- outer_constraints with original variable names, to ensure that argsP is consistent with args
- Exported map_proof_same, added implies_intr_proof' and forall_intr_proof'
- Rewriting procedures used by rewrite_proof can now access hypotheses
- Finally enabled unconstrain
1 (* Title: Pure/proofterm.ML
2 Author: Stefan Berghofer, TU Muenchen
9 signature BASIC_PROOFTERM =
11 val proofs: int Unsynchronized.ref
16 | Abst of string * typ option * proof
17 | AbsP of string * term option * proof
18 | op % of proof * term option
19 | op %% of proof * proof
21 | PAxm of string * term * typ list option
22 | OfClass of typ * class
23 | Oracle of string * term * typ list option
24 | Promise of serial * term * typ list
25 | PThm of serial * ((string * term * typ list option) * proof_body future)
26 and proof_body = PBody of
27 {oracles: (string * term) OrdList.T,
28 thms: (serial * (string * term * proof_body future)) OrdList.T,
31 val %> : proof * term -> proof
36 include BASIC_PROOFTERM
38 type oracle = string * term
39 type pthm = serial * (string * term * proof_body future)
40 val proof_of: proof_body -> proof
41 val join_proof: proof_body future -> proof
42 val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
43 val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
44 val join_bodies: proof_body list -> unit
45 val status_of: proof_body list -> {failed: bool, oracle: bool, unfinished: bool}
47 val oracle_ord: oracle * oracle -> order
48 val thm_ord: pthm * pthm -> order
49 val merge_oracles: oracle OrdList.T -> oracle OrdList.T -> oracle OrdList.T
50 val merge_thms: pthm OrdList.T -> pthm OrdList.T -> pthm OrdList.T
51 val all_oracles_of: proof_body -> oracle OrdList.T
52 val approximate_proof_body: proof -> proof_body
54 (** primitive operations **)
55 val proof_combt: proof * term list -> proof
56 val proof_combt': proof * term option list -> proof
57 val proof_combP: proof * proof list -> proof
58 val strip_combt: proof -> proof * term option list
59 val strip_combP: proof -> proof * proof list
60 val strip_thm: proof_body -> proof_body
61 val map_proof_same: term Same.operation -> typ Same.operation
62 -> (typ * class -> proof) -> proof Same.operation
63 val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation
64 val map_proof_types_same: typ Same.operation -> proof Same.operation
65 val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof
66 val map_proof_types: (typ -> typ) -> proof -> proof
67 val fold_proof_terms: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a
68 val maxidx_proof: proof -> int -> int
69 val size_of_proof: proof -> int
70 val change_type: typ list option -> proof -> proof
71 val prf_abstract_over: term -> proof -> proof
72 val prf_incr_bv: int -> int -> int -> int -> proof -> proof
73 val incr_pboundvars: int -> int -> proof -> proof
74 val prf_loose_bvar1: proof -> int -> bool
75 val prf_loose_Pbvar1: proof -> int -> bool
76 val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list
77 val norm_proof: Envir.env -> proof -> proof
78 val norm_proof': Envir.env -> proof -> proof
79 val prf_subst_bounds: term list -> proof -> proof
80 val prf_subst_pbounds: proof list -> proof -> proof
81 val freeze_thaw_prf: proof -> proof * (proof -> proof)
83 (** proof terms for specific inference rules **)
84 val implies_intr_proof: term -> proof -> proof
85 val implies_intr_proof': term -> proof -> proof
86 val forall_intr_proof: term -> string -> proof -> proof
87 val forall_intr_proof': term -> proof -> proof
88 val varify_proof: term -> (string * sort) list -> proof -> proof
89 val legacy_freezeT: term -> proof -> proof
90 val rotate_proof: term list -> term -> int -> proof -> proof
91 val permute_prems_proof: term list -> int -> int -> proof -> proof
92 val generalize: string list * string list -> int -> proof -> proof
93 val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
95 val lift_proof: term -> int -> term -> proof -> proof
96 val incr_indexes: int -> proof -> proof
97 val assumption_proof: term list -> term -> int -> proof -> proof
98 val bicompose_proof: bool -> term list -> term list -> term list -> term option ->
99 int -> int -> proof -> proof -> proof
100 val equality_axms: (string * term) list
101 val reflexive_axm: proof
102 val symmetric_axm: proof
103 val transitive_axm: proof
104 val equal_intr_axm: proof
105 val equal_elim_axm: proof
106 val abstract_rule_axm: proof
107 val combination_axm: proof
109 val symmetric: proof -> proof
110 val transitive: term -> typ -> proof -> proof -> proof
111 val abstract_rule: term -> string -> proof -> proof
112 val combination: term -> term -> term -> term -> typ -> proof -> proof -> proof
113 val equal_intr: term -> term -> proof -> proof -> proof
114 val equal_elim: term -> term -> proof -> proof -> proof
115 val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list ->
116 sort list -> proof -> proof
117 val classrel_proof: theory -> class * class -> proof
118 val arity_proof: theory -> string * sort list * class -> proof
119 val of_sort_proof: theory -> (typ * class -> proof) -> typ * sort -> proof list
120 val install_axclass_proofs:
121 {classrel_proof: theory -> class * class -> proof,
122 arity_proof: theory -> string * sort list * class -> proof} -> unit
123 val axm_proof: string -> term -> proof
124 val oracle_proof: string -> term -> oracle * proof
126 (** rewriting on proof terms **)
127 val add_prf_rrule: proof * proof -> theory -> theory
128 val add_prf_rproc: (typ list -> term option list -> proof -> (proof * proof) option) -> theory -> theory
130 val normal_skel: proof
131 val rewrite_proof: theory -> (proof * proof) list *
132 (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
133 val rewrite_proof_notypes: (proof * proof) list *
134 (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
135 val rew_proof: theory -> proof -> proof
137 val promise_proof: theory -> serial -> term -> proof
138 val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
139 val unconstrain_thm_proofs: bool Unsynchronized.ref
140 val thm_proof: theory -> string -> sort list -> term list -> term ->
141 (serial * proof_body future) list -> proof_body -> pthm * proof
142 val unconstrain_thm_proof: theory -> sort list -> term ->
143 (serial * proof_body future) list -> proof_body -> pthm * proof
144 val get_name: term list -> term -> proof -> string
145 val get_name_unconstrained: sort list -> term list -> term -> proof -> string
146 val guess_name: proof -> string
149 structure Proofterm : PROOFTERM =
152 (***** datatype proof *****)
157 | Abst of string * typ option * proof
158 | AbsP of string * term option * proof
159 | op % of proof * term option
160 | op %% of proof * proof
162 | PAxm of string * term * typ list option
163 | OfClass of typ * class
164 | Oracle of string * term * typ list option
165 | Promise of serial * term * typ list
166 | PThm of serial * ((string * term * typ list option) * proof_body future)
167 and proof_body = PBody of
168 {oracles: (string * term) OrdList.T,
169 thms: (serial * (string * term * proof_body future)) OrdList.T,
172 type oracle = string * term;
173 type pthm = serial * (string * term * proof_body future);
175 fun proof_of (PBody {proof, ...}) = proof;
176 val join_proof = Future.join #> proof_of;
179 (***** proof atoms *****)
181 fun fold_proof_atoms all f =
183 fun app (Abst (_, _, prf)) = app prf
184 | app (AbsP (_, _, prf)) = app prf
185 | app (prf % _) = app prf
186 | app (prf1 %% prf2) = app prf1 #> app prf2
187 | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
188 if Inttab.defined seen i then (x, seen)
190 let val (x', seen') =
191 (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
192 in (f prf x', seen') end)
193 | app prf = (fn (x, seen) => (f prf x, seen));
194 in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
196 fun fold_body_thms f =
198 fun app (PBody {thms, ...}) =
199 (Future.join_results (map (#3 o #2) thms);
200 thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
201 if Inttab.defined seen i then (x, seen)
204 val body' = Future.join body;
205 val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
206 in (f (name, prop, body') x', seen') end));
207 in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
209 fun join_bodies bodies = fold_body_thms (fn _ => fn () => ()) bodies ();
211 fun status_of bodies =
213 fun status (PBody {oracles, thms, ...}) x =
215 val ((oracle, unfinished, failed), seen) =
216 (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
217 if Inttab.defined seen i then (st, seen)
219 let val seen' = Inttab.update (i, ()) seen in
220 (case Future.peek body of
221 SOME (Exn.Result body') => status body' (st, seen')
222 | SOME (Exn.Exn _) =>
223 let val (oracle, unfinished, _) = st
224 in ((oracle, unfinished, true), seen') end
226 let val (oracle, _, failed) = st
227 in ((oracle, true, failed), seen') end)
229 in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
230 val (oracle, unfinished, failed) =
231 #1 (fold status bodies ((false, false, false), Inttab.empty));
232 in {oracle = oracle, unfinished = unfinished, failed = failed} end;
237 val oracle_ord = prod_ord fast_string_ord Term_Ord.fast_term_ord;
238 fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
240 val merge_oracles = OrdList.union oracle_ord;
241 val merge_thms = OrdList.union thm_ord;
245 fun collect (PBody {oracles, thms, ...}) =
246 (Future.join_results (map (#3 o #2) thms);
247 thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
248 if Inttab.defined seen i then (x, seen)
251 val body' = Future.join body;
252 val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
253 in (merge_oracles oracles x', seen') end));
254 in fn body => #1 (collect body ([], Inttab.empty)) end;
256 fun approximate_proof_body prf =
258 val (oracles, thms) = fold_proof_atoms false
259 (fn Oracle (s, prop, _) => apfst (cons (s, prop))
260 | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
261 | _ => I) [prf] ([], []);
264 {oracles = OrdList.make oracle_ord oracles,
265 thms = OrdList.make thm_ord thms,
270 (***** proof objects with different levels of detail *****)
272 fun (prf %> t) = prf % SOME t;
274 val proof_combt = Library.foldl (op %>);
275 val proof_combt' = Library.foldl (op %);
276 val proof_combP = Library.foldl (op %%);
278 fun strip_combt prf =
279 let fun stripc (prf % t, ts) = stripc (prf, t::ts)
281 in stripc (prf, []) end;
283 fun strip_combP prf =
284 let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
286 in stripc (prf, []) end;
288 fun strip_thm (body as PBody {proof, ...}) =
289 (case strip_combt (fst (strip_combP proof)) of
290 (PThm (_, (_, body')), _) => Future.join body'
293 val mk_Abst = fold_rev (fn (s, T:typ) => fn prf => Abst (s, NONE, prf));
294 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
296 fun map_proof_same term typ ofclass =
298 val typs = Same.map typ;
300 fun proof (Abst (s, T, prf)) =
301 (Abst (s, Same.map_option typ T, Same.commit proof prf)
302 handle Same.SAME => Abst (s, T, proof prf))
303 | proof (AbsP (s, t, prf)) =
304 (AbsP (s, Same.map_option term t, Same.commit proof prf)
305 handle Same.SAME => AbsP (s, t, proof prf))
307 (proof prf % Same.commit (Same.map_option term) t
308 handle Same.SAME => prf % Same.map_option term t)
309 | proof (prf1 %% prf2) =
310 (proof prf1 %% Same.commit proof prf2
311 handle Same.SAME => prf1 %% proof prf2)
312 | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
313 | proof (OfClass T_c) = ofclass T_c
314 | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
315 | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
316 | proof (PThm (i, ((a, prop, SOME Ts), body))) =
317 PThm (i, ((a, prop, SOME (typs Ts)), body))
318 | proof _ = raise Same.SAME;
321 fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
322 fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
326 in if eq (x, x') then raise Same.SAME else x' end;
328 fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
329 fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
331 fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
332 | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
333 | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
334 | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
335 | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
336 | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
337 | fold_proof_terms f g (prf1 %% prf2) =
338 fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
339 | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
340 | fold_proof_terms _ g (OfClass (T, _)) = g T
341 | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
342 | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
343 | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
344 | fold_proof_terms _ _ _ = I;
346 fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
348 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
349 | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
350 | size_of_proof (prf % _) = 1 + size_of_proof prf
351 | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
352 | size_of_proof _ = 1;
354 fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
355 | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
356 | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
357 | change_type opTs (Promise _) = raise Fail "change_type: unexpected promise"
358 | change_type opTs (PThm (i, ((name, prop, _), body))) =
359 PThm (i, ((name, prop, opTs), body))
360 | change_type _ prf = prf;
363 (***** utilities *****)
365 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
368 fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
371 (*Abstraction of a proof term over its occurrences of v,
372 which must contain no loose bound variables.
373 The resulting proof term is ready to become the body of an Abst.*)
375 fun prf_abstract_over v =
377 fun abst' lev u = if v aconv u then Bound lev else
379 Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
380 | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
381 | _ => raise Same.SAME)
382 and absth' lev t = (abst' lev t handle Same.SAME => t);
384 fun abst lev (AbsP (a, t, prf)) =
385 (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
386 handle Same.SAME => AbsP (a, t, abst lev prf))
387 | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
388 | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
389 handle Same.SAME => prf1 %% abst lev prf2)
390 | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
391 handle Same.SAME => prf % Same.map_option (abst' lev) t)
392 | abst _ _ = raise Same.SAME
393 and absth lev prf = (abst lev prf handle Same.SAME => prf);
398 (*increments a proof term's non-local bound variables
399 required when moving a proof term within abstractions
400 inc is increment for bound variables
401 lev is level at which a bound variable is considered 'loose'*)
403 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
405 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
406 if i >= Plev then PBound (i+incP) else raise Same.SAME
407 | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
408 (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
409 prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
410 AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
411 | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
412 Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
413 | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
414 (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
415 handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
416 | prf_incr_bv' incP inct Plev tlev (prf % t) =
417 (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
418 handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
419 | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
420 and prf_incr_bv incP inct Plev tlev prf =
421 (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
423 fun incr_pboundvars 0 0 prf = prf
424 | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
427 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
428 | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
429 | prf_loose_bvar1 (_ % NONE) _ = true
430 | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
431 | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
432 | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
433 | prf_loose_bvar1 _ _ = false;
435 fun prf_loose_Pbvar1 (PBound i) k = i = k
436 | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
437 | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
438 | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
439 | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
440 | prf_loose_Pbvar1 _ _ = false;
442 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
443 if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
444 | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
445 prf_add_loose_bnos plev tlev prf2
446 (prf_add_loose_bnos plev tlev prf1 p)
447 | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
448 prf_add_loose_bnos plev tlev prf (case opt of
449 NONE => (is, insert (op =) ~1 js)
450 | SOME t => (is, add_loose_bnos (t, tlev, js)))
451 | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
452 prf_add_loose_bnos (plev+1) tlev prf (case opt of
453 NONE => (is, insert (op =) ~1 js)
454 | SOME t => (is, add_loose_bnos (t, tlev, js)))
455 | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
456 prf_add_loose_bnos plev (tlev+1) prf p
457 | prf_add_loose_bnos _ _ _ _ = ([], []);
460 (**** substitutions ****)
462 fun del_conflicting_tvars envT T = Term_Subst.instantiateT
463 (map_filter (fn ixnS as (_, S) =>
464 (Type.lookup envT ixnS; NONE) handle TYPE _ =>
465 SOME (ixnS, TFree ("'dummy", S))) (OldTerm.typ_tvars T)) T;
467 fun del_conflicting_vars env t = Term_Subst.instantiate
468 (map_filter (fn ixnS as (_, S) =>
469 (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
470 SOME (ixnS, TFree ("'dummy", S))) (OldTerm.term_tvars t),
471 map_filter (fn Var (ixnT as (_, T)) =>
472 (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
473 SOME (ixnT, Free ("dummy", T))) (OldTerm.term_vars t)) t;
477 val envT = Envir.type_env env;
478 fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
479 fun htype f t = f env t handle TYPE (s, _, _) =>
480 (msg s; f env (del_conflicting_vars env t));
481 fun htypeT f T = f envT T handle TYPE (s, _, _) =>
482 (msg s; f envT (del_conflicting_tvars envT T));
483 fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
484 (msg s; f envT (map (del_conflicting_tvars envT) Ts));
486 fun norm (Abst (s, T, prf)) =
487 (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
488 handle Same.SAME => Abst (s, T, norm prf))
489 | norm (AbsP (s, t, prf)) =
490 (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
491 handle Same.SAME => AbsP (s, t, norm prf))
493 (norm prf % Option.map (htype Envir.norm_term) t
494 handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
495 | norm (prf1 %% prf2) =
496 (norm prf1 %% Same.commit norm prf2
497 handle Same.SAME => prf1 %% norm prf2)
498 | norm (PAxm (s, prop, Ts)) =
499 PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
500 | norm (OfClass (T, c)) =
501 OfClass (htypeT Envir.norm_type_same T, c)
502 | norm (Oracle (s, prop, Ts)) =
503 Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
504 | norm (Promise (i, prop, Ts)) =
505 Promise (i, prop, htypeTs Envir.norm_types_same Ts)
506 | norm (PThm (i, ((s, t, Ts), body))) =
507 PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
508 | norm _ = raise Same.SAME;
509 in Same.commit norm end;
512 (***** Remove some types in proof term (to save space) *****)
514 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
515 | remove_types (t $ u) = remove_types t $ remove_types u
516 | remove_types (Const (s, _)) = Const (s, dummyT)
517 | remove_types t = t;
519 fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
520 Envir.Envir {maxidx = maxidx, tenv = Vartab.map (apsnd remove_types) tenv, tyenv = tyenv};
522 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
525 (**** substitution of bound variables ****)
527 fun prf_subst_bounds args prf =
530 fun subst' lev (Bound i) =
531 (if i<lev then raise Same.SAME (*var is locally bound*)
532 else incr_boundvars lev (nth args (i-lev))
533 handle Subscript => Bound (i-n)) (*loose: change it*)
534 | subst' lev (Abs (a, T, body)) = Abs (a, T, subst' (lev+1) body)
535 | subst' lev (f $ t) = (subst' lev f $ substh' lev t
536 handle Same.SAME => f $ subst' lev t)
537 | subst' _ _ = raise Same.SAME
538 and substh' lev t = (subst' lev t handle Same.SAME => t);
540 fun subst lev (AbsP (a, t, body)) =
541 (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
542 handle Same.SAME => AbsP (a, t, subst lev body))
543 | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
544 | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
545 handle Same.SAME => prf %% subst lev prf')
546 | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
547 handle Same.SAME => prf % Same.map_option (subst' lev) t)
548 | subst _ _ = raise Same.SAME
549 and substh lev prf = (subst lev prf handle Same.SAME => prf);
550 in case args of [] => prf | _ => substh 0 prf end;
552 fun prf_subst_pbounds args prf =
555 fun subst (PBound i) Plev tlev =
556 (if i < Plev then raise Same.SAME (*var is locally bound*)
557 else incr_pboundvars Plev tlev (nth args (i-Plev))
558 handle Subscript => PBound (i-n) (*loose: change it*))
559 | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
560 | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
561 | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
562 handle Same.SAME => prf %% subst prf' Plev tlev)
563 | subst (prf % t) Plev tlev = subst prf Plev tlev % t
564 | subst prf _ _ = raise Same.SAME
565 and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
566 in case args of [] => prf | _ => substh prf 0 0 end;
569 (**** Freezing and thawing of variables in proof terms ****)
572 map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
575 map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
576 NONE => TFree (s, xs)
577 | SOME ixn => TVar (ixn, xs));
579 fun freeze names names' (t $ u) =
580 freeze names names' t $ freeze names names' u
581 | freeze names names' (Abs (s, T, t)) =
582 Abs (s, frzT names' T, freeze names names' t)
583 | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
584 | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
585 | freeze names names' (Var (ixn, T)) =
586 Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
587 | freeze names names' t = t;
589 fun thaw names names' (t $ u) =
590 thaw names names' t $ thaw names names' u
591 | thaw names names' (Abs (s, T, t)) =
592 Abs (s, thawT names' T, thaw names names' t)
593 | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
594 | thaw names names' (Free (s, T)) =
595 let val T' = thawT names' T
596 in case AList.lookup (op =) names s of
598 | SOME ixn => Var (ixn, T')
600 | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
601 | thaw names names' t = t;
603 fun freeze_thaw_prf prf =
605 val (fs, Tfs, vs, Tvs) = fold_proof_terms
606 (fn t => fn (fs, Tfs, vs, Tvs) =>
607 (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
608 Term.add_var_names t vs, Term.add_tvar_names t Tvs))
609 (fn T => fn (fs, Tfs, vs, Tvs) =>
610 (fs, Term.add_tfree_namesT T Tfs,
611 vs, Term.add_tvar_namesT T Tvs))
612 prf ([], [], [], []);
613 val names = vs ~~ Name.variant_list fs (map fst vs);
614 val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
615 val rnames = map swap names;
616 val rnames' = map swap names';
618 (map_proof_terms (freeze names names') (frzT names') prf,
619 map_proof_terms (thaw rnames rnames') (thawT rnames'))
623 (***** implication introduction *****)
625 fun gen_implies_intr_proof f h prf =
627 fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
628 | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
629 | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
630 | abshyp i (prf % t) = abshyp i prf % t
631 | abshyp i (prf1 %% prf2) =
632 (abshyp i prf1 %% abshyph i prf2
633 handle Same.SAME => prf1 %% abshyp i prf2)
634 | abshyp _ _ = raise Same.SAME
635 and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
637 AbsP ("H", f h, abshyph 0 prf)
640 val implies_intr_proof = gen_implies_intr_proof (K NONE);
641 val implies_intr_proof' = gen_implies_intr_proof SOME;
644 (***** forall introduction *****)
646 fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
648 fun forall_intr_proof' t prf =
649 let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
650 in Abst (a, SOME T, prf_abstract_over t prf) end;
655 fun varify_proof t fixed prf =
657 val fs = Term.fold_types (Term.fold_atyps
658 (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
659 val used = Name.context
660 |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
661 val fmap = fs ~~ #1 (Name.variants (map fst fs) used);
662 fun thaw (f as (a, S)) =
663 (case AList.lookup (op =) fmap f of
665 | SOME b => TVar ((b, 0), S));
666 in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
671 fun new_name (ix, (pairs,used)) =
672 let val v = Name.variant used (string_of_indexname ix)
673 in ((ix, v) :: pairs, v :: used) end;
675 fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
676 NONE => TVar (ix, sort)
677 | SOME name => TFree (name, sort));
681 fun legacy_freezeT t prf =
683 val used = OldTerm.it_term_types OldTerm.add_typ_tfree_names (t, [])
684 and tvars = map #1 (OldTerm.it_term_types OldTerm.add_typ_tvars (t, []));
685 val (alist, _) = List.foldr new_name ([], used) tvars;
688 [] => prf (*nothing to do!*)
690 let val frzT = map_type_tvar (freeze_one alist)
691 in map_proof_terms (map_types frzT) frzT prf end)
697 (***** rotate assumptions *****)
699 fun rotate_proof Bs Bi m prf =
701 val params = Term.strip_all_vars Bi;
702 val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
706 mk_AbsP (j+1, proof_combP (prf, map PBound
707 (j downto 1) @ [mk_Abst params (mk_AbsP (i,
708 proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
709 map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
713 (***** permute premises *****)
715 fun permute_prems_proof prems j k prf =
716 let val n = length prems
717 in mk_AbsP (n, proof_combP (prf,
718 map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
722 (***** generalization *****)
724 fun generalize (tfrees, frees) idx =
725 Same.commit (map_proof_terms_same
726 (Term_Subst.generalize_same (tfrees, frees) idx)
727 (Term_Subst.generalizeT_same tfrees idx));
730 (***** instantiation *****)
732 fun instantiate (instT, inst) =
733 Same.commit (map_proof_terms_same
734 (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
735 (Term_Subst.instantiateT_same instT));
738 (***** lifting *****)
740 fun lift_proof Bi inc prop prf =
743 strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
745 fun lift' Us Ts (Abst (s, T, prf)) =
746 (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
747 handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
748 | lift' Us Ts (AbsP (s, t, prf)) =
749 (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
750 handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
751 | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
752 handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
753 | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
754 handle Same.SAME => prf1 %% lift' Us Ts prf2)
755 | lift' _ _ (PAxm (s, prop, Ts)) =
756 PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
757 | lift' _ _ (OfClass (T, c)) =
758 OfClass (Logic.incr_tvar_same inc T, c)
759 | lift' _ _ (Oracle (s, prop, Ts)) =
760 Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
761 | lift' _ _ (Promise (i, prop, Ts)) =
762 Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
763 | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
764 PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
765 | lift' _ _ _ = raise Same.SAME
766 and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
768 val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
771 fun mk_app b (i, j, prf) =
772 if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
774 fun lift Us bs i j (Const ("==>", _) $ A $ B) =
775 AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
776 | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
777 Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
778 | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
779 map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
780 (i + k - 1 downto i));
782 mk_AbsP (k, lift [] [] 0 0 Bi)
786 Same.commit (map_proof_terms_same
787 (Logic.incr_indexes_same ([], i)) (Logic.incr_tvar_same i));
790 (***** proof by assumption *****)
792 fun mk_asm_prf t i m =
794 fun imp_prf _ i 0 = PBound i
795 | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
796 | imp_prf _ i _ = PBound i;
797 fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
798 | all_prf t = imp_prf t (~i) m
801 fun assumption_proof Bs Bi n prf =
802 mk_AbsP (length Bs, proof_combP (prf,
803 map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
806 (***** Composition of object rule with proof state *****)
808 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
809 AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
810 | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
811 Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
812 | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
813 map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
815 fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
817 val la = length newAs;
820 mk_AbsP (lb+la, proof_combP (sprf,
821 map PBound (lb + la - 1 downto la)) %%
822 proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
823 map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
824 (oldAs ~~ (la - 1 downto 0))))
828 (***** axioms for equality *****)
830 val aT = TFree ("'a", []);
831 val bT = TFree ("'b", []);
832 val x = Free ("x", aT);
833 val y = Free ("y", aT);
834 val z = Free ("z", aT);
835 val A = Free ("A", propT);
836 val B = Free ("B", propT);
837 val f = Free ("f", aT --> bT);
838 val g = Free ("g", aT --> bT);
841 [("reflexive", Logic.mk_equals (x, x)),
842 ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
844 Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
846 Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
847 ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
851 (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
852 ("combination", Logic.list_implies
853 ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
855 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
856 equal_elim_axm, abstract_rule_axm, combination_axm] =
857 map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
859 val reflexive = reflexive_axm % NONE;
861 fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
862 | symmetric prf = symmetric_axm % NONE % NONE %% prf;
864 fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
865 | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
866 | transitive u (Type ("prop", [])) prf1 prf2 =
867 transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
868 | transitive u T prf1 prf2 =
869 transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
871 fun abstract_rule x a prf =
872 abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
874 fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
875 is_some f orelse check_comb prf
876 | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
877 check_comb prf1 andalso check_comb prf2
878 | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
879 | check_comb _ = false;
881 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
883 val f = Envir.beta_norm f;
884 val g = Envir.beta_norm g;
885 val prf = if check_comb prf1 then
886 combination_axm % NONE % NONE
888 PAxm ("Pure.reflexive", _, _) % _ =>
889 combination_axm %> remove_types f % NONE
890 | _ => combination_axm %> remove_types f %> remove_types g)
893 Type ("fun", _) => prf %
895 Abs _ => SOME (remove_types t)
896 | Var _ => SOME (remove_types t)
899 Abs _ => SOME (remove_types u)
900 | Var _ => SOME (remove_types u)
901 | _ => NONE) %% prf1 %% prf2
902 | _ => prf % NONE % NONE %% prf1 %% prf2)
905 fun equal_intr A B prf1 prf2 =
906 equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
908 fun equal_elim A B prf1 prf2 =
909 equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
912 (**** type classes ****)
914 fun strip_shyps_proof algebra present witnessed extra_sorts prf =
916 fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
917 val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
918 val replacements = present @ extra @ witnessed;
920 if exists (fn (T', _) => T' = T) present then raise Same.SAME
922 (case get_first (get (Type.sort_of_atyp T)) replacements of
924 | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
925 in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
930 type axclass_proofs =
931 {classrel_proof: theory -> class * class -> proof,
932 arity_proof: theory -> string * sort list * class -> proof};
934 val axclass_proofs: axclass_proofs Single_Assignment.var =
935 Single_Assignment.var "Proofterm.axclass_proofs";
937 fun axclass_proof which thy x =
938 (case Single_Assignment.peek axclass_proofs of
939 NONE => raise Fail "Axclass proof operations not installed"
940 | SOME prfs => which prfs thy x);
944 val classrel_proof = axclass_proof #classrel_proof;
945 val arity_proof = axclass_proof #arity_proof;
947 fun install_axclass_proofs prfs = Single_Assignment.assign axclass_proofs prfs;
954 fun canonical_instance typs =
956 val names = Name.invents Name.context Name.aT (length typs);
957 val instT = map2 (fn a => fn T => (((a, 0), []), Type.strip_sorts T)) names typs;
958 in instantiate (instT, []) end;
962 fun of_sort_proof thy hyps =
963 Sorts.of_sort_derivation (Sign.classes_of thy)
964 {class_relation = fn typ => fn (prf, c1) => fn c2 =>
966 else canonical_instance [typ] (classrel_proof thy (c1, c2)) %% prf,
967 type_constructor = fn (a, typs) => fn dom => fn c =>
968 let val Ss = map (map snd) dom and prfs = maps (map fst) dom
969 in proof_combP (canonical_instance typs (arity_proof thy (a, Ss, c)), prfs) end,
970 type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)};
975 (***** axioms and theorems *****)
977 val proofs = Unsynchronized.ref 2;
979 fun vars_of t = map Var (rev (Term.add_vars t []));
980 fun frees_of t = map Free (rev (Term.add_frees t []));
982 fun test_args _ [] = true
983 | test_args is (Bound i :: ts) =
984 not (member (op =) is i) andalso test_args (i :: is) ts
985 | test_args _ _ = false;
987 fun is_fun (Type ("fun", _)) = true
988 | is_fun (TVar _) = true
991 fun add_funvars Ts (vs, t) =
992 if is_fun (fastype_of1 (Ts, t)) then
993 union (op =) vs (map_filter (fn Var (ixn, T) =>
994 if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
997 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
998 add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
999 | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
1000 add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
1001 | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
1002 | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
1003 and add_npvars' Ts (vs, t) = (case strip_comb t of
1004 (Var (ixn, _), ts) => if test_args [] ts then vs
1005 else Library.foldl (add_npvars' Ts)
1006 (AList.update (op =) (ixn,
1007 Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
1008 | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
1009 | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
1011 fun prop_vars (Const ("==>", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
1012 | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
1013 | prop_vars t = (case strip_comb t of
1014 (Var (ixn, _), _) => [ixn] | _ => []);
1018 fun is_p i t = (case strip_comb t of
1019 (Bound j, []) => false
1020 | (Bound j, ts) => j >= i orelse exists (is_p i) ts
1021 | (Abs (_, _, u), _) => is_p (i+1) u
1022 | (_, ts) => exists (is_p i) ts)
1023 in (case strip_abs_body t of
1028 fun needed_vars prop =
1029 union (op =) (Library.foldl (uncurry (union (op =)))
1030 ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
1033 fun gen_axm_proof c name prop =
1035 val nvs = needed_vars prop;
1036 val args = map (fn (v as Var (ixn, _)) =>
1037 if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
1038 map SOME (frees_of prop);
1040 proof_combt' (c (name, prop, NONE), args)
1043 val axm_proof = gen_axm_proof PAxm;
1045 val dummy = Const (Term.dummy_patternN, dummyT);
1047 fun oracle_proof name prop =
1048 if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
1049 else ((name, prop), gen_axm_proof Oracle name prop);
1053 fun shrink ls lev (prf as Abst (a, T, body)) =
1054 let val (b, is, ch, body') = shrink ls (lev+1) body
1055 in (b, is, ch, if ch then Abst (a, T, body') else prf) end
1056 | shrink ls lev (prf as AbsP (a, t, body)) =
1057 let val (b, is, ch, body') = shrink (lev::ls) lev body
1058 in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
1059 ch, if ch then AbsP (a, t, body') else prf)
1061 | shrink ls lev prf =
1062 let val (is, ch, _, prf') = shrink' ls lev [] [] prf
1063 in (false, is, ch, prf') end
1064 and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
1066 val p as (_, is', ch', prf') = shrink ls lev prf2;
1067 val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
1068 in (union (op =) is is', ch orelse ch', ts',
1069 if ch orelse ch' then prf'' %% prf' else prf)
1071 | shrink' ls lev ts prfs (prf as prf1 % t) =
1072 let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
1073 in (is, ch orelse ch', ts',
1074 if ch orelse ch' then prf' % t' else prf) end
1075 | shrink' ls lev ts prfs (prf as PBound i) =
1076 (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
1077 orelse has_duplicates (op =)
1078 (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
1079 orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
1080 | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
1081 | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
1082 | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
1083 | shrink' ls lev ts prfs prf =
1087 PAxm (_, prop, _) => prop
1088 | Oracle (_, prop, _) => prop
1089 | Promise (_, prop, _) => prop
1090 | PThm (_, ((_, prop, _), _)) => prop
1091 | _ => raise Fail "shrink: proof not in normal form");
1092 val vs = vars_of prop;
1093 val (ts', ts'') = chop (length vs) ts;
1094 val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
1095 val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
1096 insert (op =) ixn (case AList.lookup (op =) insts ixn of
1097 SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
1098 | _ => union (op =) ixns ixns'))
1099 (needed prop ts'' prfs, add_npvars false true [] ([], prop));
1101 (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
1102 | (_, x) => (false, x)) insts
1103 in ([], false, insts' @ map (pair false) ts'', prf) end
1104 and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
1105 union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
1106 | needed (Var (ixn, _)) (_::_) _ = [ixn]
1107 | needed _ _ _ = [];
1111 (**** Simple first order matching functions for terms and proofs ****)
1115 (** see pattern.ML **)
1117 fun flt (i: int) = filter (fn n => n < i);
1119 fun fomatch Ts tymatch j instsp p =
1121 fun mtch (instsp as (tyinsts, insts)) = fn
1122 (Var (ixn, T), t) =>
1123 if j>0 andalso not (null (flt j (loose_bnos t)))
1125 else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
1127 | (Free (a, T), Free (b, U)) =>
1128 if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
1129 | (Const (a, T), Const (b, U)) =>
1130 if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
1131 | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
1132 | (Bound i, Bound j) => if i=j then instsp else raise PMatch
1134 in mtch instsp (pairself Envir.beta_eta_contract p) end;
1136 fun match_proof Ts tymatch =
1138 fun optmatch _ inst (NONE, _) = inst
1139 | optmatch _ _ (SOME _, NONE) = raise PMatch
1140 | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
1142 fun matcht Ts j (pinst, tinst) (t, u) =
1143 (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
1144 fun matchT (pinst, (tyinsts, insts)) p =
1145 (pinst, (tymatch (tyinsts, K p), insts));
1146 fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
1148 fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
1149 if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
1150 else (case apfst (flt i) (apsnd (flt j)
1151 (prf_add_loose_bnos 0 0 prf ([], []))) of
1152 ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
1153 | ([], _) => if j = 0 then
1154 ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
1156 | _ => raise PMatch)
1157 | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
1158 optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
1159 | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
1160 mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
1161 | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
1162 mtch (the_default dummyT opU :: Ts) i (j+1)
1163 (optmatch matchT inst (opT, opU)) (prf1, prf2)
1164 | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
1165 mtch (the_default dummyT opU :: Ts) i (j+1) inst
1166 (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
1167 | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
1168 mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
1169 | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
1170 mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
1171 | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
1172 if s1 = s2 then optmatch matchTs inst (opTs, opUs)
1174 | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
1175 if c1 = c2 then matchT inst (T1, T2)
1177 | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
1178 if name1 = name2 andalso prop1 = prop2 then
1179 optmatch matchTs inst (opTs, opUs)
1181 | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
1182 | mtch _ _ _ _ _ = raise PMatch
1185 fun prf_subst (pinst, (tyinsts, insts)) =
1187 val substT = Envir.subst_type_same tyinsts;
1188 val substTs = Same.map substT;
1190 fun subst' lev (Var (xi, _)) =
1191 (case AList.lookup (op =) insts xi of
1192 NONE => raise Same.SAME
1193 | SOME u => incr_boundvars lev u)
1194 | subst' _ (Const (s, T)) = Const (s, substT T)
1195 | subst' _ (Free (s, T)) = Free (s, substT T)
1196 | subst' lev (Abs (a, T, body)) =
1197 (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
1198 handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
1199 | subst' lev (f $ t) =
1200 (subst' lev f $ Same.commit (subst' lev) t
1201 handle Same.SAME => f $ subst' lev t)
1202 | subst' _ _ = raise Same.SAME;
1204 fun subst plev tlev (AbsP (a, t, body)) =
1205 (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
1206 handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
1207 | subst plev tlev (Abst (a, T, body)) =
1208 (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
1209 handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
1210 | subst plev tlev (prf %% prf') =
1211 (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
1212 handle Same.SAME => prf %% subst plev tlev prf')
1213 | subst plev tlev (prf % t) =
1214 (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
1215 handle Same.SAME => prf % Same.map_option (subst' tlev) t)
1216 | subst plev tlev (Hyp (Var (xi, _))) =
1217 (case AList.lookup (op =) pinst xi of
1218 NONE => raise Same.SAME
1219 | SOME prf' => incr_pboundvars plev tlev prf')
1220 | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
1221 | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
1222 | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
1223 | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
1224 | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
1225 PThm (i, ((id, prop, Same.map_option substTs Ts), body))
1226 | subst _ _ _ = raise Same.SAME;
1227 in fn t => subst 0 0 t handle Same.SAME => t end;
1229 (*A fast unification filter: true unless the two terms cannot be unified.
1230 Terms must be NORMAL. Treats all Vars as distinct. *)
1231 fun could_unify prf1 prf2 =
1233 fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
1234 could_unify prf2 prf2' andalso matchrands prf1 prf1'
1235 | matchrands (prf % SOME t) (prf' % SOME t') =
1236 Term.could_unify (t, t') andalso matchrands prf prf'
1237 | matchrands (prf % _) (prf' % _) = matchrands prf prf'
1238 | matchrands _ _ = true
1240 fun head_of (prf %% _) = head_of prf
1241 | head_of (prf % _) = head_of prf
1244 in case (head_of prf1, head_of prf2) of
1245 (_, Hyp (Var _)) => true
1246 | (Hyp (Var _), _) => true
1247 | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
1248 | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
1249 | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
1250 a = b andalso propa = propb andalso matchrands prf1 prf2
1251 | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
1252 | (AbsP _, _) => true (*because of possible eta equality*)
1253 | (Abst _, _) => true
1254 | (_, AbsP _) => true
1255 | (_, Abst _) => true
1260 (**** rewriting on proof terms ****)
1262 val no_skel = PBound 0;
1263 val normal_skel = Hyp (Var ((Name.uu, 0), propT));
1265 fun rewrite_prf tymatch (rules, procs) prf =
1267 fun rew _ _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
1268 | rew _ _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
1270 (case get_first (fn r => r Ts hs prf) procs of
1271 NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
1272 (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
1273 handle PMatch => NONE) (filter (could_unify prf o fst) rules)
1276 fun rew0 Ts hs (prf as AbsP (_, _, prf' %% PBound 0)) =
1277 if prf_loose_Pbvar1 prf' 0 then rew Ts hs prf
1279 let val prf'' = incr_pboundvars (~1) 0 prf'
1280 in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
1281 | rew0 Ts hs (prf as Abst (_, _, prf' % SOME (Bound 0))) =
1282 if prf_loose_bvar1 prf' 0 then rew Ts hs prf
1284 let val prf'' = incr_pboundvars 0 (~1) prf'
1285 in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
1286 | rew0 Ts hs prf = rew Ts hs prf;
1288 fun rew1 _ _ (Hyp (Var _)) _ = NONE
1289 | rew1 Ts hs skel prf = (case rew2 Ts hs skel prf of
1290 SOME prf1 => (case rew0 Ts hs prf1 of
1291 SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts hs skel' prf2))
1292 | NONE => SOME prf1)
1293 | NONE => (case rew0 Ts hs prf of
1294 SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts hs skel' prf1))
1297 and rew2 Ts hs skel (prf % SOME t) = (case prf of
1298 Abst (_, _, body) =>
1299 let val prf' = prf_subst_bounds [t] body
1300 in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
1301 | _ => (case rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf of
1302 SOME prf' => SOME (prf' % SOME t)
1304 | rew2 Ts hs skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
1305 (rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf)
1306 | rew2 Ts hs skel (prf1 %% prf2) = (case prf1 of
1307 AbsP (_, _, body) =>
1308 let val prf' = prf_subst_pbounds [prf2] body
1309 in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
1311 let val (skel1, skel2) = (case skel of
1312 skel1 %% skel2 => (skel1, skel2)
1313 | _ => (no_skel, no_skel))
1314 in case rew1 Ts hs skel1 prf1 of
1315 SOME prf1' => (case rew1 Ts hs skel2 prf2 of
1316 SOME prf2' => SOME (prf1' %% prf2')
1317 | NONE => SOME (prf1' %% prf2))
1318 | NONE => (case rew1 Ts hs skel2 prf2 of
1319 SOME prf2' => SOME (prf1 %% prf2')
1322 | rew2 Ts hs skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts) hs
1323 (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
1324 SOME prf' => SOME (Abst (s, T, prf'))
1326 | rew2 Ts hs skel (AbsP (s, t, prf)) = (case rew1 Ts (t :: hs)
1327 (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
1328 SOME prf' => SOME (AbsP (s, t, prf'))
1330 | rew2 _ _ _ _ = NONE;
1332 in the_default prf (rew1 [] [] no_skel prf) end;
1334 fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
1335 Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
1337 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
1340 (**** theory data ****)
1342 structure ProofData = Theory_Data
1345 (stamp * (proof * proof)) list *
1346 (stamp * (typ list -> term option list -> proof -> (proof * proof) option)) list;
1348 val empty = ([], []);
1350 fun merge ((rules1, procs1), (rules2, procs2)) : T =
1351 (AList.merge (op =) (K true) (rules1, rules2),
1352 AList.merge (op =) (K true) (procs1, procs2));
1355 fun get_data thy = let val (rules, procs) = ProofData.get thy in (map #2 rules, map #2 procs) end;
1356 fun rew_proof thy = rewrite_prf fst (get_data thy);
1358 fun add_prf_rrule r = (ProofData.map o apfst) (cons (stamp (), r));
1359 fun add_prf_rproc p = (ProofData.map o apsnd) (cons (stamp (), p));
1362 (***** promises *****)
1364 fun promise_proof thy i prop =
1366 val _ = prop |> Term.exists_subterm (fn t =>
1367 (Term.is_Free t orelse Term.is_Var t) andalso
1368 raise Fail ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
1369 val _ = prop |> Term.exists_type (Term.exists_subtype
1370 (fn TFree (a, _) => raise Fail ("promise_proof: illegal type variable " ^ quote a)
1372 in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
1374 fun fulfill_norm_proof thy ps body0 =
1376 val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
1377 val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
1378 val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
1379 val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
1381 fun fill (Promise (i, prop, Ts)) =
1382 (case Inttab.lookup proofs i of
1384 | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
1386 val (rules, procs) = get_data thy;
1387 val proof = rewrite_prf fst (rules, K (K fill) :: procs) proof0;
1388 in PBody {oracles = oracles, thms = thms, proof = proof} end;
1390 fun fulfill_proof_future _ [] postproc body = Future.value (postproc body)
1391 | fulfill_proof_future thy promises postproc body =
1392 Future.fork_deps (map snd promises) (fn () =>
1393 postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) body));
1396 (***** abstraction over sort constraints *****)
1398 fun unconstrainT_prf thy (atyp_map, constraints) =
1401 (case AList.lookup (op =) constraints hyp of
1403 | NONE => raise Fail "unconstrainT_prf: missing constraint");
1405 val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o atyp_map);
1406 fun ofclass (ty, c) =
1407 let val ty' = Term.map_atyps atyp_map ty;
1408 in the_single (of_sort_proof thy hyp_map (ty', [c])) end;
1410 Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass)
1411 #> fold_rev (implies_intr_proof o snd) constraints
1414 fun unconstrainT_body thy constrs (PBody {oracles, thms, proof}) =
1416 {oracles = oracles, (* FIXME merge (!), unconstrain (!?!) *)
1417 thms = thms, (* FIXME merge (!) *)
1418 proof = unconstrainT_prf thy constrs proof};
1421 (***** theorems *****)
1423 fun prepare_thm_proof do_unconstrain thy name shyps hyps concl promises body =
1425 val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
1426 val prop = Logic.list_implies (hyps, concl);
1427 val nvs = needed_vars prop;
1428 val args = map (fn (v as Var (ixn, _)) =>
1429 if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
1430 map SOME (frees_of prop);
1432 val (postproc, ofclasses, prop1, args1) =
1433 if do_unconstrain then
1435 val ((atyp_map, constraints, outer_constraints), prop1) =
1436 Logic.unconstrainT shyps prop;
1437 val postproc = unconstrainT_body thy (atyp_map, constraints);
1439 (map o Option.map o Term.map_types o Term.map_atyps)
1440 (Type.strip_sorts o atyp_map) args;
1441 in (postproc, map OfClass outer_constraints, prop1, args1) end
1442 else (I, [], prop, args);
1443 val argsP = ofclasses @ map Hyp hyps;
1446 if ! proofs = 2 then
1447 #4 (shrink_proof [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)))
1449 val body0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
1451 fun new_prf () = (serial (), fulfill_proof_future thy promises postproc body0);
1453 (case strip_combt (fst (strip_combP prf)) of
1454 (PThm (i, ((old_name, prop', NONE), body')), args') =>
1455 if (old_name = "" orelse old_name = name) andalso prop1 = prop' andalso args = args'
1459 val head = PThm (i, ((name, prop1, NONE), body'));
1460 in ((i, (name, prop1, body')), head, args, argsP, args1) end;
1462 val unconstrain_thm_proofs = Unsynchronized.ref true;
1464 fun thm_proof thy name shyps hyps concl promises body =
1465 let val (pthm, head, args, argsP, _) =
1466 prepare_thm_proof (! unconstrain_thm_proofs) thy name shyps hyps concl promises body
1467 in (pthm, proof_combP (proof_combt' (head, args), argsP)) end;
1469 fun unconstrain_thm_proof thy shyps concl promises body =
1471 val (pthm, head, _, _, args) =
1472 prepare_thm_proof true thy "" shyps [] concl promises body
1473 in (pthm, proof_combt' (head, args)) end;
1476 fun get_name hyps prop prf =
1477 let val prop = Logic.list_implies (hyps, prop) in
1478 (case strip_combt (fst (strip_combP prf)) of
1479 (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
1483 fun get_name_unconstrained shyps hyps prop prf =
1484 let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in
1485 (case strip_combt (fst (strip_combP prf)) of
1486 (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
1490 fun guess_name (PThm (_, ((name, _, _), _))) = name
1491 | guess_name (prf %% Hyp _) = guess_name prf
1492 | guess_name (prf %% OfClass _) = guess_name prf
1493 | guess_name (prf % NONE) = guess_name prf
1494 | guess_name (prf % SOME (Var _)) = guess_name prf
1495 | guess_name _ = "";
1499 structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
1500 open Basic_Proofterm;