blanchet@40358
|
1 |
(* Title: HOL/Tools/Sledgehammer/sledgehammer_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@39734
|
6 |
Translation of HOL to FOL for Sledgehammer.
|
blanchet@38506
|
7 |
*)
|
blanchet@38506
|
8 |
|
blanchet@40249
|
9 |
signature SLEDGEHAMMER_ATP_TRANSLATE =
|
blanchet@38506
|
10 |
sig
|
blanchet@38506
|
11 |
type 'a problem = 'a ATP_Problem.problem
|
blanchet@40358
|
12 |
type translated_formula
|
blanchet@38506
|
13 |
|
blanchet@41382
|
14 |
datatype type_system =
|
blanchet@41382
|
15 |
Tags of bool |
|
blanchet@41382
|
16 |
Preds of bool |
|
blanchet@41382
|
17 |
Const_Args |
|
blanchet@41382
|
18 |
Overload_Args |
|
blanchet@41382
|
19 |
No_Types
|
blanchet@41382
|
20 |
|
blanchet@40445
|
21 |
val fact_prefix : string
|
blanchet@38506
|
22 |
val conjecture_prefix : string
|
blanchet@41384
|
23 |
val is_fully_typed : type_system -> bool
|
blanchet@41384
|
24 |
val num_atp_type_args : theory -> type_system -> string -> int
|
blanchet@41336
|
25 |
val translate_atp_fact :
|
blanchet@39249
|
26 |
Proof.context -> (string * 'a) * thm
|
blanchet@41339
|
27 |
-> translated_formula option * ((string * 'a) * thm)
|
blanchet@40240
|
28 |
val prepare_atp_problem :
|
blanchet@41382
|
29 |
Proof.context -> bool -> bool -> type_system -> bool -> term list -> term
|
blanchet@41339
|
30 |
-> (translated_formula option * ((string * 'a) * thm)) list
|
blanchet@39053
|
31 |
-> string problem * string Symtab.table * int * (string * 'a) list vector
|
blanchet@38506
|
32 |
end;
|
blanchet@38506
|
33 |
|
blanchet@40249
|
34 |
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
|
blanchet@38506
|
35 |
struct
|
blanchet@38506
|
36 |
|
blanchet@38506
|
37 |
open ATP_Problem
|
blanchet@39734
|
38 |
open Metis_Translate
|
blanchet@38506
|
39 |
open Sledgehammer_Util
|
blanchet@38506
|
40 |
|
blanchet@40445
|
41 |
val fact_prefix = "fact_"
|
blanchet@38506
|
42 |
val conjecture_prefix = "conj_"
|
blanchet@38506
|
43 |
val helper_prefix = "help_"
|
blanchet@38506
|
44 |
val class_rel_clause_prefix = "clrel_";
|
blanchet@38506
|
45 |
val arity_clause_prefix = "arity_"
|
blanchet@40156
|
46 |
val tfree_prefix = "tfree_"
|
blanchet@38506
|
47 |
|
blanchet@38506
|
48 |
(* Freshness almost guaranteed! *)
|
blanchet@38506
|
49 |
val sledgehammer_weak_prefix = "Sledgehammer:"
|
blanchet@38506
|
50 |
|
blanchet@40358
|
51 |
type translated_formula =
|
blanchet@38991
|
52 |
{name: string,
|
blanchet@38991
|
53 |
kind: kind,
|
blanchet@38991
|
54 |
combformula: (name, combterm) formula,
|
blanchet@38991
|
55 |
ctypes_sorts: typ list}
|
blanchet@38506
|
56 |
|
blanchet@41382
|
57 |
datatype type_system =
|
blanchet@41382
|
58 |
Tags of bool |
|
blanchet@41382
|
59 |
Preds of bool |
|
blanchet@41382
|
60 |
Const_Args |
|
blanchet@41382
|
61 |
Overload_Args |
|
blanchet@41382
|
62 |
No_Types
|
blanchet@41382
|
63 |
|
blanchet@41382
|
64 |
fun is_fully_typed (Tags full_types) = full_types
|
blanchet@41382
|
65 |
| is_fully_typed (Preds full_types) = full_types
|
blanchet@41382
|
66 |
| is_fully_typed _ = false
|
blanchet@41382
|
67 |
|
blanchet@41384
|
68 |
(* This is an approximation. If it returns "true" for a constant that isn't
|
blanchet@41384
|
69 |
overloaded (i.e., that has one uniform definition), needless clutter is
|
blanchet@41384
|
70 |
generated; if it returns "false" for an overloaded constant, the ATP gets a
|
blanchet@41384
|
71 |
license to do unsound reasoning if the type system is "overloaded_args". *)
|
blanchet@41384
|
72 |
fun is_overloaded thy s =
|
blanchet@41384
|
73 |
length (Defs.specifications_of (Theory.defs_of thy) s) > 1
|
blanchet@41384
|
74 |
|
blanchet@41384
|
75 |
fun needs_type_args thy type_sys s =
|
blanchet@41384
|
76 |
case type_sys of
|
blanchet@41384
|
77 |
Tags full_types => not full_types
|
blanchet@41384
|
78 |
| Preds full_types => not full_types
|
blanchet@41384
|
79 |
| Const_Args => true
|
blanchet@41384
|
80 |
| Overload_Args => is_overloaded thy s
|
blanchet@41384
|
81 |
| No_Types => false
|
blanchet@41384
|
82 |
|
blanchet@41384
|
83 |
fun num_atp_type_args thy type_sys s =
|
blanchet@41384
|
84 |
if needs_type_args thy type_sys s then num_type_args thy s else 0
|
blanchet@41384
|
85 |
|
blanchet@38506
|
86 |
fun mk_anot phi = AConn (ANot, [phi])
|
blanchet@38506
|
87 |
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
|
blanchet@38506
|
88 |
fun mk_ahorn [] phi = phi
|
blanchet@38506
|
89 |
| mk_ahorn (phi :: phis) psi =
|
blanchet@38506
|
90 |
AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi])
|
blanchet@38506
|
91 |
|
blanchet@38506
|
92 |
fun combformula_for_prop thy =
|
blanchet@38506
|
93 |
let
|
blanchet@40387
|
94 |
val do_term = combterm_from_term thy
|
blanchet@38506
|
95 |
fun do_quant bs q s T t' =
|
blanchet@38743
|
96 |
let val s = Name.variant (map fst bs) s in
|
blanchet@38743
|
97 |
do_formula ((s, T) :: bs) t'
|
blanchet@38743
|
98 |
#>> (fn phi => AQuant (q, [`make_bound_var s], phi))
|
blanchet@38743
|
99 |
end
|
blanchet@38506
|
100 |
and do_conn bs c t1 t2 =
|
blanchet@38506
|
101 |
do_formula bs t1 ##>> do_formula bs t2
|
blanchet@38506
|
102 |
#>> (fn (phi1, phi2) => AConn (c, [phi1, phi2]))
|
blanchet@38506
|
103 |
and do_formula bs t =
|
blanchet@38506
|
104 |
case t of
|
blanchet@38506
|
105 |
@{const Not} $ t1 =>
|
blanchet@38506
|
106 |
do_formula bs t1 #>> (fn phi => AConn (ANot, [phi]))
|
blanchet@38506
|
107 |
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
108 |
do_quant bs AForall s T t'
|
blanchet@38506
|
109 |
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
|
blanchet@38506
|
110 |
do_quant bs AExists s T t'
|
haftmann@39028
|
111 |
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
|
haftmann@39028
|
112 |
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
|
haftmann@39019
|
113 |
| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
|
haftmann@39093
|
114 |
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
|
blanchet@38506
|
115 |
do_conn bs AIff t1 t2
|
blanchet@38506
|
116 |
| _ => (fn ts => do_term bs (Envir.eta_contract t)
|
blanchet@38506
|
117 |
|>> AAtom ||> union (op =) ts)
|
blanchet@38506
|
118 |
in do_formula [] end
|
blanchet@38506
|
119 |
|
blanchet@38841
|
120 |
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
|
blanchet@38506
|
121 |
|
blanchet@38506
|
122 |
fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j
|
blanchet@38506
|
123 |
fun conceal_bounds Ts t =
|
blanchet@38506
|
124 |
subst_bounds (map (Free o apfst concealed_bound_name)
|
blanchet@38506
|
125 |
(0 upto length Ts - 1 ~~ Ts), t)
|
blanchet@38506
|
126 |
fun reveal_bounds Ts =
|
blanchet@38506
|
127 |
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
|
blanchet@38506
|
128 |
(0 upto length Ts - 1 ~~ Ts))
|
blanchet@38506
|
129 |
|
blanchet@38831
|
130 |
(* Removes the lambdas from an equation of the form "t = (%x. u)".
|
blanchet@40071
|
131 |
(Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
|
blanchet@38831
|
132 |
fun extensionalize_term t =
|
blanchet@38831
|
133 |
let
|
blanchet@38831
|
134 |
fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
|
blanchet@38831
|
135 |
| aux j (t as Const (s, Type (_, [Type (_, [_, T']),
|
blanchet@38831
|
136 |
Type (_, [_, res_T])]))
|
blanchet@38831
|
137 |
$ t2 $ Abs (var_s, var_T, t')) =
|
haftmann@39093
|
138 |
if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
|
blanchet@38831
|
139 |
let val var_t = Var ((var_s, j), var_T) in
|
blanchet@38831
|
140 |
Const (s, T' --> T' --> res_T)
|
blanchet@38831
|
141 |
$ betapply (t2, var_t) $ subst_bound (var_t, t')
|
blanchet@38831
|
142 |
|> aux (j + 1)
|
blanchet@38831
|
143 |
end
|
blanchet@38831
|
144 |
else
|
blanchet@38831
|
145 |
t
|
blanchet@38831
|
146 |
| aux _ t = t
|
blanchet@38831
|
147 |
in aux (maxidx_of_term t + 1) t end
|
blanchet@38831
|
148 |
|
blanchet@38506
|
149 |
fun introduce_combinators_in_term ctxt kind t =
|
blanchet@38716
|
150 |
let val thy = ProofContext.theory_of ctxt in
|
blanchet@38716
|
151 |
if Meson.is_fol_term thy t then
|
blanchet@38716
|
152 |
t
|
blanchet@38716
|
153 |
else
|
blanchet@38716
|
154 |
let
|
blanchet@38716
|
155 |
fun aux Ts t =
|
blanchet@38716
|
156 |
case t of
|
blanchet@38716
|
157 |
@{const Not} $ t1 => @{const Not} $ aux Ts t1
|
blanchet@38716
|
158 |
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
159 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
160 |
| (t0 as Const (@{const_name All}, _)) $ t1 =>
|
blanchet@38890
|
161 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
blanchet@38716
|
162 |
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
|
blanchet@38716
|
163 |
t0 $ Abs (s, T, aux (T :: Ts) t')
|
blanchet@38890
|
164 |
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
|
blanchet@38890
|
165 |
aux Ts (t0 $ eta_expand Ts t1 1)
|
haftmann@39028
|
166 |
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39028
|
167 |
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39019
|
168 |
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
|
haftmann@39093
|
169 |
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
|
blanchet@38716
|
170 |
$ t1 $ t2 =>
|
blanchet@38716
|
171 |
t0 $ aux Ts t1 $ aux Ts t2
|
blanchet@38716
|
172 |
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
|
blanchet@38716
|
173 |
t
|
blanchet@38716
|
174 |
else
|
blanchet@38716
|
175 |
t |> conceal_bounds Ts
|
blanchet@38716
|
176 |
|> Envir.eta_contract
|
blanchet@38716
|
177 |
|> cterm_of thy
|
blanchet@40071
|
178 |
|> Meson_Clausify.introduce_combinators_in_cterm
|
blanchet@38716
|
179 |
|> prop_of |> Logic.dest_equals |> snd
|
blanchet@38716
|
180 |
|> reveal_bounds Ts
|
blanchet@39616
|
181 |
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
|
blanchet@38716
|
182 |
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
|
blanchet@38716
|
183 |
handle THM _ =>
|
blanchet@38716
|
184 |
(* A type variable of sort "{}" will make abstraction fail. *)
|
blanchet@38836
|
185 |
if kind = Conjecture then HOLogic.false_const
|
blanchet@38836
|
186 |
else HOLogic.true_const
|
blanchet@38716
|
187 |
end
|
blanchet@38506
|
188 |
|
blanchet@38506
|
189 |
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
|
blanchet@38506
|
190 |
same in Sledgehammer to prevent the discovery of unreplable proofs. *)
|
blanchet@38506
|
191 |
fun freeze_term t =
|
blanchet@38506
|
192 |
let
|
blanchet@38506
|
193 |
fun aux (t $ u) = aux t $ aux u
|
blanchet@38506
|
194 |
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
|
blanchet@38506
|
195 |
| aux (Var ((s, i), T)) =
|
blanchet@38506
|
196 |
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
|
blanchet@38506
|
197 |
| aux t = t
|
blanchet@38506
|
198 |
in t |> exists_subterm is_Var t ? aux end
|
blanchet@38506
|
199 |
|
blanchet@38827
|
200 |
(* "Object_Logic.atomize_term" isn't as powerful as it could be; for example,
|
blanchet@38827
|
201 |
it leaves metaequalities over "prop"s alone. *)
|
blanchet@38828
|
202 |
val atomize_term =
|
blanchet@38828
|
203 |
let
|
blanchet@38828
|
204 |
fun aux (@{const Trueprop} $ t1) = t1
|
blanchet@38828
|
205 |
| aux (Const (@{const_name all}, _) $ Abs (s, T, t')) =
|
blanchet@38828
|
206 |
HOLogic.all_const T $ Abs (s, T, aux t')
|
blanchet@38828
|
207 |
| aux (@{const "==>"} $ t1 $ t2) = HOLogic.mk_imp (pairself aux (t1, t2))
|
blanchet@38828
|
208 |
| aux (Const (@{const_name "=="}, Type (_, [@{typ prop}, _])) $ t1 $ t2) =
|
blanchet@38828
|
209 |
HOLogic.eq_const HOLogic.boolT $ aux t1 $ aux t2
|
blanchet@38828
|
210 |
| aux (Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2) =
|
blanchet@38828
|
211 |
HOLogic.eq_const T $ t1 $ t2
|
blanchet@38828
|
212 |
| aux _ = raise Fail "aux"
|
blanchet@38828
|
213 |
in perhaps (try aux) end
|
blanchet@38827
|
214 |
|
blanchet@40445
|
215 |
(* making fact and conjecture formulas *)
|
blanchet@38836
|
216 |
fun make_formula ctxt presimp name kind t =
|
blanchet@38506
|
217 |
let
|
blanchet@38506
|
218 |
val thy = ProofContext.theory_of ctxt
|
blanchet@38831
|
219 |
val t = t |> Envir.beta_eta_contract
|
blanchet@38890
|
220 |
|> transform_elim_term
|
blanchet@38827
|
221 |
|> atomize_term
|
blanchet@38890
|
222 |
val need_trueprop = (fastype_of t = HOLogic.boolT)
|
blanchet@38890
|
223 |
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|
blanchet@38506
|
224 |
|> extensionalize_term
|
blanchet@38506
|
225 |
|> presimp ? presimplify_term thy
|
blanchet@38506
|
226 |
|> perhaps (try (HOLogic.dest_Trueprop))
|
blanchet@38506
|
227 |
|> introduce_combinators_in_term ctxt kind
|
blanchet@38836
|
228 |
|> kind <> Axiom ? freeze_term
|
blanchet@38506
|
229 |
val (combformula, ctypes_sorts) = combformula_for_prop thy t []
|
blanchet@38506
|
230 |
in
|
blanchet@38991
|
231 |
{name = name, combformula = combformula, kind = kind,
|
blanchet@38991
|
232 |
ctypes_sorts = ctypes_sorts}
|
blanchet@38506
|
233 |
end
|
blanchet@38506
|
234 |
|
blanchet@41339
|
235 |
fun make_fact ctxt presimp ((name, _), th) =
|
blanchet@38841
|
236 |
case make_formula ctxt presimp name Axiom (prop_of th) of
|
blanchet@38991
|
237 |
{combformula = AAtom (CombConst (("c_True", _), _, _)), ...} => NONE
|
blanchet@41339
|
238 |
| formula => SOME formula
|
blanchet@38836
|
239 |
fun make_conjecture ctxt ts =
|
blanchet@38836
|
240 |
let val last = length ts - 1 in
|
blanchet@38836
|
241 |
map2 (fn j => make_formula ctxt true (Int.toString j)
|
blanchet@38836
|
242 |
(if j = last then Conjecture else Hypothesis))
|
blanchet@38836
|
243 |
(0 upto last) ts
|
blanchet@38836
|
244 |
end
|
blanchet@38506
|
245 |
|
blanchet@38506
|
246 |
(** Helper facts **)
|
blanchet@38506
|
247 |
|
blanchet@38506
|
248 |
fun count_combterm (CombConst ((s, _), _, _)) =
|
blanchet@38506
|
249 |
Symtab.map_entry s (Integer.add 1)
|
blanchet@38506
|
250 |
| count_combterm (CombVar _) = I
|
blanchet@38506
|
251 |
| count_combterm (CombApp (t1, t2)) = fold count_combterm [t1, t2]
|
blanchet@38506
|
252 |
fun count_combformula (AQuant (_, _, phi)) = count_combformula phi
|
blanchet@38506
|
253 |
| count_combformula (AConn (_, phis)) = fold count_combformula phis
|
blanchet@38506
|
254 |
| count_combformula (AAtom tm) = count_combterm tm
|
blanchet@40358
|
255 |
fun count_translated_formula ({combformula, ...} : translated_formula) =
|
blanchet@38506
|
256 |
count_combformula combformula
|
blanchet@38506
|
257 |
|
blanchet@38506
|
258 |
val optional_helpers =
|
blanchet@40134
|
259 |
[(["c_COMBI"], @{thms Meson.COMBI_def}),
|
blanchet@40134
|
260 |
(["c_COMBK"], @{thms Meson.COMBK_def}),
|
blanchet@40134
|
261 |
(["c_COMBB"], @{thms Meson.COMBB_def}),
|
blanchet@40134
|
262 |
(["c_COMBC"], @{thms Meson.COMBC_def}),
|
blanchet@40134
|
263 |
(["c_COMBS"], @{thms Meson.COMBS_def})]
|
blanchet@41382
|
264 |
val optional_fully_typed_helpers =
|
blanchet@38917
|
265 |
[(["c_True", "c_False", "c_If"], @{thms True_or_False}),
|
blanchet@38917
|
266 |
(["c_If"], @{thms if_True if_False})]
|
blanchet@40135
|
267 |
val mandatory_helpers = @{thms Metis.fequal_def}
|
blanchet@38506
|
268 |
|
blanchet@38506
|
269 |
val init_counters =
|
blanchet@41382
|
270 |
[optional_helpers, optional_fully_typed_helpers] |> maps (maps fst)
|
blanchet@38917
|
271 |
|> sort_distinct string_ord |> map (rpair 0) |> Symtab.make
|
blanchet@38506
|
272 |
|
blanchet@41382
|
273 |
fun get_helper_facts ctxt is_FO type_sys conjectures facts =
|
blanchet@38506
|
274 |
let
|
blanchet@40250
|
275 |
val ct =
|
blanchet@40445
|
276 |
fold (fold count_translated_formula) [conjectures, facts] init_counters
|
blanchet@38506
|
277 |
fun is_needed c = the (Symtab.lookup ct c) > 0
|
blanchet@38937
|
278 |
fun baptize th = ((Thm.get_name_hint th, false), th)
|
blanchet@38506
|
279 |
in
|
blanchet@38506
|
280 |
(optional_helpers
|
blanchet@41382
|
281 |
|> is_fully_typed type_sys ? append optional_fully_typed_helpers
|
blanchet@38506
|
282 |
|> maps (fn (ss, ths) =>
|
blanchet@38937
|
283 |
if exists is_needed ss then map baptize ths else [])) @
|
blanchet@38937
|
284 |
(if is_FO then [] else map baptize mandatory_helpers)
|
blanchet@41339
|
285 |
|> map_filter (make_fact ctxt false)
|
blanchet@38506
|
286 |
end
|
blanchet@38506
|
287 |
|
blanchet@41339
|
288 |
fun translate_atp_fact ctxt = `(make_fact ctxt true)
|
blanchet@39248
|
289 |
|
blanchet@41382
|
290 |
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
|
blanchet@38506
|
291 |
let
|
blanchet@38506
|
292 |
val thy = ProofContext.theory_of ctxt
|
blanchet@41339
|
293 |
val fact_ts = map (prop_of o snd o snd) rich_facts
|
blanchet@41339
|
294 |
val (facts, fact_names) =
|
blanchet@41339
|
295 |
rich_facts
|
blanchet@41339
|
296 |
|> map_filter (fn (NONE, _) => NONE
|
blanchet@41339
|
297 |
| (SOME fact, (name, _)) => SOME (fact, name))
|
blanchet@41339
|
298 |
|> ListPair.unzip
|
blanchet@40445
|
299 |
(* Remove existing facts from the conjecture, as this can dramatically
|
blanchet@39249
|
300 |
boost an ATP's performance (for some reason). *)
|
blanchet@40445
|
301 |
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
|
blanchet@38506
|
302 |
val goal_t = Logic.list_implies (hyp_ts, concl_t)
|
blanchet@38506
|
303 |
val is_FO = Meson.is_fol_term thy goal_t
|
blanchet@38506
|
304 |
val subs = tfree_classes_of_terms [goal_t]
|
blanchet@40445
|
305 |
val supers = tvar_classes_of_terms fact_ts
|
blanchet@40445
|
306 |
val tycons = type_consts_of_terms thy (goal_t :: fact_ts)
|
blanchet@40445
|
307 |
(* TFrees in the conjecture; TVars in the facts *)
|
blanchet@38836
|
308 |
val conjectures = make_conjecture ctxt (hyp_ts @ [concl_t])
|
blanchet@41382
|
309 |
val helper_facts = get_helper_facts ctxt is_FO type_sys conjectures facts
|
blanchet@38506
|
310 |
val (supers', arity_clauses) = make_arity_clauses thy tycons supers
|
blanchet@38506
|
311 |
val class_rel_clauses = make_class_rel_clauses thy subs supers'
|
blanchet@38506
|
312 |
in
|
blanchet@40445
|
313 |
(fact_names |> map single |> Vector.fromList,
|
blanchet@40445
|
314 |
(conjectures, facts, helper_facts, class_rel_clauses, arity_clauses))
|
blanchet@38506
|
315 |
end
|
blanchet@38506
|
316 |
|
blanchet@38506
|
317 |
fun wrap_type ty t = ATerm ((type_wrapper_name, type_wrapper_name), [ty, t])
|
blanchet@38506
|
318 |
|
blanchet@38506
|
319 |
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
|
blanchet@38506
|
320 |
| fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
|
blanchet@38506
|
321 |
| fo_term_for_combtyp (CombType (name, tys)) =
|
blanchet@38506
|
322 |
ATerm (name, map fo_term_for_combtyp tys)
|
blanchet@38506
|
323 |
|
blanchet@38506
|
324 |
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
|
blanchet@38506
|
325 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@38506
|
326 |
| fo_literal_for_type_literal (TyLitFree (class, name)) =
|
blanchet@38506
|
327 |
(true, ATerm (class, [ATerm (name, [])]))
|
blanchet@38506
|
328 |
|
blanchet@38506
|
329 |
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
|
blanchet@38506
|
330 |
|
blanchet@41384
|
331 |
fun fo_term_for_combterm thy type_sys =
|
blanchet@38506
|
332 |
let
|
blanchet@38506
|
333 |
fun aux top_level u =
|
blanchet@38506
|
334 |
let
|
blanchet@38506
|
335 |
val (head, args) = strip_combterm_comb u
|
blanchet@38506
|
336 |
val (x, ty_args) =
|
blanchet@38506
|
337 |
case head of
|
blanchet@38506
|
338 |
CombConst (name as (s, s'), _, ty_args) =>
|
blanchet@41384
|
339 |
(case strip_prefix_and_unascii const_prefix s of
|
blanchet@41384
|
340 |
NONE =>
|
blanchet@41384
|
341 |
if s = "equal" then
|
blanchet@41384
|
342 |
if top_level andalso length args = 2 then (name, [])
|
blanchet@41384
|
343 |
else (("c_fequal", @{const_name Metis.fequal}), ty_args)
|
blanchet@41384
|
344 |
else
|
blanchet@41384
|
345 |
(name, ty_args)
|
blanchet@41384
|
346 |
| SOME s'' =>
|
blanchet@41384
|
347 |
let
|
blanchet@41384
|
348 |
val s'' = invert_const s''
|
blanchet@41384
|
349 |
val ty_args =
|
blanchet@41384
|
350 |
if needs_type_args thy type_sys s'' then ty_args else []
|
blanchet@41384
|
351 |
in
|
blanchet@41384
|
352 |
if top_level then
|
blanchet@41384
|
353 |
case s of
|
blanchet@41384
|
354 |
"c_False" => (("$false", s'), [])
|
blanchet@41384
|
355 |
| "c_True" => (("$true", s'), [])
|
blanchet@41384
|
356 |
| _ => (name, ty_args)
|
blanchet@41384
|
357 |
else
|
blanchet@41384
|
358 |
(name, ty_args)
|
blanchet@41384
|
359 |
end)
|
blanchet@38506
|
360 |
| CombVar (name, _) => (name, [])
|
blanchet@38506
|
361 |
| CombApp _ => raise Fail "impossible \"CombApp\""
|
blanchet@38506
|
362 |
val t = ATerm (x, map fo_term_for_combtyp ty_args @
|
blanchet@38506
|
363 |
map (aux false) args)
|
blanchet@38506
|
364 |
in
|
blanchet@41382
|
365 |
t |> (if type_sys = Tags true then
|
blanchet@41382
|
366 |
wrap_type (fo_term_for_combtyp (combtyp_of u))
|
blanchet@41382
|
367 |
else
|
blanchet@41382
|
368 |
I)
|
blanchet@38506
|
369 |
end
|
blanchet@38506
|
370 |
in aux true end
|
blanchet@38506
|
371 |
|
blanchet@41384
|
372 |
fun formula_for_combformula thy type_sys =
|
blanchet@38506
|
373 |
let
|
blanchet@38506
|
374 |
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
|
blanchet@38506
|
375 |
| aux (AConn (c, phis)) = AConn (c, map aux phis)
|
blanchet@41384
|
376 |
| aux (AAtom tm) = AAtom (fo_term_for_combterm thy type_sys tm)
|
blanchet@38506
|
377 |
in aux end
|
blanchet@38506
|
378 |
|
blanchet@41384
|
379 |
fun formula_for_fact thy type_sys
|
blanchet@40445
|
380 |
({combformula, ctypes_sorts, ...} : translated_formula) =
|
blanchet@38506
|
381 |
mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
|
blanchet@38506
|
382 |
(type_literals_for_types ctypes_sorts))
|
blanchet@41384
|
383 |
(formula_for_combformula thy type_sys combformula)
|
blanchet@38506
|
384 |
|
blanchet@41384
|
385 |
fun problem_line_for_fact thy prefix type_sys (formula as {name, kind, ...}) =
|
blanchet@41384
|
386 |
Fof (prefix ^ ascii_of name, kind, formula_for_fact thy type_sys formula)
|
blanchet@38506
|
387 |
|
blanchet@38506
|
388 |
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
|
blanchet@38506
|
389 |
superclass, ...}) =
|
blanchet@38506
|
390 |
let val ty_arg = ATerm (("T", "T"), []) in
|
blanchet@38506
|
391 |
Fof (class_rel_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@38506
|
392 |
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
|
blanchet@38506
|
393 |
AAtom (ATerm (superclass, [ty_arg]))]))
|
blanchet@38506
|
394 |
end
|
blanchet@38506
|
395 |
|
blanchet@38506
|
396 |
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
|
blanchet@38506
|
397 |
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
|
blanchet@38506
|
398 |
| fo_literal_for_arity_literal (TVarLit (c, sort)) =
|
blanchet@38506
|
399 |
(false, ATerm (c, [ATerm (sort, [])]))
|
blanchet@38506
|
400 |
|
blanchet@38506
|
401 |
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
|
blanchet@38506
|
402 |
...}) =
|
blanchet@38506
|
403 |
Fof (arity_clause_prefix ^ ascii_of name, Axiom,
|
blanchet@38506
|
404 |
mk_ahorn (map (formula_for_fo_literal o apfst not
|
blanchet@38506
|
405 |
o fo_literal_for_arity_literal) premLits)
|
blanchet@38506
|
406 |
(formula_for_fo_literal
|
blanchet@38506
|
407 |
(fo_literal_for_arity_literal conclLit)))
|
blanchet@38506
|
408 |
|
blanchet@41384
|
409 |
fun problem_line_for_conjecture thy type_sys
|
blanchet@40358
|
410 |
({name, kind, combformula, ...} : translated_formula) =
|
blanchet@38506
|
411 |
Fof (conjecture_prefix ^ name, kind,
|
blanchet@41384
|
412 |
formula_for_combformula thy type_sys combformula)
|
blanchet@38506
|
413 |
|
blanchet@40358
|
414 |
fun free_type_literals_for_conjecture
|
blanchet@40358
|
415 |
({ctypes_sorts, ...} : translated_formula) =
|
blanchet@38506
|
416 |
map fo_literal_for_type_literal (type_literals_for_types ctypes_sorts)
|
blanchet@38506
|
417 |
|
blanchet@40156
|
418 |
fun problem_line_for_free_type j lit =
|
blanchet@40156
|
419 |
Fof (tfree_prefix ^ string_of_int j, Hypothesis, formula_for_fo_literal lit)
|
blanchet@38506
|
420 |
fun problem_lines_for_free_types conjectures =
|
blanchet@38506
|
421 |
let
|
blanchet@38506
|
422 |
val litss = map free_type_literals_for_conjecture conjectures
|
blanchet@38506
|
423 |
val lits = fold (union (op =)) litss []
|
blanchet@40156
|
424 |
in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
|
blanchet@38506
|
425 |
|
blanchet@38506
|
426 |
(** "hBOOL" and "hAPP" **)
|
blanchet@38506
|
427 |
|
blanchet@38506
|
428 |
type const_info = {min_arity: int, max_arity: int, sub_level: bool}
|
blanchet@38506
|
429 |
|
blanchet@38506
|
430 |
fun consider_term top_level (ATerm ((s, _), ts)) =
|
blanchet@39692
|
431 |
(if is_atp_variable s then
|
blanchet@38506
|
432 |
I
|
blanchet@38506
|
433 |
else
|
blanchet@38506
|
434 |
let val n = length ts in
|
blanchet@38506
|
435 |
Symtab.map_default
|
blanchet@38506
|
436 |
(s, {min_arity = n, max_arity = 0, sub_level = false})
|
blanchet@38506
|
437 |
(fn {min_arity, max_arity, sub_level} =>
|
blanchet@38506
|
438 |
{min_arity = Int.min (n, min_arity),
|
blanchet@38506
|
439 |
max_arity = Int.max (n, max_arity),
|
blanchet@38506
|
440 |
sub_level = sub_level orelse not top_level})
|
blanchet@38506
|
441 |
end)
|
blanchet@38506
|
442 |
#> fold (consider_term (top_level andalso s = type_wrapper_name)) ts
|
blanchet@38506
|
443 |
fun consider_formula (AQuant (_, _, phi)) = consider_formula phi
|
blanchet@38506
|
444 |
| consider_formula (AConn (_, phis)) = fold consider_formula phis
|
blanchet@38506
|
445 |
| consider_formula (AAtom tm) = consider_term true tm
|
blanchet@38506
|
446 |
|
blanchet@38506
|
447 |
fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi
|
blanchet@38506
|
448 |
fun consider_problem problem = fold (fold consider_problem_line o snd) problem
|
blanchet@38506
|
449 |
|
blanchet@38506
|
450 |
fun const_table_for_problem explicit_apply problem =
|
blanchet@38506
|
451 |
if explicit_apply then NONE
|
blanchet@38506
|
452 |
else SOME (Symtab.empty |> consider_problem problem)
|
blanchet@38506
|
453 |
|
blanchet@41382
|
454 |
fun min_arity_of thy type_sys NONE s =
|
blanchet@38506
|
455 |
(if s = "equal" orelse s = type_wrapper_name orelse
|
blanchet@38506
|
456 |
String.isPrefix type_const_prefix s orelse
|
blanchet@38506
|
457 |
String.isPrefix class_prefix s then
|
blanchet@38506
|
458 |
16383 (* large number *)
|
blanchet@38987
|
459 |
else case strip_prefix_and_unascii const_prefix s of
|
blanchet@41384
|
460 |
SOME s' => num_atp_type_args thy type_sys (invert_const s')
|
blanchet@38506
|
461 |
| NONE => 0)
|
blanchet@38506
|
462 |
| min_arity_of _ _ (SOME the_const_tab) s =
|
blanchet@38506
|
463 |
case Symtab.lookup the_const_tab s of
|
blanchet@38506
|
464 |
SOME ({min_arity, ...} : const_info) => min_arity
|
blanchet@38506
|
465 |
| NONE => 0
|
blanchet@38506
|
466 |
|
blanchet@38506
|
467 |
fun full_type_of (ATerm ((s, _), [ty, _])) =
|
blanchet@38506
|
468 |
if s = type_wrapper_name then ty else raise Fail "expected type wrapper"
|
blanchet@38506
|
469 |
| full_type_of _ = raise Fail "expected type wrapper"
|
blanchet@38506
|
470 |
|
blanchet@38506
|
471 |
fun list_hAPP_rev _ t1 [] = t1
|
blanchet@38506
|
472 |
| list_hAPP_rev NONE t1 (t2 :: ts2) =
|
blanchet@38506
|
473 |
ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
|
blanchet@38506
|
474 |
| list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
|
blanchet@38506
|
475 |
let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
|
blanchet@38506
|
476 |
[full_type_of t2, ty]) in
|
blanchet@38506
|
477 |
ATerm (`I "hAPP", [wrap_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
|
blanchet@38506
|
478 |
end
|
blanchet@38506
|
479 |
|
blanchet@41382
|
480 |
fun repair_applications_in_term thy type_sys const_tab =
|
blanchet@38506
|
481 |
let
|
blanchet@38506
|
482 |
fun aux opt_ty (ATerm (name as (s, _), ts)) =
|
blanchet@38506
|
483 |
if s = type_wrapper_name then
|
blanchet@38506
|
484 |
case ts of
|
blanchet@38506
|
485 |
[t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
|
blanchet@38506
|
486 |
| _ => raise Fail "malformed type wrapper"
|
blanchet@38506
|
487 |
else
|
blanchet@38506
|
488 |
let
|
blanchet@38506
|
489 |
val ts = map (aux NONE) ts
|
blanchet@41382
|
490 |
val (ts1, ts2) = chop (min_arity_of thy type_sys const_tab s) ts
|
blanchet@38506
|
491 |
in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
|
blanchet@38506
|
492 |
in aux NONE end
|
blanchet@38506
|
493 |
|
blanchet@38506
|
494 |
fun boolify t = ATerm (`I "hBOOL", [t])
|
blanchet@38506
|
495 |
|
blanchet@38506
|
496 |
(* True if the constant ever appears outside of the top-level position in
|
blanchet@38506
|
497 |
literals, or if it appears with different arities (e.g., because of different
|
blanchet@38506
|
498 |
type instantiations). If false, the constant always receives all of its
|
blanchet@38506
|
499 |
arguments and is used as a predicate. *)
|
blanchet@38506
|
500 |
fun is_predicate NONE s =
|
blanchet@38812
|
501 |
s = "equal" orelse s = "$false" orelse s = "$true" orelse
|
blanchet@38812
|
502 |
String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
|
blanchet@38506
|
503 |
| is_predicate (SOME the_const_tab) s =
|
blanchet@38506
|
504 |
case Symtab.lookup the_const_tab s of
|
blanchet@38506
|
505 |
SOME {min_arity, max_arity, sub_level} =>
|
blanchet@38506
|
506 |
not sub_level andalso min_arity = max_arity
|
blanchet@38506
|
507 |
| NONE => false
|
blanchet@38506
|
508 |
|
blanchet@38506
|
509 |
fun repair_predicates_in_term const_tab (t as ATerm ((s, _), ts)) =
|
blanchet@38506
|
510 |
if s = type_wrapper_name then
|
blanchet@38506
|
511 |
case ts of
|
blanchet@38506
|
512 |
[_, t' as ATerm ((s', _), _)] =>
|
blanchet@38506
|
513 |
if is_predicate const_tab s' then t' else boolify t
|
blanchet@38506
|
514 |
| _ => raise Fail "malformed type wrapper"
|
blanchet@38506
|
515 |
else
|
blanchet@38506
|
516 |
t |> not (is_predicate const_tab s) ? boolify
|
blanchet@38506
|
517 |
|
blanchet@38506
|
518 |
fun close_universally phi =
|
blanchet@38506
|
519 |
let
|
blanchet@38506
|
520 |
fun term_vars bounds (ATerm (name as (s, _), tms)) =
|
blanchet@39692
|
521 |
(is_atp_variable s andalso not (member (op =) bounds name))
|
blanchet@38506
|
522 |
? insert (op =) name
|
blanchet@38506
|
523 |
#> fold (term_vars bounds) tms
|
blanchet@38917
|
524 |
fun formula_vars bounds (AQuant (_, xs, phi)) =
|
blanchet@38506
|
525 |
formula_vars (xs @ bounds) phi
|
blanchet@38506
|
526 |
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
|
blanchet@38506
|
527 |
| formula_vars bounds (AAtom tm) = term_vars bounds tm
|
blanchet@38506
|
528 |
in
|
blanchet@38506
|
529 |
case formula_vars [] phi [] of [] => phi | xs => AQuant (AForall, xs, phi)
|
blanchet@38506
|
530 |
end
|
blanchet@38506
|
531 |
|
blanchet@41382
|
532 |
fun repair_formula thy explicit_forall type_sys const_tab =
|
blanchet@38506
|
533 |
let
|
blanchet@38506
|
534 |
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
|
blanchet@38506
|
535 |
| aux (AConn (c, phis)) = AConn (c, map aux phis)
|
blanchet@38506
|
536 |
| aux (AAtom tm) =
|
blanchet@41382
|
537 |
AAtom (tm |> repair_applications_in_term thy type_sys const_tab
|
blanchet@38506
|
538 |
|> repair_predicates_in_term const_tab)
|
blanchet@38506
|
539 |
in aux #> explicit_forall ? close_universally end
|
blanchet@38506
|
540 |
|
blanchet@41382
|
541 |
fun repair_problem_line thy explicit_forall type_sys const_tab
|
blanchet@38506
|
542 |
(Fof (ident, kind, phi)) =
|
blanchet@41382
|
543 |
Fof (ident, kind, repair_formula thy explicit_forall type_sys const_tab phi)
|
blanchet@38506
|
544 |
fun repair_problem_with_const_table thy =
|
blanchet@38506
|
545 |
map o apsnd o map ooo repair_problem_line thy
|
blanchet@38506
|
546 |
|
blanchet@41382
|
547 |
fun repair_problem thy explicit_forall type_sys explicit_apply problem =
|
blanchet@41382
|
548 |
repair_problem_with_const_table thy explicit_forall type_sys
|
blanchet@38506
|
549 |
(const_table_for_problem explicit_apply problem) problem
|
blanchet@38506
|
550 |
|
blanchet@41382
|
551 |
fun prepare_atp_problem ctxt readable_names explicit_forall type_sys
|
blanchet@40445
|
552 |
explicit_apply hyp_ts concl_t facts =
|
blanchet@38506
|
553 |
let
|
blanchet@38506
|
554 |
val thy = ProofContext.theory_of ctxt
|
blanchet@40445
|
555 |
val (fact_names, (conjectures, facts, helper_facts, class_rel_clauses,
|
blanchet@40445
|
556 |
arity_clauses)) =
|
blanchet@41382
|
557 |
translate_formulas ctxt type_sys hyp_ts concl_t facts
|
blanchet@41384
|
558 |
val fact_lines = map (problem_line_for_fact thy fact_prefix type_sys) facts
|
blanchet@38506
|
559 |
val helper_lines =
|
blanchet@41384
|
560 |
map (problem_line_for_fact thy helper_prefix type_sys) helper_facts
|
blanchet@38506
|
561 |
val conjecture_lines =
|
blanchet@41384
|
562 |
map (problem_line_for_conjecture thy type_sys) conjectures
|
blanchet@38506
|
563 |
val tfree_lines = problem_lines_for_free_types conjectures
|
blanchet@38506
|
564 |
val class_rel_lines =
|
blanchet@38506
|
565 |
map problem_line_for_class_rel_clause class_rel_clauses
|
blanchet@38506
|
566 |
val arity_lines = map problem_line_for_arity_clause arity_clauses
|
blanchet@38506
|
567 |
(* Reordering these might or might not confuse the proof reconstruction
|
blanchet@38506
|
568 |
code or the SPASS Flotter hack. *)
|
blanchet@38506
|
569 |
val problem =
|
blanchet@40445
|
570 |
[("Relevant facts", fact_lines),
|
blanchet@38506
|
571 |
("Class relationships", class_rel_lines),
|
blanchet@38506
|
572 |
("Arity declarations", arity_lines),
|
blanchet@38506
|
573 |
("Helper facts", helper_lines),
|
blanchet@38506
|
574 |
("Conjectures", conjecture_lines),
|
blanchet@38506
|
575 |
("Type variables", tfree_lines)]
|
blanchet@41382
|
576 |
|> repair_problem thy explicit_forall type_sys explicit_apply
|
blanchet@39692
|
577 |
val (problem, pool) = nice_atp_problem readable_names problem
|
blanchet@38506
|
578 |
val conjecture_offset =
|
blanchet@40445
|
579 |
length fact_lines + length class_rel_lines + length arity_lines
|
blanchet@38506
|
580 |
+ length helper_lines
|
blanchet@38506
|
581 |
in
|
blanchet@38506
|
582 |
(problem,
|
blanchet@38506
|
583 |
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
|
blanchet@40445
|
584 |
conjecture_offset, fact_names)
|
blanchet@38506
|
585 |
end
|
blanchet@38506
|
586 |
|
blanchet@38506
|
587 |
end;
|