ensure that the lambda translation procedure is called only once with all the facts, which is necessary for soundness of lambda-lifting (freshness of new names)
1 (* Title: HOL/Tools/ATP/atp_util.ML
2 Author: Jasmin Blanchette, TU Muenchen
4 General-purpose functions used by the ATP module.
9 val timestamp : unit -> string
10 val hash_string : string -> int
11 val hash_term : term -> int
12 val strip_spaces : bool -> (char -> bool) -> string -> string
13 val nat_subscript : int -> string
14 val unyxml : string -> string
15 val maybe_quote : string -> string
16 val string_from_ext_time : bool * Time.time -> string
17 val string_from_time : Time.time -> string
18 val varify_type : Proof.context -> typ -> typ
19 val instantiate_type : theory -> typ -> typ -> typ -> typ
20 val varify_and_instantiate_type : Proof.context -> typ -> typ -> typ -> typ
22 Datatype_Aux.descr -> (Datatype_Aux.dtyp * typ) list -> Datatype_Aux.dtyp
24 val is_type_surely_finite : Proof.context -> bool -> typ -> bool
25 val is_type_surely_infinite : Proof.context -> bool -> typ -> bool
26 val s_not : term -> term
27 val s_conj : term * term -> term
28 val s_disj : term * term -> term
29 val s_imp : term * term -> term
30 val s_iff : term * term -> term
31 val monomorphic_term : Type.tyenv -> term -> term
32 val eta_expand : typ list -> term -> int -> term
33 val transform_elim_prop : term -> term
34 val specialize_type : theory -> (string * typ) -> term -> term
36 Proof.context -> thm -> int -> (string * typ) list * term list * term
39 structure ATP_Util : ATP_UTIL =
42 val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
44 (* This hash function is recommended in "Compilers: Principles, Techniques, and
45 Tools" by Aho, Sethi, and Ullman. The "hashpjw" function, which they
46 particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)
47 fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))
48 fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)
49 fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s
50 fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
51 | hashw_term (Const (s, _)) = hashw_string (s, 0w0)
52 | hashw_term (Free (s, _)) = hashw_string (s, 0w0)
55 fun hash_string s = Word.toInt (hashw_string (s, 0w0))
56 val hash_term = Word.toInt o hashw_term
58 fun strip_c_style_comment _ [] = []
59 | strip_c_style_comment is_evil (#"*" :: #"/" :: cs) =
60 strip_spaces_in_list true is_evil cs
61 | strip_c_style_comment is_evil (_ :: cs) = strip_c_style_comment is_evil cs
62 and strip_spaces_in_list _ _ [] = []
63 | strip_spaces_in_list true is_evil (#"%" :: cs) =
64 strip_spaces_in_list true is_evil
65 (cs |> chop_while (not_equal #"\n") |> snd)
66 | strip_spaces_in_list true is_evil (#"/" :: #"*" :: cs) =
67 strip_c_style_comment is_evil cs
68 | strip_spaces_in_list _ _ [c1] = if Char.isSpace c1 then [] else [str c1]
69 | strip_spaces_in_list skip_comments is_evil [c1, c2] =
70 strip_spaces_in_list skip_comments is_evil [c1] @
71 strip_spaces_in_list skip_comments is_evil [c2]
72 | strip_spaces_in_list skip_comments is_evil (c1 :: c2 :: c3 :: cs) =
73 if Char.isSpace c1 then
74 strip_spaces_in_list skip_comments is_evil (c2 :: c3 :: cs)
75 else if Char.isSpace c2 then
76 if Char.isSpace c3 then
77 strip_spaces_in_list skip_comments is_evil (c1 :: c3 :: cs)
79 str c1 :: (if forall is_evil [c1, c3] then [" "] else []) @
80 strip_spaces_in_list skip_comments is_evil (c3 :: cs)
82 str c1 :: strip_spaces_in_list skip_comments is_evil (c2 :: c3 :: cs)
83 fun strip_spaces skip_comments is_evil =
84 implode o strip_spaces_in_list skip_comments is_evil o String.explode
86 val subscript = implode o map (prefix "\<^isub>") o raw_explode (* FIXME Symbol.explode (?) *)
88 n |> string_of_int |> print_mode_active Symbol.xsymbolsN ? subscript
90 val unyxml = XML.content_of o YXML.parse_body
92 val is_long_identifier = forall Lexicon.is_identifier o space_explode "."
94 let val s = unyxml y in
95 y |> ((not (is_long_identifier (perhaps (try (unprefix "'")) s)) andalso
96 not (is_long_identifier (perhaps (try (unprefix "?")) s))) orelse
97 Keyword.is_keyword s) ? quote
100 fun string_from_ext_time (plus, time) =
101 let val ms = Time.toMilliseconds time in
102 (if plus then "> " else "") ^
103 (if plus andalso ms mod 1000 = 0 then
104 signed_string_of_int (ms div 1000) ^ " s"
105 else if ms < 1000 then
106 signed_string_of_int ms ^ " ms"
108 string_of_real (0.01 * Real.fromInt (ms div 10)) ^ " s")
111 val string_from_time = string_from_ext_time o pair false
113 fun varify_type ctxt T =
114 Variable.polymorphic_types ctxt [Const (@{const_name undefined}, T)]
115 |> snd |> the_single |> dest_Const |> snd
117 (* TODO: use "Term_Subst.instantiateT" instead? *)
118 fun instantiate_type thy T1 T1' T2 =
119 Same.commit (Envir.subst_type_same
120 (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
121 handle Type.TYPE_MATCH => raise TYPE ("instantiate_type", [T1, T1'], [])
123 fun varify_and_instantiate_type ctxt T1 T1' T2 =
124 let val thy = Proof_Context.theory_of ctxt in
125 instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2)
128 fun typ_of_dtyp _ typ_assoc (Datatype_Aux.DtTFree a) =
129 the (AList.lookup (op =) typ_assoc (Datatype_Aux.DtTFree a))
130 | typ_of_dtyp descr typ_assoc (Datatype_Aux.DtType (s, Us)) =
131 Type (s, map (typ_of_dtyp descr typ_assoc) Us)
132 | typ_of_dtyp descr typ_assoc (Datatype_Aux.DtRec i) =
133 let val (s, ds, _) = the (AList.lookup (op =) descr i) in
134 Type (s, map (typ_of_dtyp descr typ_assoc) ds)
137 fun datatype_constrs thy (T as Type (s, Ts)) =
138 (case Datatype.get_info thy s of
139 SOME {index, descr, ...} =>
140 let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
141 map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
145 | datatype_constrs _ _ = []
147 (* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
148 0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
149 cardinality 2 or more. The specified default cardinality is returned if the
150 cardinality of the type can't be determined. *)
151 fun tiny_card_of_type ctxt sound default_card T =
153 val thy = Proof_Context.theory_of ctxt
154 val max = 2 (* 1 would be too small for the "fun" case *)
155 fun aux slack avoid T =
156 if member (op =) avoid T then
159 Type (@{type_name fun}, [T1, T2]) =>
160 (case (aux slack avoid T1, aux slack avoid T2) of
161 (k, 1) => if slack andalso k = 0 then 0 else 1
165 if k1 >= max orelse k2 >= max then max
166 else Int.min (max, Integer.pow k2 k1))
168 | @{typ bool} => 2 (* optimization *)
169 | @{typ nat} => 0 (* optimization *)
170 | Type ("Int.int", []) => 0 (* optimization *)
172 (case datatype_constrs thy T of
176 map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
179 if exists (curry (op =) 0) constr_cards then 0
180 else Int.min (max, Integer.sum constr_cards)
183 case Typedef.get_info ctxt s of
184 ({abs_type, rep_type, ...}, _) :: _ =>
185 (* We cheat here by assuming that typedef types are infinite if
186 their underlying type is infinite. This is unsound in general
187 but it's hard to think of a realistic example where this would
188 not be the case. We are also slack with representation types:
189 If a representation type has the form "sigma => tau", we
190 consider it enough to check "sigma" for infiniteness. (Look
191 for "slack" in this function.) *)
192 (case varify_and_instantiate_type ctxt
193 (Logic.varifyT_global abs_type) T
194 (Logic.varifyT_global rep_type)
196 0 => if sound then default_card else 0
199 | [] => default_card)
200 (* Very slightly unsound: Type variables are assumed not to be
201 constrained to cardinality 1. (In practice, the user would most
202 likely have used "unit" directly anyway.) *)
204 if default_card = 1 andalso not sound then 2 else default_card
205 | TVar _ => default_card
206 in Int.min (max, aux false [] T) end
208 fun is_type_surely_finite ctxt sound T = tiny_card_of_type ctxt sound 0 T <> 0
209 fun is_type_surely_infinite ctxt sound T = tiny_card_of_type ctxt sound 1 T = 0
211 (* Simple simplifications to ensure that sort annotations don't leave a trail of
213 fun s_not (Const (@{const_name All}, T) $ Abs (s, T', t')) =
214 Const (@{const_name Ex}, T) $ Abs (s, T', s_not t')
215 | s_not (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
216 Const (@{const_name All}, T) $ Abs (s, T', s_not t')
217 | s_not (@{const HOL.implies} $ t1 $ t2) = @{const HOL.conj} $ t1 $ s_not t2
218 | s_not (@{const HOL.conj} $ t1 $ t2) =
219 @{const HOL.disj} $ s_not t1 $ s_not t2
220 | s_not (@{const HOL.disj} $ t1 $ t2) =
221 @{const HOL.conj} $ s_not t1 $ s_not t2
222 | s_not (@{const False}) = @{const True}
223 | s_not (@{const True}) = @{const False}
224 | s_not (@{const Not} $ t) = t
225 | s_not t = @{const Not} $ t
226 fun s_conj (@{const True}, t2) = t2
227 | s_conj (t1, @{const True}) = t1
228 | s_conj p = HOLogic.mk_conj p
229 fun s_disj (@{const False}, t2) = t2
230 | s_disj (t1, @{const False}) = t1
231 | s_disj p = HOLogic.mk_disj p
232 fun s_imp (@{const True}, t2) = t2
233 | s_imp (t1, @{const False}) = s_not t1
234 | s_imp p = HOLogic.mk_imp p
235 fun s_iff (@{const True}, t2) = t2
236 | s_iff (t1, @{const True}) = t1
237 | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
239 fun monomorphic_term subst =
240 map_types (map_type_tvar (fn v =>
241 case Type.lookup subst v of
245 fun eta_expand _ t 0 = t
246 | eta_expand Ts (Abs (s, T, t')) n =
247 Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
248 | eta_expand Ts t n =
249 fold_rev (fn T => fn t' => Abs ("x" ^ nat_subscript n, T, t'))
250 (List.take (binder_types (fastype_of1 (Ts, t)), n))
251 (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
253 (* Converts an elim-rule into an equivalent theorem that does not have the
254 predicate variable. Leaves other theorems unchanged. We simply instantiate
255 the conclusion variable to False. (Cf. "transform_elim_theorem" in
256 "Meson_Clausify".) *)
257 fun transform_elim_prop t =
258 case Logic.strip_imp_concl t of
259 @{const Trueprop} $ Var (z, @{typ bool}) =>
260 subst_Vars [(z, @{const False})] t
261 | Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t
264 fun specialize_type thy (s, T) t =
266 fun subst_for (Const (s', T')) =
268 SOME (Sign.typ_match thy (T', T) Vartab.empty)
269 handle Type.TYPE_MATCH => NONE
272 | subst_for (t1 $ t2) =
273 (case subst_for t1 of SOME x => SOME x | NONE => subst_for t2)
274 | subst_for (Abs (_, _, t')) = subst_for t'
278 SOME subst => monomorphic_term subst t
279 | NONE => raise Type.TYPE_MATCH
282 fun strip_subgoal ctxt goal i =
284 val (t, (frees, params)) =
285 Logic.goal_params (prop_of goal) i
286 ||> (map dest_Free #> Variable.variant_frees ctxt [] #> `(map Free))
287 val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees)
288 val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees
289 in (rev params, hyp_ts, concl_t) end