
| (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args
|
blanchet@43841
|
925 |
| (false, s) =>
|
blanchet@44968
|
926 |
if is_tptp_equal s andalso length args = 2 then
|
blanchet@44968
|
927 |
IConst (`I tptp_equal, T, [])
|
blanchet@44968
|
928 |
else
|
blanchet@45453
|
929 |
(* Use a proxy even for partially applied THF0 equality,
|
blanchet@45453
|
930 |
because the LEO-II and Satallax parsers complain about not
|
blanchet@45453
|
931 |
being able to infer the type of "=". *)
|
blanchet@44968
|
932 |
IConst (proxy_base |>> prefix const_prefix, T, T_args)
|
blanchet@44858
|
933 |
| _ => IConst (name, T, [])
|
blanchet@43440
|
934 |
else
|
blanchet@44858
|
935 |
IConst (proxy_base |>> prefix const_prefix, T, T_args)
|
nik@45350
|
936 |
| NONE => if s = tptp_choice then
|
nik@45350
|
937 |
tweak_ho_quant tptp_choice T args
|
blanchet@45453
|
938 |
else
|
blanchet@45453
|
939 |
IConst (name, T, T_args))
|
blanchet@44858
|
940 |
| intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm)
|
blanchet@44858
|
941 |
| intro _ _ tm = tm
|
blanchet@44858
|
942 |
in intro true [] end
|
blanchet@43439
|
943 |
|
nik@45350
|
944 |
fun iformula_from_prop thy format type_enc eq_as_iff =
|
blanchet@38506
|
945 |
let
|
blanchet@43439
|
946 |
fun do_term bs t atomic_types =
|
nik@45350
|
947 |
iterm_from_term thy format bs (Envir.eta_contract t)
|
blanchet@44493
|
948 |
|>> (introduce_proxies type_enc #> AAtom)
|
blanchet@43439
|
949 |
||> union (op =) atomic_types
|
blanchet@45262
|
950 |
fun do_quant bs q pos s T t' =
|
blanchet@45262
|
951 |
let
|
blanchet@45262
|
952 |
val s = singleton (Name.variant_list (map fst bs)) s
|
blanchet@45262
|
953 |
val universal = Option.map (q = AExists ? not) pos
|
blanchet@45262
|
954 |
val name =
|
blanchet@45262
|
955 |
s |> `(case universal of
|
blanchet@45262
|
956 |
SOME true => make_all_bound_var
|
blanchet@45262
|
957 |
| SOME false => make_exist_bound_var
|
blanchet@45262
|
958 |
| NONE => make_bound_var)
|
blanchet@45262
|
959 |
in
|
blanchet@45262
|
960 |
do_formula ((s, (name, T)) :: bs) pos t'
|
blanchet@45262
|
961 |
#>> mk_aquant q [(name, SOME T)]
|
blanchet@38743
|
962 |
end
|
blanchet@45262
|
963 |
and do_conn bs c pos1 t1 pos2 t2 =
|
blanchet@45262
|
964 |
do_formula bs pos1 t1 ##>> do_formula bs pos2 t2 #>> uncurry (mk_aconn c)
|
blanchet@45262
|
965 |
and do_formula bs pos t =
|
blanchet@38506
|
966 |
case t of
|
blanchet@45262
|
967 |
@{const Trueprop} $ t1 => do_formula bs pos t1
|
blanchet@45262
|
968 |
| @{const Not} $ t1 => do_formula bs (Option.map not pos) t1 #>> mk_anot
|
blanchet@38506
|
969 |
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
|
blanchet@45262
|
970 |
do_quant bs AForall pos s T t'
|
blanchet@38506
|
971 |
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
|
blanchet@45262
|
972 |
do_quant bs AExists pos s T t'
|
blanchet@45262
|
973 |
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd pos t1 pos t2
|
blanchet@45262
|
974 |
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr pos t1 pos t2
|
blanchet@45262
|
975 |
| @{const HOL.implies} $ t1 $ t2 =>
|
blanchet@45262
|
976 |
do_conn bs AImplies (Option.map not pos) t1 pos t2
|
haftmann@39093
|
977 |
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
|
blanchet@45262
|
978 |
if eq_as_iff then do_conn bs AIff NONE t1 NONE t2 else do_term bs t
|
blanchet@41388
|
979 |
| _ => do_term bs t
|
blanchet@38506
|
980 |
in do_formula [] end
|
blanchet@38506
|
981 |
|
blanchet@44105
|
982 |
fun presimplify_term _ [] t = t
|
blanchet@44105
|
983 |
| presimplify_term ctxt presimp_consts t =
|
blanchet@44105
|
984 |
t |> exists_Const (member (op =) presimp_consts o fst) t
|
blanchet@44105
|
985 |
? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
|
blanchet@44105
|
986 |
#> Meson.presimplify ctxt
|
blanchet@44105
|
987 |
#> prop_of)
|
blanchet@38506
|
988 |
|
blanchet@44734
|
989 |
fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j
|
blanchet@38506
|
990 |
fun conceal_bounds Ts t =
|
blanchet@38506
|
991 |
subst_bounds (map (Free o apfst concealed_bound_name)
|
blanchet@38506
|
992 |
(0 upto length Ts - 1 ~~ Ts), t)
|
blanchet@38506
|
993 |
fun reveal_bounds Ts =
|
blanchet@38506
|
994 |
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
|
blanchet@38506
|
995 |
(0 upto length Ts - 1 ~~ Ts))
|
blanchet@38506
|
996 |
|
blanchet@44106
|
997 |
fun is_fun_equality (@{const_name HOL.eq},
|
blanchet@44106
|
998 |
Type (_, [Type (@{type_name fun}, _), _])) = true
|
blanchet@44106
|
999 |
| is_fun_equality _ = false
|
blanchet@44106
|
1000 |
|
blanchet@43612
|
1001 |
fun extensionalize_term ctxt t =
|
blanchet@44106
|
1002 |
if exists_Const is_fun_equality t then
|
blanchet@44106
|
1003 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@44106
|
1004 |
t |> cterm_of thy |> Meson.extensionalize_conv ctxt
|
blanchet@44106
|
1005 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@44106
|
1006 |
end
|
blanchet@44106
|
1007 |
else
|
blanchet@44106
|
1008 |
t
|
blanchet@38831
|
1009 |
|
blanchet@44733
|
1010 |
fun simple_translate_lambdas do_lambdas ctxt t =
|
blanchet@44734
|
1011 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@44734
|
1012 |
if Meson.is_fol_term thy t then
|
blanchet@44734
|
1013 |
t
|
blanchet@44734
|
1014 |
else
|
blanchet@44734
|
1015 |
let
|
blanchet@44734
|
1016 |
fun aux Ts t =
|
blanchet@44734
|
1017 |
case t of
|
blanchet@44734
|
1018 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@44734
|
1019 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@44734
|
1020 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@44734
|
1021 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@44734
|
1022 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@44734
|
1023 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@44734
|
1024 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@44734
|
1025 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@44734
|
1026 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@44734
|
1027 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@44734
|
1028 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@44734
|
1029 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@44734
|
1030 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@44734
|
1031 |
$ t1 $ t2 =>
|
blanchet@44734
|
1032 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@44734
|
1033 |
| _ =>
|
blanchet@44734
|
1034 |
if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
|
blanchet@44734
|
1035 |
else t |> Envir.eta_contract |> do_lambdas ctxt Ts
|
blanchet@44734
|
1036 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@44734
|
1037 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@44734
|
1038 |
end
|
blanchet@44727
|
1039 |
|
blanchet@44868
|
1040 |
fun do_cheaply_conceal_lambdas Ts (t1 $ t2) =
|
blanchet@44868
|
1041 |
do_cheaply_conceal_lambdas Ts t1
|
blanchet@44868
|
1042 |
$ do_cheaply_conceal_lambdas Ts t2
|
blanchet@44868
|
1043 |
| do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) =
|
blanchet@44868
|
1044 |
Free (polymorphic_free_prefix ^ serial_string (),
|
blanchet@44868
|
1045 |
T --> fastype_of1 (T :: Ts, t))
|
blanchet@44868
|
1046 |
| do_cheaply_conceal_lambdas _ t = t
|
blanchet@44691
|
1047 |
|
blanchet@44733
|
1048 |
fun do_introduce_combinators ctxt Ts t =
|
blanchet@44727
|
1049 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@44776
|
1050 |
t |> conceal_bounds Ts
|
blanchet@44776
|
1051 |
|> cterm_of thy
|
blanchet@44776
|
1052 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@44776
|
1053 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@44776
|
1054 |
|> reveal_bounds Ts
|
blanchet@44727
|
1055 |
end
|
blanchet@44733
|
1056 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@44868
|
1057 |
handle THM _ => t |> do_cheaply_conceal_lambdas Ts
|
blanchet@44733
|
1058 |
val introduce_combinators = simple_translate_lambdas do_introduce_combinators
|
blanchet@44727
|
1059 |
|
blanchet@44735
|
1060 |
fun preprocess_abstractions_in_terms trans_lambdas facts =
|
blanchet@44733
|
1061 |
let
|
blanchet@44734
|
1062 |
val (facts, lambda_ts) =
|
blanchet@45356
|
1063 |
facts |> map (snd o snd) |> trans_lambdas
|
blanchet@44734
|
1064 |
|>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
|
blanchet@44734
|
1065 |
val lambda_facts =
|
blanchet@44734
|
1066 |
map2 (fn t => fn j =>
|
blanchet@44734
|
1067 |
((lambda_fact_prefix ^ Int.toString j, Helper), (Axiom, t)))
|
blanchet@44734
|
1068 |
lambda_ts (1 upto length lambda_ts)
|
blanchet@44734
|
1069 |
in (facts, lambda_facts) end
|
blanchet@38506
|
1070 |
|
blanchet@38506
|
1071 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@43224
|
1072 |
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
|
blanchet@38506
|
1073 |
fun freeze_term t =
|
blanchet@38506
|
1074 |
let
|
blanchet@38506
|
1075 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
1076 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
1077 |
| aux (Var ((s, i), T)) =
|
blanchet@44734
|
1078 |
Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
1079 |
| aux t = t
|
blanchet@38506
|
1080 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
1081 |
|
blanchet@44734
|
1082 |
fun presimp_prop ctxt presimp_consts t =
|
blanchet@38506
|
1083 |
let
|
wenzelm@43232
|
1084 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@38831
|
1085 |
val t = t |> Envir.beta_eta_contract
|
blanchet@43785
|
1086 |
|> transform_elim_prop
|
blanchet@41459
|
1087 |
|> Object_Logic.atomize_term thy
|
blanchet@43434
|
1088 |
val need_trueprop = (fastype_of t = @{typ bool})
|
blanchet@43937
|
1089 |
in
|
blanchet@43937
|
1090 |
t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@43937
|
1091 |
|> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
|
blanchet@43937
|
1092 |
|> extensionalize_term ctxt
|
blanchet@44105
|
1093 |
|> presimplify_term ctxt presimp_consts
|
blanchet@43961
|
1094 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@43937
|
1095 |
end
|
blanchet@43937
|
1096 |
|
blanchet@43937
|
1097 |
(* making fact and conjecture formulas *)
|
nik@45350
|
1098 |
fun make_formula thy format type_enc eq_as_iff name loc kind t =
|
blanchet@43937
|
1099 |
let
|
blanchet@44730
|
1100 |
val (iformula, atomic_types) =
|
nik@45350
|
1101 |
iformula_from_prop thy format type_enc eq_as_iff (SOME (kind <> Conjecture)) t []
|
blanchet@38506
|
1102 |
in
|
blanchet@44730
|
1103 |
{name = name, locality = loc, kind = kind, iformula = iformula,
|
blanchet@43433
|
1104 |
atomic_types = atomic_types}
|
blanchet@38506
|
1105 |
end
|
blanchet@38506
|
1106 |
|
blanchet@44731
|
1107 |
fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
|
blanchet@43937
|
1108 |
let val thy = Proof_Context.theory_of ctxt in
|
nik@45350
|
1109 |
case t |> make_formula thy format type_enc (eq_as_iff andalso format <> CNF)
|
nik@45350
|
1110 |
name loc Axiom of
|
blanchet@44730
|
1111 |
formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
|
blanchet@43937
|
1112 |
if s = tptp_true then NONE else SOME formula
|
blanchet@44153
|
1113 |
| formula => SOME formula
|
blanchet@43937
|
1114 |
end
|
blanchet@43432
|
1115 |
|
blanchet@45317
|
1116 |
fun s_not_trueprop (@{const Trueprop} $ t) = @{const Trueprop} $ s_not t
|
blanchet@45317
|
1117 |
| s_not_trueprop t = s_not t
|
blanchet@45317
|
1118 |
|
blanchet@45320
|
1119 |
fun make_conjecture thy format type_enc =
|
blanchet@45320
|
1120 |
map (fn ((name, loc), (kind, t)) =>
|
blanchet@45320
|
1121 |
t |> kind = Conjecture ? s_not_trueprop
|
nik@45350
|
1122 |
|> make_formula thy format type_enc (format <> CNF) name loc kind)
|
blanchet@38506
|
1123 |
|
blanchet@43552
|
1124 |
(** Finite and infinite type inference **)
|
blanchet@43552
|
1125 |
|
blanchet@45258
|
1126 |
type monotonicity_info =
|
blanchet@45258
|
1127 |
{maybe_finite_Ts : typ list,
|
blanchet@45258
|
1128 |
surely_finite_Ts : typ list,
|
blanchet@45258
|
1129 |
maybe_infinite_Ts : typ list,
|
blanchet@45258
|
1130 |
surely_infinite_Ts : typ list,
|
blanchet@45258
|
1131 |
maybe_nonmono_Ts : typ list}
|
blanchet@45258
|
1132 |
|
blanchet@45256
|
1133 |
(* These types witness that the type classes they belong to allow infinite
|
blanchet@45256
|
1134 |
models and hence that any types with these type classes is monotonic. *)
|
blanchet@45256
|
1135 |
val known_infinite_types =
|
blanchet@45256
|
1136 |
[@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
|
blanchet@45256
|
1137 |
|
blanchet@45355
|
1138 |
fun is_type_kind_of_surely_infinite ctxt soundness cached_Ts T =
|
blanchet@45256
|
1139 |
soundness <> Sound andalso
|
blanchet@45355
|
1140 |
is_type_surely_infinite ctxt (soundness <> Unsound) cached_Ts T
|
blanchet@43755
|
1141 |
|
blanchet@43552
|
1142 |
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
|
blanchet@43552
|
1143 |
dangerous because their "exhaust" properties can easily lead to unsound ATP
|
blanchet@43552
|
1144 |
proofs. On the other hand, all HOL infinite types can be given the same
|
blanchet@43552
|
1145 |
models in first-order logic (via Löwenheim-Skolem). *)
|
blanchet@43552
|
1146 |
|
blanchet@45258
|
1147 |
fun should_encode_type _ (_ : monotonicity_info) All_Types _ = true
|
blanchet@45258
|
1148 |
| should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts,
|
blanchet@45258
|
1149 |
maybe_nonmono_Ts, ...}
|
blanchet@45258
|
1150 |
(Noninf_Nonmono_Types soundness) T =
|
blanchet@45346
|
1151 |
exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
|
blanchet@45258
|
1152 |
not (exists (type_instance ctxt T) surely_infinite_Ts orelse
|
blanchet@45258
|
1153 |
(not (member (type_aconv ctxt) maybe_finite_Ts T) andalso
|
blanchet@45355
|
1154 |
is_type_kind_of_surely_infinite ctxt soundness surely_infinite_Ts T))
|
blanchet@45258
|
1155 |
| should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts,
|
blanchet@45258
|
1156 |
maybe_nonmono_Ts, ...}
|
blanchet@45258
|
1157 |
Fin_Nonmono_Types T =
|
blanchet@45346
|
1158 |
exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
|
blanchet@45346
|
1159 |
(exists (type_generalization ctxt T) surely_finite_Ts orelse
|
blanchet@45258
|
1160 |
(not (member (type_aconv ctxt) maybe_infinite_Ts T) andalso
|
blanchet@45258
|
1161 |
is_type_surely_finite ctxt T))
|
blanchet@43552
|
1162 |
| should_encode_type _ _ _ _ = false
|
blanchet@43552
|
1163 |
|
blanchet@45261
|
1164 |
fun should_guard_type ctxt mono (Guards (_, level, uniformity)) should_guard_var
|
blanchet@45258
|
1165 |
T =
|
blanchet@45261
|
1166 |
(uniformity = Uniform orelse should_guard_var ()) andalso
|
blanchet@45258
|
1167 |
should_encode_type ctxt mono level T
|
blanchet@45258
|
1168 |
| should_guard_type _ _ _ _ _ = false
|
blanchet@43552
|
1169 |
|
blanchet@45262
|
1170 |
fun is_maybe_universal_var (IConst ((s, _), _, _)) =
|
blanchet@45262
|
1171 |
String.isPrefix bound_var_prefix s orelse
|
blanchet@45262
|
1172 |
String.isPrefix all_bound_var_prefix s
|
blanchet@45262
|
1173 |
| is_maybe_universal_var (IVar _) = true
|
blanchet@45262
|
1174 |
| is_maybe_universal_var _ = false
|
blanchet@43707
|
1175 |
|
blanchet@44232
|
1176 |
datatype tag_site =
|
blanchet@44232
|
1177 |
Top_Level of bool option |
|
blanchet@44232
|
1178 |
Eq_Arg of bool option |
|
blanchet@44232
|
1179 |
Elsewhere
|
blanchet@43700
|
1180 |
|
blanchet@44232
|
1181 |
fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
|
blanchet@45261
|
1182 |
| should_tag_with_type ctxt mono (Tags (_, level, uniformity)) site u T =
|
blanchet@45261
|
1183 |
(case uniformity of
|
blanchet@45261
|
1184 |
Uniform => should_encode_type ctxt mono level T
|
blanchet@45261
|
1185 |
| Nonuniform =>
|
blanchet@45262
|
1186 |
case (site, is_maybe_universal_var u) of
|
blanchet@45258
|
1187 |
(Eq_Arg _, true) => should_encode_type ctxt mono level T
|
blanchet@43700
|
1188 |
| _ => false)
|
blanchet@43700
|
1189 |
| should_tag_with_type _ _ _ _ _ _ = false
|
blanchet@43552
|
1190 |
|
blanchet@45458
|
1191 |
fun fused_type ctxt mono level =
|
blanchet@43835
|
1192 |
let
|
blanchet@45258
|
1193 |
val should_encode = should_encode_type ctxt mono level
|
blanchet@45458
|
1194 |
fun fuse 0 T = if should_encode T then T else fused_infinite_type
|
blanchet@45458
|
1195 |
| fuse ary (Type (@{type_name fun}, [T1, T2])) =
|
blanchet@45458
|
1196 |
fuse 0 T1 --> fuse (ary - 1) T2
|
blanchet@45458
|
1197 |
| fuse _ _ = raise Fail "expected function type"
|
blanchet@45458
|
1198 |
in fuse end
|
blanchet@43552
|
1199 |
|
blanchet@45307
|
1200 |
(** predicators and application operators **)
|
blanchet@41561
|
1201 |
|
blanchet@43445
|
1202 |
type sym_info =
|
blanchet@43905
|
1203 |
{pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
|
blanchet@43434
|
1204 |
|
blanchet@44730
|
1205 |
fun add_iterm_syms_to_table ctxt explicit_apply =
|
blanchet@43429
|
1206 |
let
|
blanchet@43905
|
1207 |
fun consider_var_arity const_T var_T max_ary =
|
blanchet@43905
|
1208 |
let
|
blanchet@43905
|
1209 |
fun iter ary T =
|
blanchet@45258
|
1210 |
if ary = max_ary orelse type_instance ctxt var_T T orelse
|
blanchet@45258
|
1211 |
type_instance ctxt T var_T then
|
blanchet@44051
|
1212 |
ary
|
blanchet@44051
|
1213 |
else
|
blanchet@44051
|
1214 |
iter (ary + 1) (range_type T)
|
blanchet@43905
|
1215 |
in iter 0 const_T end
|
blanchet@45262
|
1216 |
fun add_universal_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
|
blanchet@44042
|
1217 |
if explicit_apply = NONE andalso
|
blanchet@44042
|
1218 |
(can dest_funT T orelse T = @{typ bool}) then
|
blanchet@44042
|
1219 |
let
|
blanchet@44042
|
1220 |
val bool_vars' = bool_vars orelse body_type T = @{typ bool}
|
blanchet@44042
|
1221 |
fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
|
blanchet@44042
|
1222 |
{pred_sym = pred_sym andalso not bool_vars',
|
blanchet@44054
|
1223 |
min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
|
blanchet@44042
|
1224 |
max_ary = max_ary, types = types}
|
blanchet@44042
|
1225 |
val fun_var_Ts' =
|
blanchet@44042
|
1226 |
fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
|
blanchet@44042
|
1227 |
in
|
blanchet@44042
|
1228 |
if bool_vars' = bool_vars andalso
|
blanchet@44042
|
1229 |
pointer_eq (fun_var_Ts', fun_var_Ts) then
|
blanchet@44042
|
1230 |
accum
|
blanchet@44008
|
1231 |
else
|
blanchet@44054
|
1232 |
((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
|
blanchet@44042
|
1233 |
end
|
blanchet@44042
|
1234 |
else
|
blanchet@44042
|
1235 |
accum
|
blanchet@44042
|
1236 |
fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
|
blanchet@44730
|
1237 |
let val (head, args) = strip_iterm_comb tm in
|
blanchet@43429
|
1238 |
(case head of
|
blanchet@44730
|
1239 |
IConst ((s, _), T, _) =>
|
blanchet@45262
|
1240 |
if String.isPrefix bound_var_prefix s orelse
|
blanchet@45262
|
1241 |
String.isPrefix all_bound_var_prefix s then
|
blanchet@45262
|
1242 |
add_universal_var T accum
|
blanchet@45307
|
1243 |
else if String.isPrefix exist_bound_var_prefix s then
|
blanchet@45307
|
1244 |
accum
|
blanchet@43429
|
1245 |
else
|
blanchet@43980
|
1246 |
let val ary = length args in
|
blanchet@44042
|
1247 |
((bool_vars, fun_var_Ts),
|
blanchet@43905
|
1248 |
case Symtab.lookup sym_tab s of
|
blanchet@43905
|
1249 |
SOME {pred_sym, min_ary, max_ary, types} =>
|
blanchet@43905
|
1250 |
let
|
blanchet@44042
|
1251 |
val pred_sym =
|
blanchet@44042
|
1252 |
pred_sym andalso top_level andalso not bool_vars
|
blanchet@43905
|
1253 |
val types' = types |> insert_type ctxt I T
|
blanchet@43905
|
1254 |
val min_ary =
|
blanchet@43905
|
1255 |
if is_some explicit_apply orelse
|
blanchet@43905
|
1256 |
pointer_eq (types', types) then
|
blanchet@43905
|
1257 |
min_ary
|
blanchet@43905
|
1258 |
else
|
blanchet@44042
|
1259 |
fold (consider_var_arity T) fun_var_Ts min_ary
|
blanchet@43905
|
1260 |
in
|
blanchet@44042
|
1261 |
Symtab.update (s, {pred_sym = pred_sym,
|
blanchet@43905
|
1262 |
min_ary = Int.min (ary, min_ary),
|
blanchet@43905
|
1263 |
max_ary = Int.max (ary, max_ary),
|
blanchet@43905
|
1264 |
types = types'})
|
blanchet@43905
|
1265 |
sym_tab
|
blanchet@43905
|
1266 |
end
|
blanchet@43905
|
1267 |
| NONE =>
|
blanchet@43905
|
1268 |
let
|
blanchet@44042
|
1269 |
val pred_sym = top_level andalso not bool_vars
|
blanchet@43905
|
1270 |
val min_ary =
|
blanchet@43905
|
1271 |
case explicit_apply of
|
blanchet@43905
|
1272 |
SOME true => 0
|
blanchet@43905
|
1273 |
| SOME false => ary
|
blanchet@44042
|
1274 |
| NONE => fold (consider_var_arity T) fun_var_Ts ary
|
blanchet@43905
|
1275 |
in
|
blanchet@44042
|
1276 |
Symtab.update_new (s, {pred_sym = pred_sym,
|
blanchet@43905
|
1277 |
min_ary = min_ary, max_ary = ary,
|
blanchet@43905
|
1278 |
types = [T]})
|
blanchet@43905
|
1279 |
sym_tab
|
blanchet@43905
|
1280 |
end)
|
blanchet@43905
|
1281 |
end
|
blanchet@45262
|
1282 |
| IVar (_, T) => add_universal_var T accum
|
blanchet@45262
|
1283 |
| IAbs ((_, T), tm) => accum |> add_universal_var T |> add false tm
|
blanchet@43905
|
1284 |
| _ => accum)
|
blanchet@43905
|
1285 |
|> fold (add false) args
|
blanchet@43429
|
1286 |
end
|
blanchet@43905
|
1287 |
in add true end
|
blanchet@43905
|
1288 |
fun add_fact_syms_to_table ctxt explicit_apply =
|
blanchet@45356
|
1289 |
K (add_iterm_syms_to_table ctxt explicit_apply)
|
blanchet@45356
|
1290 |
|> formula_fold NONE |> fact_lift
|
blanchet@38506
|
1291 |
|
blanchet@43980
|
1292 |
val default_sym_tab_entries : (string * sym_info) list =
|
blanchet@44015
|
1293 |
(prefixed_predicator_name,
|
blanchet@45363
|
1294 |
{pred_sym = true, min_ary = 1, max_ary = 1, types = []})
|
blanchet@45363
|
1295 |
(* FIXME: needed? *) ::
|
nik@45350
|
1296 |
(make_fixed_const NONE @{const_name undefined},
|
blanchet@44837
|
1297 |
{pred_sym = false, min_ary = 0, max_ary = 0, types = []}) ::
|
blanchet@43439
|
1298 |
([tptp_false, tptp_true]
|
blanchet@43980
|
1299 |
|> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
|
blanchet@43980
|
1300 |
([tptp_equal, tptp_old_equal]
|
blanchet@43980
|
1301 |
|> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
|
blanchet@41388
|
1302 |
|
blanchet@45351
|
1303 |
fun sym_table_for_facts ctxt explicit_apply facts =
|
blanchet@44042
|
1304 |
((false, []), Symtab.empty)
|
blanchet@44042
|
1305 |
|> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
|
blanchet@43980
|
1306 |
|> fold Symtab.update default_sym_tab_entries
|
blanchet@38506
|
1307 |
|
blanchet@43429
|
1308 |
fun min_arity_of sym_tab s =
|
blanchet@43429
|
1309 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
1310 |
SOME ({min_ary, ...} : sym_info) => min_ary
|
blanchet@43429
|
1311 |
| NONE =>
|
blanchet@43429
|
1312 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43418
|
1313 |
SOME s =>
|
blanchet@43441
|
1314 |
let val s = s |> unmangled_const_name |> invert_const in
|
blanchet@43807
|
1315 |
if s = predicator_name then 1
|
blanchet@43807
|
1316 |
else if s = app_op_name then 2
|
blanchet@45255
|
1317 |
else if s = type_guard_name then 1
|
blanchet@43428
|
1318 |
else 0
|
blanchet@43418
|
1319 |
end
|
blanchet@38506
|
1320 |
| NONE => 0
|
blanchet@38506
|
1321 |
|
blanchet@38506
|
1322 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
1323 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
1324 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
1325 |
arguments and is used as a predicate. *)
|
blanchet@43429
|
1326 |
fun is_pred_sym sym_tab s =
|
blanchet@43429
|
1327 |
case Symtab.lookup sym_tab s of
|
blanchet@43445
|
1328 |
SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
|
blanchet@43445
|
1329 |
pred_sym andalso min_ary = max_ary
|
blanchet@43429
|
1330 |
| NONE => false
|
blanchet@38506
|
1331 |
|
blanchet@43439
|
1332 |
val predicator_combconst =
|
nik@45350
|
1333 |
IConst (`(make_fixed_const NONE) predicator_name, @{typ "bool => bool"}, [])
|
blanchet@44730
|
1334 |
fun predicator tm = IApp (predicator_combconst, tm)
|
blanchet@38506
|
1335 |
|
blanchet@44730
|
1336 |
fun introduce_predicators_in_iterm sym_tab tm =
|
blanchet@44730
|
1337 |
case strip_iterm_comb tm of
|
blanchet@44730
|
1338 |
(IConst ((s, _), _, _), _) =>
|
blanchet@43439
|
1339 |
if is_pred_sym sym_tab s then tm else predicator tm
|
blanchet@43439
|
1340 |
| _ => predicator tm
|
blanchet@38506
|
1341 |
|
blanchet@44730
|
1342 |
fun list_app head args = fold (curry (IApp o swap)) args head
|
blanchet@38506
|
1343 |
|
nik@45350
|
1344 |
val app_op = `(make_fixed_const NONE) app_op_name
|
blanchet@43971
|
1345 |
|
blanchet@43415
|
1346 |
fun explicit_app arg head =
|
blanchet@43415
|
1347 |
let
|
blanchet@44730
|
1348 |
val head_T = ityp_of head
|
blanchet@43563
|
1349 |
val (arg_T, res_T) = dest_funT head_T
|
blanchet@44730
|
1350 |
val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
|
blanchet@43415
|
1351 |
in list_app explicit_app [head, arg] end
|
blanchet@43415
|
1352 |
fun list_explicit_app head args = fold explicit_app args head
|
blanchet@43415
|
1353 |
|
blanchet@44730
|
1354 |
fun introduce_explicit_apps_in_iterm sym_tab =
|
blanchet@43415
|
1355 |
let
|
blanchet@43415
|
1356 |
fun aux tm =
|
blanchet@44730
|
1357 |
case strip_iterm_comb tm of
|
blanchet@44730
|
1358 |
(head as IConst ((s, _), _, _), args) =>
|
blanchet@43415
|
1359 |
args |> map aux
|
blanchet@43428
|
1360 |
|> chop (min_arity_of sym_tab s)
|
blanchet@43415
|
1361 |
|>> list_app head
|
blanchet@43415
|
1362 |
|-> list_explicit_app
|
blanchet@43415
|
1363 |
| (head, args) => list_explicit_app head (map aux args)
|
blanchet@43415
|
1364 |
in aux end
|
blanchet@43415
|
1365 |
|
blanchet@43618
|
1366 |
fun chop_fun 0 T = ([], T)
|
blanchet@43618
|
1367 |
| chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
|
blanchet@43618
|
1368 |
chop_fun (n - 1) ran_T |>> cons dom_T
|
blanchet@43618
|
1369 |
| chop_fun _ _ = raise Fail "unexpected non-function"
|
blanchet@43618
|
1370 |
|
blanchet@43651
|
1371 |
fun filter_type_args _ _ _ [] = []
|
blanchet@43651
|
1372 |
| filter_type_args thy s arity T_args =
|
blanchet@45458
|
1373 |
let val U = robust_const_type thy s in
|
blanchet@43652
|
1374 |
case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
|
blanchet@43652
|
1375 |
[] => []
|
blanchet@43652
|
1376 |
| res_U_vars =>
|
blanchet@43652
|
1377 |
let val U_args = (s, U) |> Sign.const_typargs thy in
|
blanchet@43652
|
1378 |
U_args ~~ T_args
|
blanchet@44264
|
1379 |
|> map (fn (U, T) =>
|
blanchet@44264
|
1380 |
if member (op =) res_U_vars (dest_TVar U) then T
|
blanchet@44264
|
1381 |
else dummyT)
|
blanchet@43652
|
1382 |
end
|
blanchet@43651
|
1383 |
end
|
blanchet@43651
|
1384 |
handle TYPE _ => T_args
|
blanchet@43618
|
1385 |
|
blanchet@44730
|
1386 |
fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
|
blanchet@43618
|
1387 |
let
|
blanchet@43618
|
1388 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@44730
|
1389 |
fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
|
blanchet@44730
|
1390 |
| aux arity (IConst (name as (s, _), T, T_args)) =
|
blanchet@44020
|
1391 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@44832
|
1392 |
NONE =>
|
nik@45350
|
1393 |
(name, if level_of_type_enc type_enc = No_Types orelse s = tptp_choice
|
nik@45350
|
1394 |
then [] else T_args)
|
blanchet@44020
|
1395 |
| SOME s'' =>
|
blanchet@44020
|
1396 |
let
|
blanchet@44020
|
1397 |
val s'' = invert_const s''
|
blanchet@44020
|
1398 |
fun filtered_T_args false = T_args
|
blanchet@44020
|
1399 |
| filtered_T_args true = filter_type_args thy s'' arity T_args
|
blanchet@44020
|
1400 |
in
|
blanchet@44493
|
1401 |
case type_arg_policy type_enc s'' of
|
blanchet@44020
|
1402 |
Explicit_Type_Args drop_args =>
|
blanchet@44020
|
1403 |
(name, filtered_T_args drop_args)
|
blanchet@44020
|
1404 |
| Mangled_Type_Args drop_args =>
|
blanchet@44493
|
1405 |
(mangled_const_name format type_enc (filtered_T_args drop_args)
|
blanchet@44020
|
1406 |
name, [])
|
blanchet@44020
|
1407 |
| No_Type_Args => (name, [])
|
blanchet@44020
|
1408 |
end)
|
blanchet@44730
|
1409 |
|> (fn (name, T_args) => IConst (name, T, T_args))
|
blanchet@44730
|
1410 |
| aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
|
blanchet@43618
|
1411 |
| aux _ tm = tm
|
blanchet@43618
|
1412 |
in aux 0 end
|
blanchet@43444
|
1413 |
|
blanchet@44730
|
1414 |
fun repair_iterm ctxt format type_enc sym_tab =
|
blanchet@44493
|
1415 |
not (is_type_enc_higher_order type_enc)
|
blanchet@44730
|
1416 |
? (introduce_explicit_apps_in_iterm sym_tab
|
blanchet@44730
|
1417 |
#> introduce_predicators_in_iterm sym_tab)
|
blanchet@44730
|
1418 |
#> enforce_type_arg_policy_in_iterm ctxt format type_enc
|
blanchet@44493
|
1419 |
fun repair_fact ctxt format type_enc sym_tab =
|
blanchet@44730
|
1420 |
update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
|
blanchet@43444
|
1421 |
|
blanchet@43444
|
1422 |
(** Helper facts **)
|
blanchet@43444
|
1423 |
|
blanchet@45307
|
1424 |
val not_ffalse = @{lemma "~ fFalse" by (unfold fFalse_def) fast}
|
blanchet@45307
|
1425 |
val ftrue = @{lemma "fTrue" by (unfold fTrue_def) fast}
|
blanchet@45307
|
1426 |
|
blanchet@44035
|
1427 |
(* The Boolean indicates that a fairly sound type encoding is needed. *)
|
blanchet@43926
|
1428 |
val helper_table =
|
blanchet@44035
|
1429 |
[(("COMBI", false), @{thms Meson.COMBI_def}),
|
blanchet@44035
|
1430 |
(("COMBK", false), @{thms Meson.COMBK_def}),
|
blanchet@44035
|
1431 |
(("COMBB", false), @{thms Meson.COMBB_def}),
|
blanchet@44035
|
1432 |
(("COMBC", false), @{thms Meson.COMBC_def}),
|
blanchet@44035
|
1433 |
(("COMBS", false), @{thms Meson.COMBS_def}),
|
blanchet@45307
|
1434 |
((predicator_name, false), [not_ffalse, ftrue]),
|
blanchet@45307
|
1435 |
(("fFalse", false), [not_ffalse]),
|
blanchet@44035
|
1436 |
(("fFalse", true), @{thms True_or_False}),
|
blanchet@45307
|
1437 |
(("fTrue", false), [ftrue]),
|
blanchet@44035
|
1438 |
(("fTrue", true), @{thms True_or_False}),
|
blanchet@44035
|
1439 |
(("fNot", false),
|
blanchet@44035
|
1440 |
@{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
|
blanchet@44035
|
1441 |
fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
|
blanchet@44035
|
1442 |
(("fconj", false),
|
blanchet@44035
|
1443 |
@{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
|
blanchet@44035
|
1444 |
by (unfold fconj_def) fast+}),
|
blanchet@44035
|
1445 |
(("fdisj", false),
|
blanchet@44035
|
1446 |
@{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
|
blanchet@44035
|
1447 |
by (unfold fdisj_def) fast+}),
|
blanchet@44035
|
1448 |
(("fimplies", false),
|
blanchet@44051
|
1449 |
@{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
|
blanchet@44035
|
1450 |
by (unfold fimplies_def) fast+}),
|
nik@44537
|
1451 |
(("fequal", true),
|
nik@44537
|
1452 |
(* This is a lie: Higher-order equality doesn't need a sound type encoding.
|
nik@44537
|
1453 |
However, this is done so for backward compatibility: Including the
|
nik@44537
|
1454 |
equality helpers by default in Metis breaks a few existing proofs. *)
|
nik@44537
|
1455 |
@{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
|
nik@44537
|
1456 |
fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
|
blanchet@44874
|
1457 |
(* Partial characterization of "fAll" and "fEx". A complete characterization
|
blanchet@44874
|
1458 |
would require the axiom of choice for replay with Metis. *)
|
blanchet@44874
|
1459 |
(("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]),
|
blanchet@44874
|
1460 |
(("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]),
|
blanchet@44035
|
1461 |
(("If", true), @{thms if_True if_False True_or_False})]
|
blanchet@44035
|
1462 |
|> map (apsnd (map zero_var_indexes))
|
blanchet@43926
|
1463 |
|
blanchet@45483
|
1464 |
fun bound_tvars type_enc =
|
blanchet@45483
|
1465 |
mk_ahorn o formulas_for_types type_enc add_sorts_on_tvar
|
blanchet@45263
|
1466 |
|
blanchet@45263
|
1467 |
fun eq_formula type_enc atomic_Ts pred_sym tm1 tm2 =
|
blanchet@45263
|
1468 |
(if pred_sym then AConn (AIff, [AAtom tm1, AAtom tm2])
|
blanchet@45263
|
1469 |
else AAtom (ATerm (`I tptp_equal, [tm1, tm2])))
|
blanchet@45263
|
1470 |
|> bound_tvars type_enc atomic_Ts
|
blanchet@45457
|
1471 |
|> close_formula_universally type_enc
|
blanchet@45263
|
1472 |
|
nik@45350
|
1473 |
val type_tag = `(make_fixed_const NONE) type_tag_name
|
blanchet@43971
|
1474 |
|
blanchet@45263
|
1475 |
fun type_tag_idempotence_fact type_enc =
|
blanchet@43444
|
1476 |
let
|
blanchet@43444
|
1477 |
fun var s = ATerm (`I s, [])
|
blanchet@45267
|
1478 |
fun tag tm = ATerm (type_tag, [var "A", tm])
|
blanchet@45267
|
1479 |
val tagged_var = tag (var "X")
|
blanchet@43444
|
1480 |
in
|
blanchet@44000
|
1481 |
Formula (type_tag_idempotence_helper_name, Axiom,
|
blanchet@45264
|
1482 |
eq_formula type_enc [] false (tag tagged_var) tagged_var,
|
blanchet@45263
|
1483 |
isabelle_info simpN, NONE)
|
blanchet@43444
|
1484 |
end
|
blanchet@43444
|
1485 |
|
blanchet@44493
|
1486 |
fun should_specialize_helper type_enc t =
|
blanchet@45348
|
1487 |
polymorphism_of_type_enc type_enc <> Polymorphic andalso
|
blanchet@44495
|
1488 |
level_of_type_enc type_enc <> No_Types andalso
|
blanchet@44495
|
1489 |
not (null (Term.hidden_polymorphism t))
|
blanchet@44000
|
1490 |
|
blanchet@44729
|
1491 |
fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
|
blanchet@43444
|
1492 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43444
|
1493 |
SOME mangled_s =>
|
blanchet@43444
|
1494 |
let
|
blanchet@43444
|
1495 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@43444
|
1496 |
val unmangled_s = mangled_s |> unmangled_const_name
|
blanchet@44495
|
1497 |
fun dub needs_fairly_sound j k =
|
blanchet@44495
|
1498 |
(unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
|
blanchet@44495
|
1499 |
(if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
|
blanchet@44495
|
1500 |
(if needs_fairly_sound then typed_helper_suffix
|
blanchet@44495
|
1501 |
else untyped_helper_suffix),
|
blanchet@44495
|
1502 |
Helper)
|
blanchet@44000
|
1503 |
fun dub_and_inst needs_fairly_sound (th, j) =
|
blanchet@44495
|
1504 |
let val t = prop_of th in
|
blanchet@44495
|
1505 |
if should_specialize_helper type_enc t then
|
blanchet@44495
|
1506 |
map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
|
blanchet@44495
|
1507 |
types
|
blanchet@44495
|
1508 |
else
|
blanchet@44495
|
1509 |
[t]
|
blanchet@44495
|
1510 |
end
|
blanchet@44495
|
1511 |
|> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
|
blanchet@44731
|
1512 |
val make_facts = map_filter (make_fact ctxt format type_enc false)
|
blanchet@44493
|
1513 |
val fairly_sound = is_type_enc_fairly_sound type_enc
|
blanchet@43444
|
1514 |
in
|
blanchet@43926
|
1515 |
helper_table
|
blanchet@44035
|
1516 |
|> maps (fn ((helper_s, needs_fairly_sound), ths) =>
|
blanchet@44000
|
1517 |
if helper_s <> unmangled_s orelse
|
blanchet@43765
|
1518 |
(needs_fairly_sound andalso not fairly_sound) then
|
blanchet@43444
|
1519 |
[]
|
blanchet@43444
|
1520 |
else
|
blanchet@43444
|
1521 |
ths ~~ (1 upto length ths)
|
blanchet@44495
|
1522 |
|> maps (dub_and_inst needs_fairly_sound)
|
blanchet@44000
|
1523 |
|> make_facts)
|
blanchet@43444
|
1524 |
end
|
blanchet@43444
|
1525 |
| NONE => []
|
blanchet@44729
|
1526 |
fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
|
blanchet@44729
|
1527 |
Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
|
blanchet@44729
|
1528 |
[]
|
blanchet@43444
|
1529 |
|
blanchet@43926
|
1530 |
(***************************************************************)
|
blanchet@43926
|
1531 |
(* Type Classes Present in the Axiom or Conjecture Clauses *)
|
blanchet@43926
|
1532 |
(***************************************************************)
|
blanchet@43926
|
1533 |
|
blanchet@43926
|
1534 |
fun set_insert (x, s) = Symtab.update (x, ()) s
|
blanchet@43926
|
1535 |
|
blanchet@43926
|
1536 |
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
|
blanchet@43926
|
1537 |
|
blanchet@43926
|
1538 |
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
|
blanchet@43926
|
1539 |
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
|
blanchet@43926
|
1540 |
|
blanchet@43934
|
1541 |
fun classes_of_terms get_Ts =
|
blanchet@43962
|
1542 |
map (map snd o get_Ts)
|
blanchet@43934
|
1543 |
#> List.foldl add_classes Symtab.empty
|
blanchet@43934
|
1544 |
#> delete_type #> Symtab.keys
|
blanchet@43926
|
1545 |
|
wenzelm@45004
|
1546 |
val tfree_classes_of_terms = classes_of_terms Misc_Legacy.term_tfrees
|
wenzelm@45004
|
1547 |
val tvar_classes_of_terms = classes_of_terms Misc_Legacy.term_tvars
|
blanchet@43926
|
1548 |
|
blanchet@44489
|
1549 |
fun fold_type_constrs f (Type (s, Ts)) x =
|
blanchet@44489
|
1550 |
fold (fold_type_constrs f) Ts (f (s, x))
|
blanchet@44030
|
1551 |
| fold_type_constrs _ _ x = x
|
blanchet@43926
|
1552 |
|
blanchet@44778
|
1553 |
(* Type constructors used to instantiate overloaded constants are the only ones
|
blanchet@44778
|
1554 |
needed. *)
|
blanchet@44030
|
1555 |
fun add_type_constrs_in_term thy =
|
blanchet@43926
|
1556 |
let
|
blanchet@44029
|
1557 |
fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
|
blanchet@44022
|
1558 |
| add (t $ u) = add t #> add u
|
blanchet@44029
|
1559 |
| add (Const (x as (s, _))) =
|
blanchet@44029
|
1560 |
if String.isPrefix skolem_const_prefix s then I
|
blanchet@44030
|
1561 |
else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
|
blanchet@44778
|
1562 |
| add (Free (s, T)) =
|
blanchet@44807
|
1563 |
if String.isPrefix polymorphic_free_prefix s then
|
blanchet@44778
|
1564 |
T |> fold_type_constrs set_insert
|
blanchet@44778
|
1565 |
else
|
blanchet@44778
|
1566 |
I
|
blanchet@44022
|
1567 |
| add (Abs (_, _, u)) = add u
|
blanchet@44022
|
1568 |
| add _ = I
|
blanchet@44022
|
1569 |
in add end
|
blanchet@43926
|
1570 |
|
blanchet@44030
|
1571 |
fun type_constrs_of_terms thy ts =
|
blanchet@44030
|
1572 |
Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
|
blanchet@43926
|
1573 |
|
blanchet@44727
|
1574 |
fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
|
blanchet@44692
|
1575 |
hyp_ts concl_t facts =
|
blanchet@43444
|
1576 |
let
|
blanchet@43444
|
1577 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@44105
|
1578 |
val presimp_consts = Meson.presimplified_consts ctxt
|
blanchet@44732
|
1579 |
val fact_ts = facts |> map snd
|
blanchet@43444
|
1580 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@43444
|
1581 |
boost an ATP's performance (for some reason). *)
|
blanchet@44033
|
1582 |
val hyp_ts =
|
blanchet@44033
|
1583 |
hyp_ts
|
blanchet@44033
|
1584 |
|> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
|
blanchet@44735
|
1585 |
val facts = facts |> map (apsnd (pair Axiom))
|
blanchet@44735
|
1586 |
val conjs =
|
blanchet@45317
|
1587 |
map (pair prem_kind) hyp_ts @ [(Conjecture, s_not_trueprop concl_t)]
|
blanchet@44734
|
1588 |
|> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts)
|
blanchet@44735
|
1589 |
val ((conjs, facts), lambdas) =
|
blanchet@44735
|
1590 |
if preproc then
|
blanchet@44735
|
1591 |
conjs @ facts
|
blanchet@44735
|
1592 |
|> map (apsnd (apsnd (presimp_prop ctxt presimp_consts)))
|
blanchet@44735
|
1593 |
|> preprocess_abstractions_in_terms trans_lambdas
|
blanchet@44735
|
1594 |
|>> chop (length conjs)
|
blanchet@44735
|
1595 |
|>> apfst (map (apsnd (apsnd freeze_term)))
|
blanchet@44735
|
1596 |
else
|
blanchet@44735
|
1597 |
((conjs, facts), [])
|
blanchet@45317
|
1598 |
val conjs = conjs |> make_conjecture thy format type_enc
|
blanchet@44734
|
1599 |
val (fact_names, facts) =
|
blanchet@44735
|
1600 |
facts
|
blanchet@44734
|
1601 |
|> map_filter (fn (name, (_, t)) =>
|
blanchet@44734
|
1602 |
make_fact ctxt format type_enc true (name, t)
|
blanchet@44734
|
1603 |
|> Option.map (pair name))
|
blanchet@44732
|
1604 |
|> ListPair.unzip
|
blanchet@44734
|
1605 |
val lambdas =
|
blanchet@44735
|
1606 |
lambdas |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
|
blanchet@44732
|
1607 |
val all_ts = concl_t :: hyp_ts @ fact_ts
|
blanchet@43444
|
1608 |
val subs = tfree_classes_of_terms all_ts
|
blanchet@43444
|
1609 |
val supers = tvar_classes_of_terms all_ts
|
blanchet@44030
|
1610 |
val tycons = type_constrs_of_terms thy all_ts
|
blanchet@44732
|
1611 |
val (supers, arity_clauses) =
|
blanchet@44493
|
1612 |
if level_of_type_enc type_enc = No_Types then ([], [])
|
blanchet@43444
|
1613 |
else make_arity_clauses thy tycons supers
|
blanchet@44732
|
1614 |
val class_rel_clauses = make_class_rel_clauses thy subs supers
|
blanchet@43444
|
1615 |
in
|
blanchet@45459
|
1616 |
(fact_names |> map single, union (op =) subs supers, conjs, facts @ lambdas,
|
blanchet@45459
|
1617 |
class_rel_clauses, arity_clauses)
|
blanchet@43444
|
1618 |
end
|
blanchet@43444
|
1619 |
|
nik@45350
|
1620 |
val type_guard = `(make_fixed_const NONE) type_guard_name
|
blanchet@43971
|
1621 |
|
blanchet@45255
|
1622 |
fun type_guard_iterm ctxt format type_enc T tm =
|
blanchet@45255
|
1623 |
IApp (IConst (type_guard, T --> @{typ bool}, [T])
|
blanchet@44730
|
1624 |
|> enforce_type_arg_policy_in_iterm ctxt format type_enc, tm)
|
blanchet@43444
|
1625 |
|
blanchet@44282
|
1626 |
fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
|
blanchet@44282
|
1627 |
| is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
|
blanchet@43841
|
1628 |
accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
|
blanchet@44558
|
1629 |
| is_var_positively_naked_in_term _ _ _ _ = true
|
blanchet@45262
|
1630 |
|
blanchet@45265
|
1631 |
fun should_guard_var_in_formula pos phi (SOME true) name =
|
blanchet@44282
|
1632 |
formula_fold pos (is_var_positively_naked_in_term name) phi false
|
blanchet@45265
|
1633 |
| should_guard_var_in_formula _ _ _ _ = true
|
blanchet@43705
|
1634 |
|
blanchet@45264
|
1635 |
fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false
|
blanchet@45264
|
1636 |
| should_generate_tag_bound_decl ctxt mono (Tags (_, level, Nonuniform)) _ T =
|
blanchet@45263
|
1637 |
should_encode_type ctxt mono level T
|
blanchet@45264
|
1638 |
| should_generate_tag_bound_decl _ _ _ _ _ = false
|
blanchet@45263
|
1639 |
|
nik@44536
|
1640 |
fun mk_aterm format type_enc name T_args args =
|
nik@44536
|
1641 |
ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
|
blanchet@43835
|
1642 |
|
blanchet@45258
|
1643 |
fun tag_with_type ctxt format mono type_enc pos T tm =
|
blanchet@44730
|
1644 |
IConst (type_tag, T --> T, [T])
|
blanchet@44730
|
1645 |
|> enforce_type_arg_policy_in_iterm ctxt format type_enc
|
blanchet@45258
|
1646 |
|> ho_term_from_iterm ctxt format mono type_enc (Top_Level pos)
|
blanchet@44558
|
1647 |
|> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
|
blanchet@44558
|
1648 |
| _ => raise Fail "unexpected lambda-abstraction")
|
blanchet@45258
|
1649 |
and ho_term_from_iterm ctxt format mono type_enc =
|
blanchet@43444
|
1650 |
let
|
blanchet@43803
|
1651 |
fun aux site u =
|
blanchet@43803
|
1652 |
let
|
blanchet@44730
|
1653 |
val (head, args) = strip_iterm_comb u
|
nik@44536
|
1654 |
val pos =
|
nik@44536
|
1655 |
case site of
|
nik@44536
|
1656 |
Top_Level pos => pos
|
nik@44536
|
1657 |
| Eq_Arg pos => pos
|
nik@44536
|
1658 |
| Elsewhere => NONE
|
nik@44536
|
1659 |
val t =
|
blanchet@43803
|
1660 |
case head of
|
blanchet@44730
|
1661 |
IConst (name as (s, _), _, T_args) =>
|
nik@44536
|
1662 |
let
|
nik@44536
|
1663 |
val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
|
nik@44536
|
1664 |
in
|
nik@44536
|
1665 |
mk_aterm format type_enc name T_args (map (aux arg_site) args)
|
nik@44536
|
1666 |
end
|
blanchet@44730
|
1667 |
| IVar (name, _) =>
|
blanchet@44730
|
1668 |
mk_aterm format type_enc name [] (map (aux Elsewhere) args)
|
blanchet@44730
|
1669 |
| IAbs ((name, T), tm) =>
|
blanchet@44730
|
1670 |
AAbs ((name, ho_type_from_typ format type_enc true 0 T),
|
blanchet@44730
|
1671 |
aux Elsewhere tm)
|
blanchet@44730
|
1672 |
| IApp _ => raise Fail "impossible \"IApp\""
|
blanchet@44730
|
1673 |
val T = ityp_of u
|
blanchet@43803
|
1674 |
in
|
blanchet@45258
|
1675 |
t |> (if should_tag_with_type ctxt mono type_enc site u T then
|
blanchet@45258
|
1676 |
tag_with_type ctxt format mono type_enc pos T
|
blanchet@43803
|
1677 |
else
|
blanchet@43803
|
1678 |
I)
|
blanchet@43803
|
1679 |
end
|
blanchet@43803
|
1680 |
in aux end
|
blanchet@45258
|
1681 |
and formula_from_iformula ctxt format mono type_enc should_guard_var =
|
blanchet@43700
|
1682 |
let
|
blanchet@45258
|
1683 |
val do_term = ho_term_from_iterm ctxt format mono type_enc o Top_Level
|
blanchet@43444
|
1684 |
val do_bound_type =
|
blanchet@44493
|
1685 |
case type_enc of
|
blanchet@45458
|
1686 |
Simple_Types (_, _, level) => fused_type ctxt mono level 0
|
nik@44536
|
1687 |
#> ho_type_from_typ format type_enc false 0 #> SOME
|
blanchet@43552
|
1688 |
| _ => K NONE
|
blanchet@43747
|
1689 |
fun do_out_of_bound_type pos phi universal (name, T) =
|
blanchet@45258
|
1690 |
if should_guard_type ctxt mono type_enc
|
blanchet@45258
|
1691 |
(fn () => should_guard_var pos phi universal name) T then
|
blanchet@44730
|
1692 |
IVar (name, T)
|
blanchet@45255
|
1693 |
|> type_guard_iterm ctxt format type_enc T
|
blanchet@44232
|
1694 |
|> do_term pos |> AAtom |> SOME
|
blanchet@45264
|
1695 |
else if should_generate_tag_bound_decl ctxt mono type_enc universal T then
|
blanchet@45264
|
1696 |
let
|
blanchet@45264
|
1697 |
val var = ATerm (name, [])
|
blanchet@45360
|
1698 |
val tagged_var = var |> tag_with_type ctxt format mono type_enc pos T
|
blanchet@45264
|
1699 |
in SOME (AAtom (ATerm (`I tptp_equal, [tagged_var, var]))) end
|
blanchet@43444
|
1700 |
else
|
blanchet@43444
|
1701 |
NONE
|
blanchet@43747
|
1702 |
fun do_formula pos (AQuant (q, xs, phi)) =
|
blanchet@43747
|
1703 |
let
|
blanchet@43747
|
1704 |
val phi = phi |> do_formula pos
|
blanchet@43747
|
1705 |
val universal = Option.map (q = AExists ? not) pos
|
blanchet@43747
|
1706 |
in
|
blanchet@43705
|
1707 |
AQuant (q, xs |> map (apsnd (fn NONE => NONE
|
blanchet@43705
|
1708 |
| SOME T => do_bound_type T)),
|
blanchet@43705
|
1709 |
(if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
|
blanchet@43705
|
1710 |
(map_filter
|
blanchet@43705
|
1711 |
(fn (_, NONE) => NONE
|
blanchet@43705
|
1712 |
| (s, SOME T) =>
|
blanchet@43747
|
1713 |
do_out_of_bound_type pos phi universal (s, T))
|
blanchet@43747
|
1714 |
xs)
|
blanchet@43705
|
1715 |
phi)
|
blanchet@43705
|
1716 |
end
|
blanchet@43747
|
1717 |
| do_formula pos (AConn conn) = aconn_map pos do_formula conn
|
blanchet@44232
|
1718 |
| do_formula pos (AAtom tm) = AAtom (do_term pos tm)
|
blanchet@44364
|
1719 |
in do_formula end
|
blanchet@43444
|
1720 |
|
blanchet@43444
|
1721 |
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
|
blanchet@43444
|
1722 |
of monomorphization). The TPTP explicitly forbids name clashes, and some of
|
blanchet@43444
|
1723 |
the remote provers might care. *)
|
blanchet@45258
|
1724 |
fun formula_line_for_fact ctxt format prefix encode freshen pos mono type_enc
|
blanchet@45258
|
1725 |
(j, {name, locality, kind, iformula, atomic_types}) =
|
blanchet@44735
|
1726 |
(prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
|
blanchet@44730
|
1727 |
iformula
|
blanchet@44730
|
1728 |
|> close_iformula_universally
|
blanchet@45258
|
1729 |
|> formula_from_iformula ctxt format mono type_enc
|
blanchet@45258
|
1730 |
should_guard_var_in_formula
|
blanchet@44730
|
1731 |
(if pos then SOME true else NONE)
|
blanchet@44493
|
1732 |
|> bound_tvars type_enc atomic_types
|
blanchet@45457
|
1733 |
|> close_formula_universally type_enc,
|
blanchet@44364
|
1734 |
NONE,
|
blanchet@44364
|
1735 |
case locality of
|
blanchet@44559
|
1736 |
Intro => isabelle_info introN
|
blanchet@44559
|
1737 |
| Elim => isabelle_info elimN
|
blanchet@44559
|
1738 |
| Simp => isabelle_info simpN
|
blanchet@44364
|
1739 |
| _ => NONE)
|
blanchet@44364
|
1740 |
|> Formula
|
blanchet@43444
|
1741 |
|
blanchet@45457
|
1742 |
fun formula_line_for_class_rel_clause type_enc
|
blanchet@45457
|
1743 |
({name, subclass, superclass, ...} : class_rel_clause) =
|
blanchet@45480
|
1744 |
let val ty_arg = ATerm (tvar_a_name, []) in
|
blanchet@43448
|
1745 |
Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@45480
|
1746 |
AConn (AImplies,
|
blanchet@45483
|
1747 |
[type_class_formula type_enc subclass ty_arg,
|
blanchet@45483
|
1748 |
type_class_formula type_enc superclass ty_arg])
|
blanchet@45457
|
1749 |
|> close_formula_universally type_enc, isabelle_info introN, NONE)
|
blanchet@43444
|
1750 |
end
|
blanchet@43444
|
1751 |
|
blanchet@45483
|
1752 |
fun formula_from_arity_atom type_enc (class, t, args) =
|
blanchet@45483
|
1753 |
ATerm (t, map (fn arg => ATerm (arg, [])) args)
|
blanchet@45483
|
1754 |
|> type_class_formula type_enc class
|
blanchet@43444
|
1755 |
|
blanchet@45457
|
1756 |
fun formula_line_for_arity_clause type_enc
|
blanchet@45483
|
1757 |
({name, prem_atoms, concl_atom, ...} : arity_clause) =
|
blanchet@44366
|
1758 |
Formula (arity_clause_prefix ^ name, Axiom,
|
blanchet@45483
|
1759 |
mk_ahorn (map (formula_from_arity_atom type_enc) prem_atoms)
|
blanchet@45483
|
1760 |
(formula_from_arity_atom type_enc concl_atom)
|
blanchet@45457
|
1761 |
|> close_formula_universally type_enc, isabelle_info introN, NONE)
|
blanchet@43444
|
1762 |
|
blanchet@45258
|
1763 |
fun formula_line_for_conjecture ctxt format mono type_enc
|
blanchet@44730
|
1764 |
({name, kind, iformula, atomic_types, ...} : translated_formula) =
|
blanchet@43448
|
1765 |
Formula (conjecture_prefix ^ name, kind,
|
blanchet@45258
|
1766 |
formula_from_iformula ctxt format mono type_enc
|
blanchet@45258
|
1767 |
should_guard_var_in_formula (SOME false)
|
blanchet@44730
|
1768 |
(close_iformula_universally iformula)
|
blanchet@44493
|
1769 |
|> bound_tvars type_enc atomic_types
|
blanchet@45457
|
1770 |
|> close_formula_universally type_enc, NONE, NONE)
|
blanchet@43444
|
1771 |
|
blanchet@45483
|
1772 |
fun formula_line_for_free_type j phi =
|
blanchet@45483
|
1773 |
Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis, phi, NONE, NONE)
|
blanchet@44493
|
1774 |
fun formula_lines_for_free_types type_enc facts =
|
blanchet@43444
|
1775 |
let
|
blanchet@45483
|
1776 |
val phis =
|
blanchet@45483
|
1777 |
fold (union (op =)) (map #atomic_types facts) []
|
blanchet@45483
|
1778 |
|> formulas_for_types type_enc add_sorts_on_tfree
|
blanchet@45483
|
1779 |
in map2 formula_line_for_free_type (0 upto length phis - 1) phis end
|
blanchet@43444
|
1780 |
|
blanchet@43444
|
1781 |
(** Symbol declarations **)
|
blanchet@43415
|
1782 |
|
blanchet@45459
|
1783 |
fun decl_line_for_class s =
|
blanchet@45459
|
1784 |
let val name as (s, _) = `make_type_class s in
|
blanchet@45480
|
1785 |
Decl (sym_decl_prefix ^ s, name,
|
blanchet@45480
|
1786 |
if exploit_tff1_dummy_type_vars then
|
blanchet@45480
|
1787 |
AFun (atype_of_types, bool_atype)
|
blanchet@45480
|
1788 |
else
|
blanchet@45480
|
1789 |
ATyAbs ([tvar_a_name], AFun (a_itself_atype, bool_atype)))
|
blanchet@45459
|
1790 |
end
|
blanchet@45459
|
1791 |
|
blanchet@45459
|
1792 |
fun decl_lines_for_classes type_enc classes =
|
blanchet@45459
|
1793 |
case type_enc of
|
blanchet@45459
|
1794 |
Simple_Types (_, Polymorphic, _) => map decl_line_for_class classes
|
blanchet@45459
|
1795 |
| _ => []
|
blanchet@45459
|
1796 |
|
blanchet@44855
|
1797 |
fun sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
|
blanchet@44855
|
1798 |
(conjs, facts) =
|
blanchet@43445
|
1799 |
let
|
blanchet@44837
|
1800 |
fun add_iterm_syms in_conj tm =
|
blanchet@44730
|
1801 |
let val (head, args) = strip_iterm_comb tm in
|
blanchet@43445
|
1802 |
(case head of
|
blanchet@44730
|
1803 |
IConst ((s, s'), T, T_args) =>
|
blanchet@45458
|
1804 |
let
|
blanchet@45458
|
1805 |
val pred_sym = is_pred_sym repaired_sym_tab s
|
blanchet@45458
|
1806 |
val decl_sym =
|
blanchet@45458
|
1807 |
(case type_enc of
|
blanchet@45458
|
1808 |
Guards _ => not pred_sym
|
blanchet@45458
|
1809 |
| _ => true) andalso
|
blanchet@45458
|
1810 |
is_tptp_user_symbol s
|
blanchet@45458
|
1811 |
in
|
blanchet@45458
|
1812 |
if decl_sym then
|
blanchet@43447
|
1813 |
Symtab.map_default (s, [])
|
blanchet@43755
|
1814 |
(insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
|
blanchet@43755
|
1815 |
in_conj))
|
blanchet@43445
|
1816 |
else
|
blanchet@43445
|
1817 |
I
|
blanchet@43445
|
1818 |
end
|
blanchet@44837
|
1819 |
| IAbs (_, tm) => add_iterm_syms in_conj tm
|
blanchet@43445
|
1820 |
| _ => I)
|
blanchet@44837
|
1821 |
#> fold (add_iterm_syms in_conj) args
|
blanchet@43445
|
1822 |
end
|
blanchet@44837
|
1823 |
fun add_fact_syms in_conj =
|
blanchet@45356
|
1824 |
K (add_iterm_syms in_conj) |> formula_fold NONE |> fact_lift
|
blanchet@44837
|
1825 |
fun add_formula_var_types (AQuant (_, xs, phi)) =
|
blanchet@44837
|
1826 |
fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs
|
blanchet@44837
|
1827 |
#> add_formula_var_types phi
|
blanchet@44837
|
1828 |
| add_formula_var_types (AConn (_, phis)) =
|
blanchet@44837
|
1829 |
fold add_formula_var_types phis
|
blanchet@44837
|
1830 |
| add_formula_var_types _ = I
|
blanchet@44837
|
1831 |
fun var_types () =
|
blanchet@44837
|
1832 |
if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a]
|
blanchet@44837
|
1833 |
else fold (fact_lift add_formula_var_types) (conjs @ facts) []
|
blanchet@44837
|
1834 |
fun add_undefined_const T =
|
blanchet@44855
|
1835 |
let
|
blanchet@44855
|
1836 |
val (s, s') =
|
blanchet@45480
|
1837 |
`(make_fixed_const NONE) @{const_name undefined}
|
blanchet@44872
|
1838 |
|> (case type_arg_policy type_enc @{const_name undefined} of
|
blanchet@44872
|
1839 |
Mangled_Type_Args _ => mangled_const_name format type_enc [T]
|
blanchet@44872
|
1840 |
| _ => I)
|
blanchet@44855
|
1841 |
in
|
blanchet@44855
|
1842 |
Symtab.map_default (s, [])
|
blanchet@44855
|
1843 |
(insert_type ctxt #3 (s', [T], T, false, 0, false))
|
blanchet@44855
|
1844 |
end
|
blanchet@45480
|
1845 |
fun add_TYPE_const () =
|
blanchet@45480
|
1846 |
let val (s, s') = TYPE_name in
|
blanchet@45480
|
1847 |
Symtab.map_default (s, [])
|
blanchet@45480
|
1848 |
(insert_type ctxt #3
|
blanchet@45480
|
1849 |
(s', [tvar_a], @{typ "'a itself"}, false, 0, false))
|
blanchet@45480
|
1850 |
end
|
blanchet@43568
|
1851 |
in
|
blanchet@43568
|
1852 |
Symtab.empty
|
blanchet@44493
|
1853 |
|> is_type_enc_fairly_sound type_enc
|
blanchet@44837
|
1854 |
? (fold (add_fact_syms true) conjs
|
blanchet@44837
|
1855 |
#> fold (add_fact_syms false) facts
|
blanchet@44856
|
1856 |
#> (case type_enc of
|
blanchet@45480
|
1857 |
Simple_Types (_, poly, _) =>
|
blanchet@45480
|
1858 |
if poly = Polymorphic then add_TYPE_const () else I
|
blanchet@44856
|
1859 |
| _ => fold add_undefined_const (var_types ())))
|
blanchet@43568
|
1860 |
end
|
blanchet@43445
|
1861 |
|
blanchet@45258
|
1862 |
(* We add "bool" in case the helper "True_or_False" is included later. *)
|
blanchet@45258
|
1863 |
val default_mono =
|
blanchet@45258
|
1864 |
{maybe_finite_Ts = [@{typ bool}],
|
blanchet@45258
|
1865 |
surely_finite_Ts = [@{typ bool}],
|
blanchet@45258
|
1866 |
maybe_infinite_Ts = known_infinite_types,
|
blanchet@45258
|
1867 |
surely_infinite_Ts = known_infinite_types,
|
blanchet@45258
|
1868 |
maybe_nonmono_Ts = [@{typ bool}]}
|
blanchet@45258
|
1869 |
|
blanchet@43555
|
1870 |
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
|
blanchet@43555
|
1871 |
out with monotonicity" paper presented at CADE 2011. *)
|
blanchet@45258
|
1872 |
fun add_iterm_mononotonicity_info _ _ (SOME false) _ mono = mono
|
blanchet@45258
|
1873 |
| add_iterm_mononotonicity_info ctxt level _
|
blanchet@45258
|
1874 |
(IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2))
|
blanchet@45258
|
1875 |
(mono as {maybe_finite_Ts, surely_finite_Ts, maybe_infinite_Ts,
|
blanchet@45258
|
1876 |
surely_infinite_Ts, maybe_nonmono_Ts}) =
|
blanchet@45262
|
1877 |
if is_tptp_equal s andalso exists is_maybe_universal_var [tm1, tm2] then
|
blanchet@45258
|
1878 |
case level of
|
blanchet@45256
|
1879 |
Noninf_Nonmono_Types soundness =>
|
blanchet@45258
|
1880 |
if exists (type_instance ctxt T) surely_infinite_Ts orelse
|
blanchet@45258
|
1881 |
member (type_aconv ctxt) maybe_finite_Ts T then
|
blanchet@45258
|
1882 |
mono
|
blanchet@45355
|
1883 |
else if is_type_kind_of_surely_infinite ctxt soundness
|
blanchet@45355
|
1884 |
surely_infinite_Ts T then
|
blanchet@45258
|
1885 |
{maybe_finite_Ts = maybe_finite_Ts,
|
blanchet@45258
|
1886 |
surely_finite_Ts = surely_finite_Ts,
|
blanchet@45258
|
1887 |
maybe_infinite_Ts = maybe_infinite_Ts,
|
blanchet@45258
|
1888 |
surely_infinite_Ts = surely_infinite_Ts |> insert_type ctxt I T,
|
blanchet@45258
|
1889 |
maybe_nonmono_Ts = maybe_nonmono_Ts}
|
blanchet@45258
|
1890 |
else
|
blanchet@45258
|
1891 |
{maybe_finite_Ts = maybe_finite_Ts |> insert (type_aconv ctxt) T,
|
blanchet@45258
|
1892 |
surely_finite_Ts = surely_finite_Ts,
|
blanchet@45258
|
1893 |
maybe_infinite_Ts = maybe_infinite_Ts,
|
blanchet@45258
|
1894 |
surely_infinite_Ts = surely_infinite_Ts,
|
blanchet@45258
|
1895 |
maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
|
blanchet@45258
|
1896 |
| Fin_Nonmono_Types =>
|
blanchet@45258
|
1897 |
if exists (type_instance ctxt T) surely_finite_Ts orelse
|
blanchet@45258
|
1898 |
member (type_aconv ctxt) maybe_infinite_Ts T then
|
blanchet@45258
|
1899 |
mono
|
blanchet@45258
|
1900 |
else if is_type_surely_finite ctxt T then
|
blanchet@45258
|
1901 |
{maybe_finite_Ts = maybe_finite_Ts,
|
blanchet@45258
|
1902 |
surely_finite_Ts = surely_finite_Ts |> insert_type ctxt I T,
|
blanchet@45258
|
1903 |
maybe_infinite_Ts = maybe_infinite_Ts,
|
blanchet@45258
|
1904 |
surely_infinite_Ts = surely_infinite_Ts,
|
blanchet@45258
|
1905 |
maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
|
blanchet@45258
|
1906 |
else
|
blanchet@45258
|
1907 |
{maybe_finite_Ts = maybe_finite_Ts,
|
blanchet@45258
|
1908 |
surely_finite_Ts = surely_finite_Ts,
|
blanchet@45258
|
1909 |
maybe_infinite_Ts = maybe_infinite_Ts |> insert (type_aconv ctxt) T,
|
blanchet@45258
|
1910 |
surely_infinite_Ts = surely_infinite_Ts,
|
blanchet@45258
|
1911 |
maybe_nonmono_Ts = maybe_nonmono_Ts}
|
blanchet@45258
|
1912 |
| _ => mono
|
blanchet@45258
|
1913 |
else
|
blanchet@45258
|
1914 |
mono
|
blanchet@45258
|
1915 |
| add_iterm_mononotonicity_info _ _ _ _ mono = mono
|
blanchet@45258
|
1916 |
fun add_fact_mononotonicity_info ctxt level
|
blanchet@45258
|
1917 |
({kind, iformula, ...} : translated_formula) =
|
blanchet@43705
|
1918 |
formula_fold (SOME (kind <> Conjecture))
|
blanchet@45258
|
1919 |
(add_iterm_mononotonicity_info ctxt level) iformula
|
blanchet@45258
|
1920 |
fun mononotonicity_info_for_facts ctxt type_enc facts =
|
blanchet@44493
|
1921 |
let val level = level_of_type_enc type_enc in
|
blanchet@45258
|
1922 |
default_mono
|
blanchet@45258
|
1923 |
|> is_type_level_monotonicity_based level
|
blanchet@45258
|
1924 |
? fold (add_fact_mononotonicity_info ctxt level) facts
|
blanchet@43700
|
1925 |
end
|
blanchet@43547
|
1926 |
|
blanchet@45356
|
1927 |
fun add_iformula_monotonic_types ctxt mono type_enc =
|
blanchet@45356
|
1928 |
let
|
blanchet@45356
|
1929 |
val level = level_of_type_enc type_enc
|
blanchet@45356
|
1930 |
val should_encode = should_encode_type ctxt mono level
|
blanchet@45359
|
1931 |
fun add_type T = not (should_encode T) ? insert_type ctxt I T
|
blanchet@45361
|
1932 |
fun add_args (IApp (tm1, tm2)) = add_args tm1 #> add_term tm2
|
blanchet@45361
|
1933 |
| add_args _ = I
|
blanchet@45361
|
1934 |
and add_term tm = add_type (ityp_of tm) #> add_args tm
|
blanchet@45356
|
1935 |
in formula_fold NONE (K add_term) end
|
blanchet@45356
|
1936 |
fun add_fact_monotonic_types ctxt mono type_enc =
|
blanchet@45356
|
1937 |
add_iformula_monotonic_types ctxt mono type_enc |> fact_lift
|
blanchet@45356
|
1938 |
fun monotonic_types_for_facts ctxt mono type_enc facts =
|
blanchet@45356
|
1939 |
[] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso
|
blanchet@45356
|
1940 |
is_type_level_monotonicity_based (level_of_type_enc type_enc))
|
blanchet@45356
|
1941 |
? fold (add_fact_monotonic_types ctxt mono type_enc) facts
|
blanchet@45356
|
1942 |
|
blanchet@45258
|
1943 |
fun formula_line_for_guards_mono_type ctxt format mono type_enc T =
|
blanchet@45255
|
1944 |
Formula (guards_sym_formula_prefix ^
|
blanchet@45255
|
1945 |
ascii_of (mangled_type format type_enc T),
|
blanchet@45255
|
1946 |
Axiom,
|
blanchet@45255
|
1947 |
IConst (`make_bound_var "X", T, [])
|
blanchet@45255
|
1948 |
|> type_guard_iterm ctxt format type_enc T
|
blanchet@45255
|
1949 |
|> AAtom
|
blanchet@45258
|
1950 |
|> formula_from_iformula ctxt format mono type_enc
|
blanchet@45255
|
1951 |
(K (K (K (K true)))) (SOME true)
|
blanchet@45255
|
1952 |
|> bound_tvars type_enc (atyps_of T)
|
blanchet@45457
|
1953 |
|> close_formula_universally type_enc,
|
blanchet@45255
|
1954 |
isabelle_info introN, NONE)
|
blanchet@45255
|
1955 |
|
blanchet@45258
|
1956 |
fun formula_line_for_tags_mono_type ctxt format mono type_enc T =
|
blanchet@45255
|
1957 |
let val x_var = ATerm (`make_bound_var "X", []) in
|
blanchet@45255
|
1958 |
Formula (tags_sym_formula_prefix ^
|
blanchet@45255
|
1959 |
ascii_of (mangled_type format type_enc T),
|
blanchet@45255
|
1960 |
Axiom,
|
blanchet@45255
|
1961 |
eq_formula type_enc (atyps_of T) false
|
blanchet@45258
|
1962 |
(tag_with_type ctxt format mono type_enc NONE T x_var)
|
blanchet@45255
|
1963 |
x_var,
|
blanchet@45255
|
1964 |
isabelle_info simpN, NONE)
|
blanchet@45255
|
1965 |
end
|
blanchet@45255
|
1966 |
|
blanchet@45258
|
1967 |
fun problem_lines_for_mono_types ctxt format mono type_enc Ts =
|
blanchet@45255
|
1968 |
case type_enc of
|
blanchet@45255
|
1969 |
Simple_Types _ => []
|
blanchet@45255
|
1970 |
| Guards _ =>
|
blanchet@45258
|
1971 |
map (formula_line_for_guards_mono_type ctxt format mono type_enc) Ts
|
blanchet@45258
|
1972 |
| Tags _ => map (formula_line_for_tags_mono_type ctxt format mono type_enc) Ts
|
blanchet@45255
|
1973 |
|
blanchet@45258
|
1974 |
fun decl_line_for_sym ctxt format mono type_enc s
|
blanchet@43835
|
1975 |
(s', T_args, T, pred_sym, ary, _) =
|
blanchet@43835
|
1976 |
let
|
blanchet@45458
|
1977 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@45458
|
1978 |
val (T, T_args) =
|
blanchet@45458
|
1979 |
if null T_args then
|
blanchet@45458
|
1980 |
(T, [])
|
blanchet@45458
|
1981 |
else case strip_prefix_and_unascii const_prefix s of
|
blanchet@45458
|
1982 |
SOME s' =>
|
blanchet@45458
|
1983 |
let
|
blanchet@45458
|
1984 |
val s' = s' |> invert_const
|
blanchet@45458
|
1985 |
val T = s' |> robust_const_type thy
|
blanchet@45458
|
1986 |
in (T, robust_const_typargs thy (s', T)) end
|
blanchet@45458
|
1987 |
| NONE =>
|
blanchet@45458
|
1988 |
case strip_prefix_and_unascii fixed_var_prefix s of
|
blanchet@45458
|
1989 |
SOME s' =>
|
blanchet@45458
|
1990 |
if String.isPrefix polymorphic_free_prefix s' then (tvar_a, [tvar_a])
|
blanchet@45458
|
1991 |
else raise Fail "unexpected type arguments to free variable"
|
blanchet@45458
|
1992 |
| NONE => raise Fail "unexpected type arguments"
|
blanchet@43835
|
1993 |
in
|
blanchet@43839
|
1994 |
Decl (sym_decl_prefix ^ s, (s, s'),
|
blanchet@45458
|
1995 |
T |> fused_type ctxt mono (level_of_type_enc type_enc) ary
|
blanchet@45458
|
1996 |
|> ho_type_from_typ format type_enc pred_sym ary
|
blanchet@45458
|
1997 |
|> not (null T_args)
|
blanchet@45458
|
1998 |
? curry ATyAbs (map (tvar_name o fst o dest_TVar) T_args))
|
blanchet@43835
|
1999 |
end
|
blanchet@43450
|
2000 |
|
blanchet@45258
|
2001 |
fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s
|
blanchet@45258
|
2002 |
j (s', T_args, T, _, ary, in_conj) =
|
blanchet@43450
|
2003 |
let
|
blanchet@43580
|
2004 |
val (kind, maybe_negate) =
|
blanchet@43580
|
2005 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43580
|
2006 |
else (Axiom, I)
|
blanchet@43618
|
2007 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@44262
|
2008 |
val num_args = length arg_Ts
|
blanchet@43450
|
2009 |
val bound_names =
|
blanchet@44262
|
2010 |
1 upto num_args |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
2011 |
val bounds =
|
blanchet@44730
|
2012 |
bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
|
blanchet@44778
|
2013 |
val sym_needs_arg_types = exists (curry (op =) dummyT) T_args
|
blanchet@44264
|
2014 |
fun should_keep_arg_type T =
|
blanchet@45252
|
2015 |
sym_needs_arg_types andalso
|
blanchet@45258
|
2016 |
should_guard_type ctxt mono type_enc (K true) T
|
blanchet@43450
|
2017 |
val bound_Ts =
|
blanchet@44264
|
2018 |
arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
|
blanchet@43450
|
2019 |
in
|
blanchet@44860
|
2020 |
Formula (guards_sym_formula_prefix ^ s ^
|
blanchet@43580
|
2021 |
(if n > 1 then "_" ^ string_of_int j else ""), kind,
|
blanchet@44730
|
2022 |
IConst ((s, s'), T, T_args)
|
blanchet@44730
|
2023 |
|> fold (curry (IApp o swap)) bounds
|
blanchet@45255
|
2024 |
|> type_guard_iterm ctxt format type_enc res_T
|
blanchet@43804
|
2025 |
|> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
|
blanchet@45258
|
2026 |
|> formula_from_iformula ctxt format mono type_enc
|
blanchet@44730
|
2027 |
(K (K (K (K true)))) (SOME true)
|
blanchet@44493
|
2028 |
|> n > 1 ? bound_tvars type_enc (atyps_of T)
|
blanchet@45457
|
2029 |
|> close_formula_universally type_enc
|
blanchet@43580
|
2030 |
|> maybe_negate,
|
blanchet@44559
|
2031 |
isabelle_info introN, NONE)
|
blanchet@43450
|
2032 |
end
|
blanchet@43450
|
2033 |
|
blanchet@45264
|
2034 |
fun formula_lines_for_nonuniform_tags_sym_decl ctxt format conj_sym_kind mono
|
blanchet@45258
|
2035 |
type_enc n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
|
blanchet@43700
|
2036 |
let
|
blanchet@43700
|
2037 |
val ident_base =
|
blanchet@45255
|
2038 |
tags_sym_formula_prefix ^ s ^
|
blanchet@43966
|
2039 |
(if n > 1 then "_" ^ string_of_int j else "")
|
blanchet@43721
|
2040 |
val (kind, maybe_negate) =
|
blanchet@43721
|
2041 |
if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
|
blanchet@43721
|
2042 |
else (Axiom, I)
|
blanchet@43700
|
2043 |
val (arg_Ts, res_T) = chop_fun ary T
|
blanchet@43700
|
2044 |
val bound_names =
|
blanchet@43700
|
2045 |
1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
|
blanchet@43700
|
2046 |
val bounds = bound_names |> map (fn name => ATerm (name, []))
|
nik@44536
|
2047 |
val cst = mk_aterm format type_enc (s, s') T_args
|
blanchet@45255
|
2048 |
val eq = maybe_negate oo eq_formula type_enc (atyps_of T) pred_sym
|
blanchet@45257
|
2049 |
val should_encode =
|
blanchet@45258
|
2050 |
should_encode_type ctxt mono (level_of_type_enc type_enc)
|
blanchet@45258
|
2051 |
val tag_with = tag_with_type ctxt format mono type_enc NONE
|
blanchet@43700
|
2052 |
val add_formula_for_res =
|
blanchet@43700
|
2053 |
if should_encode res_T then
|
blanchet@43721
|
2054 |
cons (Formula (ident_base ^ "_res", kind,
|
blanchet@45255
|
2055 |
eq (tag_with res_T (cst bounds)) (cst bounds),
|
blanchet@44559
|
2056 |
isabelle_info simpN, NONE))
|
blanchet@43700
|
2057 |
else
|
blanchet@43700
|
2058 |
I
|
blanchet@43700
|
2059 |
fun add_formula_for_arg k =
|
blanchet@43700
|
2060 |
let val arg_T = nth arg_Ts k in
|
blanchet@43700
|
2061 |
if should_encode arg_T then
|
blanchet@43700
|
2062 |
case chop k bounds of
|
blanchet@43700
|
2063 |
(bounds1, bound :: bounds2) =>
|
blanchet@43721
|
2064 |
cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
|
blanchet@45255
|
2065 |
eq (cst (bounds1 @ tag_with arg_T bound :: bounds2))
|
blanchet@45255
|
2066 |
(cst bounds),
|
blanchet@44559
|
2067 |
isabelle_info simpN, NONE))
|
blanchet@43700
|
2068 |
| _ => raise Fail "expected nonempty tail"
|
blanchet@43700
|
2069 |
else
|
blanchet@43700
|
2070 |
I
|
blanchet@43700
|
2071 |
end
|
blanchet@43700
|
2072 |
in
|
blanchet@43705
|
2073 |
[] |> not pred_sym ? add_formula_for_res
|
blanchet@45351
|
2074 |
|> Config.get ctxt type_tag_arguments
|
blanchet@45351
|
2075 |
? fold add_formula_for_arg (ary - 1 downto 0)
|
blanchet@43700
|
2076 |
end
|
blanchet@43700
|
2077 |
|
blanchet@43707
|
2078 |
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
|
blanchet@43707
|
2079 |
|
blanchet@45258
|
2080 |
fun problem_lines_for_sym_decls ctxt format conj_sym_kind mono type_enc
|
blanchet@45255
|
2081 |
(s, decls) =
|
blanchet@44493
|
2082 |
case type_enc of
|
blanchet@43839
|
2083 |
Simple_Types _ =>
|
blanchet@45258
|
2084 |
decls |> map (decl_line_for_sym ctxt format mono type_enc s)
|
blanchet@45257
|
2085 |
| Guards (_, level, _) =>
|
blanchet@43839
|
2086 |
let
|
blanchet@43839
|
2087 |
val decls =
|
blanchet@43839
|
2088 |
case decls of
|
blanchet@43839
|
2089 |
decl :: (decls' as _ :: _) =>
|
blanchet@43839
|
2090 |
let val T = result_type_of_decl decl in
|
blanchet@45258
|
2091 |
if forall (type_generalization ctxt T o result_type_of_decl)
|
blanchet@45258
|
2092 |
decls' then
|
blanchet@43839
|
2093 |
[decl]
|
blanchet@43839
|
2094 |
else
|
blanchet@43839
|
2095 |
decls
|
blanchet@43839
|
2096 |
end
|
blanchet@43839
|
2097 |
| _ => decls
|
blanchet@43839
|
2098 |
val n = length decls
|
blanchet@43839
|
2099 |
val decls =
|
blanchet@45258
|
2100 |
decls |> filter (should_encode_type ctxt mono level
|
blanchet@44264
|
2101 |
o result_type_of_decl)
|
blanchet@43839
|
2102 |
in
|
blanchet@43839
|
2103 |
(0 upto length decls - 1, decls)
|
blanchet@45258
|
2104 |
|-> map2 (formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono
|
blanchet@45258
|
2105 |
type_enc n s)
|
blanchet@43839
|
2106 |
end
|
blanchet@45261
|
2107 |
| Tags (_, _, uniformity) =>
|
blanchet@45261
|
2108 |
(case uniformity of
|
blanchet@45261
|
2109 |
Uniform => []
|
blanchet@45261
|
2110 |
| Nonuniform =>
|
blanchet@43839
|
2111 |
let val n = length decls in
|
blanchet@43839
|
2112 |
(0 upto n - 1 ~~ decls)
|
blanchet@45264
|
2113 |
|> maps (formula_lines_for_nonuniform_tags_sym_decl ctxt format
|
blanchet@45258
|
2114 |
conj_sym_kind mono type_enc n s)
|
blanchet@43839
|
2115 |
end)
|
blanchet@43450
|
2116 |
|
blanchet@45258
|
2117 |
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono type_enc
|
blanchet@45356
|
2118 |
mono_Ts sym_decl_tab =
|
blanchet@45255
|
2119 |
let
|
blanchet@45255
|
2120 |
val syms = sym_decl_tab |> Symtab.dest |> sort_wrt fst
|
blanchet@45255
|
2121 |
val mono_lines =
|
blanchet@45258
|
2122 |
problem_lines_for_mono_types ctxt format mono type_enc mono_Ts
|
blanchet@45255
|
2123 |
val decl_lines =
|
blanchet@45255
|
2124 |
fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
|
blanchet@45258
|
2125 |
mono type_enc)
|
blanchet@45255
|
2126 |
syms []
|
blanchet@45255
|
2127 |
in mono_lines @ decl_lines end
|
blanchet@43414
|
2128 |
|
blanchet@45351
|
2129 |
fun needs_type_tag_idempotence ctxt (Tags (poly, level, uniformity)) =
|
blanchet@45351
|
2130 |
Config.get ctxt type_tag_idempotence andalso
|
blanchet@44026
|
2131 |
poly <> Mangled_Monomorphic andalso
|
blanchet@45261
|
2132 |
((level = All_Types andalso uniformity = Nonuniform) orelse
|
blanchet@45256
|
2133 |
is_type_level_monotonicity_based level)
|
blanchet@45351
|
2134 |
| needs_type_tag_idempotence _ _ = false
|
blanchet@43702
|
2135 |
|
blanchet@43780
|
2136 |
fun offset_of_heading_in_problem _ [] j = j
|
blanchet@43780
|
2137 |
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
|
blanchet@43780
|
2138 |
if heading = needle then j
|
blanchet@43780
|
2139 |
else offset_of_heading_in_problem needle problem (j + length lines)
|
blanchet@43780
|
2140 |
|
blanchet@43839
|
2141 |
val implicit_declsN = "Should-be-implicit typings"
|
blanchet@43839
|
2142 |
val explicit_declsN = "Explicit typings"
|
blanchet@41405
|
2143 |
val factsN = "Relevant facts"
|
blanchet@41405
|
2144 |
val class_relsN = "Class relationships"
|
blanchet@43414
|
2145 |
val aritiesN = "Arities"
|
blanchet@41405
|
2146 |
val helpersN = "Helper facts"
|
blanchet@41405
|
2147 |
val conjsN = "Conjectures"
|
blanchet@41561
|
2148 |
val free_typesN = "Type variables"
|
blanchet@41405
|
2149 |
|
blanchet@44692
|
2150 |
val explicit_apply = NONE (* for experiments *)
|
blanchet@44100
|
2151 |
|
blanchet@45256
|
2152 |
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter
|
blanchet@45256
|
2153 |
lambda_trans readable_names preproc hyp_ts concl_t facts =
|
blanchet@38506
|
2154 |
let
|
blanchet@45275
|
2155 |
val type_enc = type_enc |> adjust_type_enc format
|
blanchet@44959
|
2156 |
val lambda_trans =
|
blanchet@44959
|
2157 |
if lambda_trans = smartN then
|
blanchet@44959
|
2158 |
if is_type_enc_higher_order type_enc then lambdasN else combinatorsN
|
blanchet@44959
|
2159 |
else if lambda_trans = lambdasN andalso
|
blanchet@44959
|
2160 |
not (is_type_enc_higher_order type_enc) then
|
blanchet@44959
|
2161 |
error ("Lambda translation method incompatible with first-order \
|
blanchet@44959
|
2162 |
\encoding.")
|
blanchet@44959
|
2163 |
else
|
blanchet@44959
|
2164 |
lambda_trans
|
blanchet@44959
|
2165 |
val trans_lambdas =
|
blanchet@44959
|
2166 |
if lambda_trans = no_lambdasN then
|
blanchet@44959
|
2167 |
rpair []
|
blanchet@44959
|
2168 |
else if lambda_trans = concealedN then
|
blanchet@44959
|
2169 |
lift_lambdas ctxt type_enc ##> K []
|
blanchet@44959
|
2170 |
else if lambda_trans = liftingN then
|
blanchet@44959
|
2171 |
lift_lambdas ctxt type_enc
|
blanchet@44959
|
2172 |
else if lambda_trans = combinatorsN then
|
blanchet@44959
|
2173 |
map (introduce_combinators ctxt) #> rpair []
|
blanchet@44959
|
2174 |
else if lambda_trans = hybridN then
|
blanchet@44959
|
2175 |
lift_lambdas ctxt type_enc
|
blanchet@44959
|
2176 |
##> maps (fn t => [t, introduce_combinators ctxt
|
blanchet@44959
|
2177 |
(intentionalize_def t)])
|
blanchet@44959
|
2178 |
else if lambda_trans = lambdasN then
|
blanchet@44959
|
2179 |
map (Envir.eta_contract) #> rpair []
|
blanchet@44959
|
2180 |
else
|
blanchet@44959
|
2181 |
error ("Unknown lambda translation method: " ^
|
blanchet@44959
|
2182 |
quote lambda_trans ^ ".")
|
blanchet@45459
|
2183 |
val (fact_names, classes, conjs, facts, class_rel_clauses, arity_clauses) =
|
blanchet@44727
|
2184 |
translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
|
blanchet@44692
|
2185 |
hyp_ts concl_t facts
|
blanchet@45351
|
2186 |
val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
|
blanchet@45258
|
2187 |
val mono = conjs @ facts |> mononotonicity_info_for_facts ctxt type_enc
|
blanchet@44493
|
2188 |
val repair = repair_fact ctxt format type_enc sym_tab
|
blanchet@43552
|
2189 |
val (conjs, facts) = (conjs, facts) |> pairself (map repair)
|
blanchet@43905
|
2190 |
val repaired_sym_tab =
|
blanchet@45351
|
2191 |
conjs @ facts |> sym_table_for_facts ctxt (SOME false)
|
blanchet@43444
|
2192 |
val helpers =
|
blanchet@44729
|
2193 |
repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
|
blanchet@44729
|
2194 |
|> map repair
|
blanchet@45356
|
2195 |
val mono_Ts =
|
blanchet@45356
|
2196 |
helpers @ conjs @ facts
|
blanchet@45356
|
2197 |
|> monotonic_types_for_facts ctxt mono type_enc
|
blanchet@45459
|
2198 |
val class_decl_lines = decl_lines_for_classes type_enc classes
|
blanchet@43550
|
2199 |
val sym_decl_lines =
|
blanchet@43596
|
2200 |
(conjs, helpers @ facts)
|
blanchet@44855
|
2201 |
|> sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
|
blanchet@45258
|
2202 |
|> problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono
|
blanchet@45356
|
2203 |
type_enc mono_Ts
|
blanchet@43750
|
2204 |
val helper_lines =
|
blanchet@43797
|
2205 |
0 upto length helpers - 1 ~~ helpers
|
blanchet@45258
|
2206 |
|> map (formula_line_for_fact ctxt format helper_prefix I false true mono
|
blanchet@45258
|
2207 |
type_enc)
|
blanchet@45351
|
2208 |
|> (if needs_type_tag_idempotence ctxt type_enc then
|
blanchet@45263
|
2209 |
cons (type_tag_idempotence_fact type_enc)
|
blanchet@44000
|
2210 |
else
|
blanchet@44000
|
2211 |
I)
|
blanchet@43393
|
2212 |
(* Reordering these might confuse the proof reconstruction code or the SPASS
|
blanchet@43880
|
2213 |
FLOTTER hack. *)
|
blanchet@38506
|
2214 |
val problem =
|
blanchet@45459
|
2215 |
[(explicit_declsN, class_decl_lines @ sym_decl_lines),
|
blanchet@43797
|
2216 |
(factsN,
|
blanchet@44372
|
2217 |
map (formula_line_for_fact ctxt format fact_prefix ascii_of
|
blanchet@45459
|
2218 |
(not exporter) (not exporter) mono type_enc)
|
blanchet@43797
|
2219 |
(0 upto length facts - 1 ~~ facts)),
|
blanchet@45457
|
2220 |
(class_relsN,
|
blanchet@45457
|
2221 |
map (formula_line_for_class_rel_clause type_enc) class_rel_clauses),
|
blanchet@45457
|
2222 |
(aritiesN, map (formula_line_for_arity_clause type_enc) arity_clauses),
|
blanchet@43750
|
2223 |
(helpersN, helper_lines),
|
blanchet@43803
|
2224 |
(conjsN,
|
blanchet@45258
|
2225 |
map (formula_line_for_conjecture ctxt format mono type_enc) conjs),
|
blanchet@44493
|
2226 |
(free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
|
blanchet@43414
|
2227 |
val problem =
|
blanchet@43432
|
2228 |
problem
|
blanchet@43933
|
2229 |
|> (case format of
|
blanchet@43933
|
2230 |
CNF => ensure_cnf_problem
|
blanchet@43933
|
2231 |
| CNF_UEQ => filter_cnf_ueq_problem
|
blanchet@45453
|
2232 |
| FOF => I
|
blanchet@45453
|
2233 |
| TFF (_, TFF_Implicit) => I
|
blanchet@45453
|
2234 |
| _ => declare_undeclared_syms_in_atp_problem type_decl_prefix
|
blanchet@45453
|
2235 |
implicit_declsN)
|
blanchet@43933
|
2236 |
val (problem, pool) = problem |> nice_atp_problem readable_names
|
blanchet@43750
|
2237 |
val helpers_offset = offset_of_heading_in_problem helpersN problem 0
|
blanchet@43750
|
2238 |
val typed_helpers =
|
blanchet@43750
|
2239 |
map_filter (fn (j, {name, ...}) =>
|
blanchet@43750
|
2240 |
if String.isSuffix typed_helper_suffix name then SOME j
|
blanchet@43750
|
2241 |
else NONE)
|
blanchet@43750
|
2242 |
((helpers_offset + 1 upto helpers_offset + length helpers)
|
blanchet@43750
|
2243 |
~~ helpers)
|
blanchet@43649
|
2244 |
fun add_sym_arity (s, {min_ary, ...} : sym_info) =
|
blanchet@43620
|
2245 |
if min_ary > 0 then
|
blanchet@43620
|
2246 |
case strip_prefix_and_unascii const_prefix s of
|
blanchet@43620
|
2247 |
SOME s => Symtab.insert (op =) (s, min_ary)
|
blanchet@43620
|
2248 |
| NONE => I
|
blanchet@43620
|
2249 |
else
|
blanchet@43620
|
2250 |
I
|
blanchet@38506
|
2251 |
in
|
blanchet@38506
|
2252 |
(problem,
|
blanchet@38506
|
2253 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@43456
|
2254 |
offset_of_heading_in_problem conjsN problem 0,
|
blanchet@43412
|
2255 |
offset_of_heading_in_problem factsN problem 0,
|
blanchet@43620
|
2256 |
fact_names |> Vector.fromList,
|
blanchet@43750
|
2257 |
typed_helpers,
|
blanchet@43620
|
2258 |
Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
|
blanchet@38506
|
2259 |
end
|
blanchet@38506
|
2260 |
|
blanchet@41561
|
2261 |
(* FUDGE *)
|
blanchet@41561
|
2262 |
val conj_weight = 0.0
|
blanchet@42641
|
2263 |
val hyp_weight = 0.1
|
blanchet@42641
|
2264 |
val fact_min_weight = 0.2
|
blanchet@41561
|
2265 |
val fact_max_weight = 1.0
|
blanchet@43479
|
2266 |
val type_info_default_weight = 0.8
|
blanchet@41561
|
2267 |
|
blanchet@41561
|
2268 |
fun add_term_weights weight (ATerm (s, tms)) =
|
nik@44535
|
2269 |
is_tptp_user_symbol s ? Symtab.default (s, weight)
|
nik@44535
|
2270 |
#> fold (add_term_weights weight) tms
|
nik@44535
|
2271 |
| add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
|
blanchet@43448
|
2272 |
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
|
blanchet@43705
|
2273 |
formula_fold NONE (K (add_term_weights weight)) phi
|
blanchet@43399
|
2274 |
| add_problem_line_weights _ _ = I
|
blanchet@41561
|
2275 |
|
blanchet@41561
|
2276 |
fun add_conjectures_weights [] = I
|
blanchet@41561
|
2277 |
| add_conjectures_weights conjs =
|
blanchet@41561
|
2278 |
let val (hyps, conj) = split_last conjs in
|
blanchet@41561
|
2279 |
add_problem_line_weights conj_weight conj
|
blanchet@41561
|
2280 |
#> fold (add_problem_line_weights hyp_weight) hyps
|
blanchet@41561
|
2281 |
end
|
blanchet@41561
|
2282 |
|
blanchet@41561
|
2283 |
fun add_facts_weights facts =
|
blanchet@41561
|
2284 |
let
|
blanchet@41561
|
2285 |
val num_facts = length facts
|
blanchet@41561
|
2286 |
fun weight_of j =
|
blanchet@41561
|
2287 |
fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
|
blanchet@41561
|
2288 |
/ Real.fromInt num_facts
|
blanchet@41561
|
2289 |
in
|
blanchet@41561
|
2290 |
map weight_of (0 upto num_facts - 1) ~~ facts
|
blanchet@41561
|
2291 |
|> fold (uncurry add_problem_line_weights)
|
blanchet@41561
|
2292 |
end
|
blanchet@41561
|
2293 |
|
blanchet@41561
|
2294 |
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
|
blanchet@41561
|
2295 |
fun atp_problem_weights problem =
|
blanchet@43479
|
2296 |
let val get = these o AList.lookup (op =) problem in
|
blanchet@43479
|
2297 |
Symtab.empty
|
blanchet@43479
|
2298 |
|> add_conjectures_weights (get free_typesN @ get conjsN)
|
blanchet@43479
|
2299 |
|> add_facts_weights (get factsN)
|
blanchet@43479
|
2300 |
|> fold (fold (add_problem_line_weights type_info_default_weight) o get)
|
blanchet@43839
|
2301 |
[explicit_declsN, class_relsN, aritiesN]
|
blanchet@43479
|
2302 |
|> Symtab.dest
|
blanchet@43479
|
2303 |
|> sort (prod_ord Real.compare string_ord o pairself swap)
|
blanchet@43479
|
2304 |
end
|
blanchet@41561
|
2305 |
|
blanchet@38506
|
2306 |
end;
|