# HG changeset patch # User berghofe # Date 999267425 -7200 # Node ID 42fbb6abed5afc55515842298c7bc7c2e97411c5 # Parent 80acc6ce26c385a72554ed6bee88ddbd5f7d32b0 Initial revision of tools for proof terms. diff -r 80acc6ce26c3 -r 42fbb6abed5a src/Pure/Proof/proof_rewrite_rules.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/Proof/proof_rewrite_rules.ML Fri Aug 31 16:17:05 2001 +0200 @@ -0,0 +1,103 @@ +(* Title: Pure/Proof/proof_rewrite_rules.ML + ID: $Id$ + Author: Stefan Berghofer + Copyright 2000 TU Muenchen + +Simplification function for partial proof terms involving +meta level rules. +*) + +signature PROOF_REWRITE_RULES = +sig + val rprocs : (string * (typ list -> Proofterm.proof -> Proofterm.proof option)) list +end; + +structure ProofRewriteRules : PROOF_REWRITE_RULES = +struct + +open Proofterm; + +fun rew _ (PThm (("ProtoPure.rev_triv_goal", _), _, _, _) %% _ % + (PThm (("ProtoPure.triv_goal", _), _, _, _) %% _ % prf)) = Some prf + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % + (PAxm ("ProtoPure.equal_intr", _, _) %% _ %% _ % prf % _)) = Some prf + | rew _ (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % + (PAxm ("ProtoPure.equal_intr", _, _) %% A %% B % prf1 % prf2)) = + Some (equal_intr_axm %% B %% A % prf2 % prf1) + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % + (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ % + (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2)) = + let + val _ $ A $ C = Envir.beta_norm X; + val _ $ B $ D = Envir.beta_norm Y + in Some (AbsP ("H1", None, AbsP ("H2", None, + equal_elim_axm %%% C %%% D % incr_pboundvars 2 0 prf2 % + (PBound 1 % (equal_elim_axm %%% B %%% A % + (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf1) % PBound 0))))) + end + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % + (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % + (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ % + (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2))) = + let + val _ $ A $ C = Envir.beta_norm Y; + val _ $ B $ D = Envir.beta_norm X + in Some (AbsP ("H1", None, AbsP ("H2", None, + equal_elim_axm %%% D %%% C % + (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf2) + % (PBound 1 % (equal_elim_axm %%% A %%% B % incr_pboundvars 2 0 prf1 % PBound 0))))) + end + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % + (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _) % + (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf))) = + let + val _ $ P = Envir.beta_norm X; + val _ $ Q = Envir.beta_norm Y; + in Some (AbsP ("H", None, Abst ("x", None, + equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 % + (incr_pboundvars 1 1 prf %%% Bound 0) % (PBound 0 %%% Bound 0)))) + end + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % + (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % + (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _) % + (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf)))) = + let + val _ $ P = Envir.beta_norm X; + val _ $ Q = Envir.beta_norm Y; + in Some (AbsP ("H", None, Abst ("x", None, + equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 % + (symmetric_axm %% None %% None % (incr_pboundvars 1 1 prf %%% Bound 0)) + % (PBound 0 %%% Bound 0)))) + end + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C % + (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2) % prf3) = + Some (equal_elim_axm %%% B %%% C % prf2 % + (equal_elim_axm %%% A %%% B % prf1 % prf3)) + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C % + (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % + (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2)) % prf3) = + Some (equal_elim_axm %%% B %%% C % (symmetric_axm %% None %% None % prf1) % + (equal_elim_axm %%% A %%% B % (symmetric_axm %% None %% None % prf2) % prf3)) + + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf) = Some prf + | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % + (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % + (PAxm ("ProtoPure.reflexive", _, _) %% _)) % prf) = Some prf + + | rew _ _ = None; + +val rprocs = [("Pure/meta_equality", rew)]; + +end; + +Proofterm.add_prf_rprocs ProtoPure.thy ProofRewriteRules.rprocs; diff -r 80acc6ce26c3 -r 42fbb6abed5a src/Pure/Proof/proof_syntax.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/Proof/proof_syntax.ML Fri Aug 31 16:17:05 2001 +0200 @@ -0,0 +1,267 @@ +(* Title: Pure/Proof/proof_syntax.ML + ID: $Id$ + Author: Stefan Berghofer + Copyright 2000 TU Muenchen + +Function for parsing and printing proof terms. +*) + +signature PROOF_SYNTAX = +sig + val proofT : typ + val add_proof_syntax : Sign.sg -> Sign.sg + val disambiguate_names : theory -> Proofterm.proof -> + Proofterm.proof * Proofterm.proof Symtab.table + val proof_of_term : theory -> Proofterm.proof Symtab.table -> + bool -> term -> Proofterm.proof + val term_of_proof : Proofterm.proof -> term + val cterm_of_proof : theory -> Proofterm.proof -> cterm * (cterm -> Proofterm.proof) + val read_term : theory -> typ -> string -> term + val read_proof : theory -> bool -> string -> Proofterm.proof + val pretty_proof : Sign.sg -> Proofterm.proof -> Pretty.T + val pretty_proof_of : bool -> thm -> Pretty.T + val print_proof_of : bool -> thm -> unit +end; + +structure ProofSyntax : PROOF_SYNTAX = +struct + +open Proofterm; + +(**** add special syntax for embedding proof terms ****) + +val proofT = Type ("proof", []); +val lamT = Type ("lam_syn", []); +val idtT = Type ("idt", []); +val aT = TFree ("'a", ["logic"]); + +(** constants for theorems and axioms **) + +fun add_prefix a b = NameSpace.pack (a :: NameSpace.unpack b); + +fun add_proof_atom_consts names sg = Sign.add_consts_i + (map (fn name => (name, proofT, NoSyn)) names) (Sign.add_path "//" sg); + +(** constants for application and abstraction **) + +fun add_proof_syntax sg = + sg + |> Sign.copy + |> Sign.add_path "/" + |> Sign.add_defsort_i ["logic"] + |> Sign.add_types [("proof", 0, NoSyn)] + |> Sign.add_arities [("proof", [], "logic")] + |> Sign.add_consts_i + [("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ %%/ _)", [4, 5], 4)), + ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ %/ _)", [4, 5], 4)), + ("Abst", (aT --> proofT) --> proofT, NoSyn), + ("AbsP", [propT, proofT --> proofT] ---> proofT, NoSyn)] + |> Sign.add_nonterminals ["lam_syn"] + |> Sign.add_syntax_i + [("_Lam", [lamT, proofT] ---> proofT, Mixfix ("(3Lam _./ _)", [0,0], 1)), + ("_Lam0", [lamT, lamT] ---> lamT, Mixfix ("_,/ _", [1, 0], 0)), + ("_Lam1", [idtT, propT] ---> lamT, Mixfix ("_ : _", [0, 0], 1)), + ("_Lam2", idtT --> lamT, Mixfix ("_", [0], 1))] + |> Sign.add_modesyntax_i (("xsymbols", true), + [("_Lam", [lamT, proofT] ---> proofT, Mixfix ("(3\\_./ _)", [0,0], 1)), + ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\/ _)", [4, 5], 4)), + ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\/ _)", [4, 5], 4))]) + |> Sign.add_trrules_i (map Syntax.ParsePrintRule + [(Syntax.mk_appl (Constant "_Lam") + [Syntax.mk_appl (Constant "_Lam1") [Variable "x", Variable "A"], Variable "B"], + Syntax.mk_appl (Constant "AbsP") [Variable "A", + (Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "B"])]), + (Syntax.mk_appl (Constant "_Lam") + [Syntax.mk_appl (Constant "_Lam2") [Variable "x"], Variable "A"], + Syntax.mk_appl (Constant "Abst") + [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])]), + (Syntax.mk_appl (Constant "_Lam") + [Syntax.mk_appl (Constant "_Lam0") [Variable "l", Variable "m"], Variable "A"], + Syntax.mk_appl (Constant "_Lam") + [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]])]); + + +(**** create unambiguous theorem names ****) + +fun disambiguate_names thy prf = + let + val thms = thms_of_proof Symtab.empty prf; + val thms' = map (apsnd (#prop o rep_thm)) (flat + (map PureThy.thms_of (thy :: Theory.ancestors_of thy))); + + val tab = Symtab.foldl (fn (tab, (key, ps)) => + let val prop = if_none (assoc (thms', key)) (Bound 0) + in fst (foldr (fn ((prop', prf), x as (tab, i)) => + if prop <> prop' then + (Symtab.update ((key ^ "_" ^ string_of_int i, prf), tab), i+1) + else x) (ps, (tab, 1))) + end) (Symtab.empty, thms); + + fun rename (Abst (s, T, prf)) = Abst (s, T, rename prf) + | rename (AbsP (s, t, prf)) = AbsP (s, t, rename prf) + | rename (prf1 % prf2) = rename prf1 % rename prf2 + | rename (prf %% t) = rename prf %% t + | rename (prf' as PThm ((s, tags), prf, prop, Ts)) = + let + val prop' = if_none (assoc (thms', s)) (Bound 0); + val ps = map fst (the (Symtab.lookup (thms, s))) \ prop' + in if prop = prop' then prf' else + PThm ((s ^ "_" ^ string_of_int (length ps - find_index_eq prop ps), tags), + prf, prop, Ts) + end + | rename prf = prf + + in (rename prf, tab) end; + + +(**** translation between proof terms and pure terms ****) + +fun change_type T (PThm (name, prf, prop, _)) = PThm (name, prf, prop, T) + | change_type T (PAxm (name, prop, _)) = PAxm (name, prop, T) + | change_type _ _ = error "Not a proper theorem"; + +fun proof_of_term thy tab ty = + let + val thys = thy :: Theory.ancestors_of thy; + val thms = flat (map thms_of thys); + val axms = flat (map (Symtab.dest o #axioms o rep_theory) thys); + + fun prf_of [] (Bound i) = PBound i + | prf_of Ts (Const (s, Type ("proof", _))) = + change_type (if ty then Some Ts else None) + (case NameSpace.unpack s of + "Axm" :: xs => + let + val name = NameSpace.pack xs; + val prop = (case assoc (axms, name) of + Some prop => prop + | None => error ("Unknown axiom " ^ quote name)) + in PAxm (name, prop, None) end + | "Thm" :: xs => + let val name = NameSpace.pack xs; + in (case assoc (thms, name) of + Some thm => fst (strip_combt (#2 (#der (rep_thm thm)))) + | None => (case Symtab.lookup (tab, name) of + Some prf => prf + | None => error ("Unknown theorem " ^ quote name))) + end + | _ => error ("Illegal proof constant name: " ^ quote s)) + | prf_of Ts (v as Var ((_, Type ("proof", _)))) = Hyp v + | prf_of [] (Const ("Abst", _) $ Abs (s, T, prf)) = + Abst (s, if ty then Some T else None, + incr_pboundvars (~1) 0 (prf_of [] prf)) + | prf_of [] (Const ("AbsP", _) $ t $ Abs (s, _, prf)) = + AbsP (s, case t of Const ("dummy_pattern", _) => None | _ => Some t, + incr_pboundvars 0 (~1) (prf_of [] prf)) + | prf_of [] (Const ("AppP", _) $ prf1 $ prf2) = + prf_of [] prf1 % prf_of [] prf2 + | prf_of Ts (Const ("Appt", _) $ prf $ Const ("TYPE", Type (_, [T]))) = + prf_of (T::Ts) prf + | prf_of [] (Const ("Appt", _) $ prf $ t) = prf_of [] prf %% + (case t of Const ("dummy_pattern", _) => None | _ => Some t) + | prf_of _ t = error ("Not a proof term:\n" ^ + Sign.string_of_term (sign_of thy) t) + + in prf_of [] end; + + +val AbsPt = Const ("AbsP", [propT, proofT --> proofT] ---> proofT); +val AppPt = Const ("AppP", [proofT, proofT] ---> proofT); +val Hypt = Free ("Hyp", propT --> proofT); +val Oraclet = Free ("Oracle", propT --> proofT); +val MinProoft = Free ("?", proofT); + +val mk_tyapp = foldl (fn (prf, T) => Const ("Appt", + [proofT, itselfT T] ---> proofT) $ prf $ Logic.mk_type T); + +fun term_of _ (PThm ((name, _), _, _, None)) = + Const (add_prefix "Thm" name, proofT) + | term_of _ (PThm ((name, _), _, _, Some Ts)) = + mk_tyapp (Const (add_prefix "Thm" name, proofT), Ts) + | term_of _ (PAxm (name, _, None)) = Const (add_prefix "Axm" name, proofT) + | term_of _ (PAxm (name, _, Some Ts)) = + mk_tyapp (Const (add_prefix "Axm" name, proofT), Ts) + | term_of _ (PBound i) = Bound i + | term_of Ts (Abst (s, opT, prf)) = + let val T = if_none opT dummyT + in Const ("Abst", (T --> proofT) --> proofT) $ + Abs (s, T, term_of (T::Ts) (incr_pboundvars 1 0 prf)) + end + | term_of Ts (AbsP (s, t, prf)) = + AbsPt $ if_none t (Const ("dummy_pattern", propT)) $ + Abs (s, proofT, term_of (proofT::Ts) (incr_pboundvars 0 1 prf)) + | term_of Ts (prf1 % prf2) = + AppPt $ term_of Ts prf1 $ term_of Ts prf2 + | term_of Ts (prf %% opt) = + let val t = if_none opt (Const ("dummy_pattern", dummyT)) + in Const ("Appt", + [proofT, fastype_of1 (Ts, t) handle TERM _ => dummyT] ---> proofT) $ + term_of Ts prf $ t + end + | term_of Ts (Hyp t) = Hypt $ t + | term_of Ts (Oracle (_, t, _)) = Oraclet $ t + | term_of Ts (MinProof _) = MinProoft; + +val term_of_proof = term_of []; + +fun cterm_of_proof thy prf = + let + val (prf', tab) = disambiguate_names thy prf; + val thys = thy :: Theory.ancestors_of thy; + val thm_names = filter_out (equal "") (map fst (flat (map thms_of thys))) @ + map fst (Symtab.dest tab); + val axm_names = map fst (flat (map (Symtab.dest o #axioms o rep_theory) thys)); + val sg = sign_of thy |> + add_proof_syntax |> + add_proof_atom_consts + (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names) + in + (cterm_of sg (term_of_proof prf'), + proof_of_term thy tab true o Thm.term_of) + end; + +fun read_term thy = + let + val thys = thy :: Theory.ancestors_of thy; + val thm_names = filter_out (equal "") (map fst (flat (map thms_of thys))); + val axm_names = map fst (flat (map (Symtab.dest o #axioms o rep_theory) thys)); + val sg = sign_of thy |> + add_proof_syntax |> + add_proof_atom_consts + (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names) + in + (fn T => fn s => Thm.term_of (read_cterm sg (s, T))) + end; + +fun read_proof thy = + let val rd = read_term thy proofT + in + (fn ty => fn s => proof_of_term thy Symtab.empty ty (Logic.varify (rd s))) + end; + +fun pretty_proof sg prf = + let + val thm_names = map fst (Symtab.dest (thms_of_proof Symtab.empty prf)) \ ""; + val axm_names = map fst (Symtab.dest (axms_of_proof Symtab.empty prf)); + val sg' = sg |> + add_proof_syntax |> + add_proof_atom_consts + (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names) + in + Sign.pretty_term sg' (term_of_proof prf) + end; + +fun pretty_proof_of full thm = + let + val {sign, der = (_, prf), prop, ...} = rep_thm thm; + val prf' = (case strip_combt (fst (strip_combP prf)) of + (PThm (_, prf', prop', _), _) => if prop=prop' then prf' else prf + | _ => prf) + in + pretty_proof sign + (if full then Reconstruct.reconstruct_prf sign prop prf' else prf') + end; + +val print_proof_of = Pretty.writeln oo pretty_proof_of; + +end; diff -r 80acc6ce26c3 -r 42fbb6abed5a src/Pure/Proof/proofchecker.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/Proof/proofchecker.ML Fri Aug 31 16:17:05 2001 +0200 @@ -0,0 +1,104 @@ +(* Title: Pure/Proof/proofchecker.ML + ID: $Id$ + Author: Stefan Berghofer + Copyright 2000 TU Muenchen + +Simple proof checker based only on the core inference rules +of Isabelle/Pure. +*) + +signature PROOF_CHECKER = +sig + val thm_of_proof : theory -> Proofterm.proof -> thm +end; + +structure ProofChecker = +struct + +open Proofterm; + +(***** construct a theorem out of a proof term *****) + +fun lookup_thm thy = + let val tab = foldr Symtab.update + (flat (map thms_of (thy :: Theory.ancestors_of thy)), Symtab.empty) + in + (fn s => case Symtab.lookup (tab, s) of + None => error ("Unknown theorem " ^ quote s) + | Some thm => thm) + end; + +fun beta_eta_convert thm = + let + val beta_thm = beta_conversion true (cprop_of thm); + val (_, rhs) = Drule.dest_equals (cprop_of beta_thm); + in Thm.equal_elim (Thm.transitive beta_thm (eta_conversion rhs)) thm end; + +fun thm_of_proof thy prf = + let + val names = add_prf_names ([], prf); + val sg = sign_of thy; + val lookup = lookup_thm thy; + + fun thm_of _ _ (PThm ((name, _), _, prop', Some Ts)) = + let + val thm = lookup name; + val {prop, ...} = rep_thm thm; + val _ = if prop=prop' then () else + error ("Duplicate use of theorem name " ^ quote name); + val tvars = term_tvars prop; + val ctye = map fst tvars ~~ map (Thm.ctyp_of sg) Ts + in + Thm.instantiate (ctye, []) (forall_intr_vars thm) + end + + | thm_of _ _ (PAxm (name, _, Some Ts)) = + let + val thm = get_axiom thy name; + val {prop, ...} = rep_thm thm; + val tvars = term_tvars prop; + val ctye = map fst tvars ~~ map (Thm.ctyp_of sg) Ts + in + Thm.instantiate (ctye, []) (forall_intr_vars thm) + end + + | thm_of _ Hs (PBound i) = nth_elem (i, Hs) + + | thm_of vs Hs (Abst (s, Some T, prf)) = + let + val x = variant (names @ map fst vs) s; + val thm = thm_of ((x, T) :: vs) Hs prf + in + Thm.forall_intr (Thm.cterm_of sg (Free (x, T))) thm + end + + | thm_of vs Hs (prf %% Some t) = + let + val thm = thm_of vs Hs prf + val ct = Thm.cterm_of sg (Term.subst_bounds (map Free vs, t)) + in Thm.forall_elim ct thm end + + | thm_of vs Hs (AbsP (s, Some t, prf)) = + let + val ct = Thm.cterm_of sg (Term.subst_bounds (map Free vs, t)); + val thm = thm_of vs (Thm.assume ct :: Hs) prf + in + Thm.implies_intr ct thm + end + + | thm_of vs Hs (prf % prf') = + let + val thm = beta_eta_convert (thm_of vs Hs prf); + val thm' = beta_eta_convert (thm_of vs Hs prf') + in + Thm.implies_elim thm thm' + end + + | thm_of _ _ (Hyp t) = Thm.assume (Thm.cterm_of sg t) + + | thm_of _ _ _ = error "thm_of_proof: partial proof term"; + + in thm_of [] [] prf end; + +end; + diff -r 80acc6ce26c3 -r 42fbb6abed5a src/Pure/Proof/reconstruct.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/Proof/reconstruct.ML Fri Aug 31 16:17:05 2001 +0200 @@ -0,0 +1,346 @@ +(* Title: Pure/Proof/reconstruct.ML + ID: $Id$ + Author: Stefan Berghofer + Copyright 2000 TU Muenchen + +Reconstruction of partial proof terms. +*) + +signature RECONSTRUCT = +sig + val quiet_mode : bool ref + val reconstruct_prf : Sign.sg -> term -> Proofterm.proof -> Proofterm.proof + val expand_proof : Sign.sg -> string list -> Proofterm.proof -> Proofterm.proof +end; + +structure Reconstruct : RECONSTRUCT = +struct + +open Proofterm; + +val quiet_mode = ref true; +fun message s = if !quiet_mode then () else writeln s; + +fun vars_of t = rev (foldl_aterms + (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t)); + +fun forall_intr (t, prop) = + let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p) + in all T $ Abs (a, T, abstract_over (t, prop)) end; + +fun forall_intr_vfs prop = foldr forall_intr + (vars_of prop @ sort (make_ord atless) (term_frees prop), prop); + +fun merge_envs (Envir.Envir {asol=asol1, iTs=iTs1, maxidx=maxidx1}) + (Envir.Envir {asol=asol2, iTs=iTs2, maxidx=maxidx2}) = + Envir.Envir {asol=Vartab.merge (op aconv) (asol1, asol2), + iTs=Vartab.merge (op =) (iTs1, iTs2), + maxidx=Int.max (maxidx1, maxidx2)}; + +fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t + | strip_abs _ t = t; + + +(******************************************************************************** + generate constraints for proof term +*********************************************************************************) + +fun mk_var env Ts T = + let val (env', v) = Envir.genvar "a" (env, rev Ts ---> T) + in (env', list_comb (v, map Bound (length Ts - 1 downto 0))) end; + +fun mk_tvar (Envir.Envir {iTs, asol, maxidx}, s) = + (Envir.Envir {iTs = iTs, asol = asol, maxidx = maxidx+1}, + TVar (("'t", maxidx+1), s)); + +fun mk_abs Ts t = foldl (fn (u, T) => Abs ("", T, u)) (t, Ts); + +fun make_Tconstraints_cprf maxidx cprf = + let + fun mk_Tcnstrts maxidx Ts (Abst (s, Some T, cprf)) = + let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx (T::Ts) cprf; + in (cs, Abst (s, Some T, cprf'), maxidx') end + | mk_Tcnstrts maxidx Ts (Abst (s, None, cprf)) = + let + val T' = TVar (("'t", maxidx+1), ["logic"]); + val (cs, cprf', maxidx') = mk_Tcnstrts (maxidx+1) (T'::Ts) cprf; + in (cs, Abst (s, Some T', cprf'), maxidx') end + | mk_Tcnstrts maxidx Ts (AbsP (s, Some t, cprf)) = + let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf; + in ((mk_abs Ts t, rev Ts ---> propT)::cs, AbsP (s, Some t, cprf'), maxidx') end + | mk_Tcnstrts maxidx Ts (AbsP (s, None, cprf)) = + let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf; + in (cs, AbsP (s, None, cprf'), maxidx') end + | mk_Tcnstrts maxidx Ts (cprf1 % cprf2) = + let + val (cs, cprf1', maxidx') = mk_Tcnstrts maxidx Ts cprf1; + val (cs', cprf2', maxidx'') = mk_Tcnstrts maxidx' Ts cprf2; + in (cs' @ cs, cprf1' % cprf2', maxidx'') end + | mk_Tcnstrts maxidx Ts (cprf %% Some t) = + let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf; + in ((mk_abs Ts t, rev Ts ---> TypeInfer.logicT)::cs, + cprf' %% Some t, maxidx') + end + | mk_Tcnstrts maxidx Ts (cprf %% None) = + let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf; + in (cs, cprf %% None, maxidx') end + | mk_Tcnstrts maxidx _ cprf = ([], cprf, maxidx); + in mk_Tcnstrts maxidx [] cprf end; + +fun unifyT sg env T U = + let + val Envir.Envir {asol, iTs, maxidx} = env; + val (iTs', maxidx') = Type.unify (Sign.tsig_of sg) maxidx iTs (T, U) + in Envir.Envir {asol=asol, iTs=iTs', maxidx=maxidx'} end; + +fun decompose sg env Ts + (Const ("all", _) $ Abs (_, T, t)) (Const ("all", _) $ Abs (_, U, u)) = + decompose sg (unifyT sg env T U) (T::Ts) t u + | decompose sg env Ts + (Const ("==>", _) $ t1 $ t2) (Const ("==>", _) $ u1 $ u2) = + apsnd (cons (mk_abs Ts t1, mk_abs Ts u1)) (decompose sg env Ts t2 u2) + | decompose sg env Ts t u = (env, [(mk_abs Ts t, mk_abs Ts u)]); + +fun cantunify sg t u = error ("Cannot unify:\n" ^ + Sign.string_of_term sg t ^ "\n\n" ^ Sign.string_of_term sg u); + +fun make_constraints_cprf sg env ts cprf = + let + fun add_cnstrt Ts prop prf cs env ts (t, u) = + let + val t' = mk_abs Ts t; + val u' = mk_abs Ts u; + val nt = Envir.norm_term env t'; + val nu = Envir.norm_term env u' + in + if Pattern.pattern nt andalso Pattern.pattern nu then + let + val env' = (Pattern.unify (sg, env, [(nt, nu)]) handle Pattern.Unif => + cantunify sg nt nu); + in (Envir.norm_term env' prop, prf, cs, env', ts) end + else + let val (env', cs') = decompose sg env [] nt nu + in (Envir.norm_term env' prop, prf, cs @ cs', env', ts) end + end; + + fun mk_cnstrts_atom env ts prop opTs mk_prf = + let + val tvars = term_tvars prop; + val (env', Ts) = if_none (apsome (pair env) opTs) + (foldl_map (mk_tvar o apsnd snd) (env, tvars)); + val prop' = subst_TVars (map fst tvars ~~ Ts) (forall_intr_vfs prop); + in (prop', mk_prf (Some Ts), [], env', ts) end; + + fun mk_cnstrts env _ Hs ts (PBound i) = (nth_elem (i, Hs), PBound i, [], env, ts) + | mk_cnstrts env Ts Hs ts (Abst (s, Some T, cprf)) = + let val (t, prf, cnstrts, env', ts') = + mk_cnstrts env (T::Ts) (map (incr_boundvars 1) Hs) ts cprf; + in (Const ("all", (T --> propT) --> propT) $ Abs (s, T, t), Abst (s, Some T, prf), + cnstrts, env', ts') + end + | mk_cnstrts env Ts Hs (t::ts) (AbsP (s, Some _, cprf)) = + let + val (u, prf, cnstrts, env', ts') = mk_cnstrts env Ts (t::Hs) ts cprf; + val t' = strip_abs Ts t; + in (Logic.mk_implies (t', u), AbsP (s, Some t', prf), cnstrts, env', ts') + end + | mk_cnstrts env Ts Hs ts (AbsP (s, None, cprf)) = + let + val (env', t) = mk_var env Ts propT; + val (u, prf, cnstrts, env'', ts') = mk_cnstrts env' Ts (t::Hs) ts cprf; + in (Logic.mk_implies (t, u), AbsP (s, Some t, prf), cnstrts, env'', ts') + end + | mk_cnstrts env Ts Hs ts (cprf1 % cprf2) = + let val (u, prf2, cnstrts, env', ts') = mk_cnstrts env Ts Hs ts cprf2 + in (case mk_cnstrts env' Ts Hs ts' cprf1 of + (Const ("==>", _) $ u' $ t', prf1, cnstrts', env'', ts'') => + add_cnstrt Ts t' (prf1 % prf2) (cnstrts' @ cnstrts) + env'' ts'' (u, u') + | (t, prf1, cnstrts', env'', ts'') => + let val (env''', v) = mk_var env'' Ts propT + in add_cnstrt Ts v (prf1 % prf2) (cnstrts' @ cnstrts) + env''' ts'' (t, Logic.mk_implies (u, v)) + end) + end + | mk_cnstrts env Ts Hs (t::ts) (cprf %% Some _) = + let val t' = strip_abs Ts t + in (case mk_cnstrts env Ts Hs ts cprf of + (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f, + prf, cnstrts, env', ts') => + let val env'' = unifyT sg env' T + (fastype_of1 (map (Envir.norm_type env') Ts, t')) + in (betapply (f, t'), prf %% Some t', cnstrts, env'', ts') + end + | (u, prf, cnstrts, env', ts') => + let + val T = fastype_of1 (map (Envir.norm_type env') Ts, t'); + val (env'', v) = mk_var env' Ts (T --> propT); + in + add_cnstrt Ts (v $ t') (prf %% Some t') cnstrts env'' ts' + (u, Const ("all", (T --> propT) --> propT) $ v) + end) + end + | mk_cnstrts env Ts Hs ts (cprf %% None) = + (case mk_cnstrts env Ts Hs ts cprf of + (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f, + prf, cnstrts, env', ts') => + let val (env'', t) = mk_var env' Ts T + in (betapply (f, t), prf %% Some t, cnstrts, env'', ts') + end + | (u, prf, cnstrts, env', ts') => + let + val (env1, T) = mk_tvar (env', ["logic"]); + val (env2, v) = mk_var env1 Ts (T --> propT); + val (env3, t) = mk_var env2 Ts T + in + add_cnstrt Ts (v $ t) (prf %% Some t) cnstrts env3 ts' + (u, Const ("all", (T --> propT) --> propT) $ v) + end) + | mk_cnstrts env _ _ ts (PThm (name, prf, prop, opTs)) = + mk_cnstrts_atom env ts prop opTs (fn x => PThm (name, prf, prop, x)) + | mk_cnstrts env _ _ ts (PAxm (name, prop, opTs)) = + mk_cnstrts_atom env ts prop opTs (fn x => PAxm (name, prop, x)) + | mk_cnstrts env _ _ ts (Oracle (name, prop, opTs)) = + mk_cnstrts_atom env ts prop opTs (fn x => Oracle (name, prop, x)) + | mk_cnstrts env _ _ ts (Hyp t) = (t, Hyp t, [], env, ts) + | mk_cnstrts _ _ _ _ _ = error "reconstruct_prf: minimal proof object" + in mk_cnstrts env [] [] ts cprf end; + +fun add_term_ixns (is, Var (i, T)) = add_typ_ixns (i ins is, T) + | add_term_ixns (is, Free (_, T)) = add_typ_ixns (is, T) + | add_term_ixns (is, Const (_, T)) = add_typ_ixns (is, T) + | add_term_ixns (is, t1 $ t2) = add_term_ixns (add_term_ixns (is, t1), t2) + | add_term_ixns (is, Abs (_, T, t)) = add_term_ixns (add_typ_ixns (is, T), t) + | add_term_ixns (is, _) = is; + + +(******************************************************************************** + update list of free variables of constraints +*********************************************************************************) + +fun upd_constrs env cs = + let + val Envir.Envir {asol, iTs, ...} = env; + val dom = Vartab.foldl (uncurry (cons o fst) o Library.swap) + (Vartab.foldl (uncurry (cons o fst) o Library.swap) ([], asol), iTs); + val vran = Vartab.foldl (add_typ_ixns o apsnd snd) + (Vartab.foldl (add_term_ixns o apsnd snd) ([], asol), iTs); + fun check_cs [] = [] + | check_cs ((u, p, vs)::ps) = + let val vs' = vs \\ dom; + in if vs = vs' then (u, p, vs)::check_cs ps + else (true, p, vs' union vran)::check_cs ps + end + in check_cs cs end; + +(******************************************************************************** + solution of constraints +*********************************************************************************) + +exception IMPOSS; + +fun solve _ [] bigenv = bigenv + | solve sg cs bigenv = + let + fun search env [] = raise IMPOSS + | search env ((u, p as (t1, t2), vs)::ps) = + if u then + let + val tn1 = Envir.norm_term bigenv t1; + val tn2 = Envir.norm_term bigenv t2 + in + if Pattern.pattern tn1 andalso Pattern.pattern tn2 then + ((Pattern.unify (sg, env, [(tn1, tn2)]), ps) handle Pattern.Unif => + cantunify sg tn1 tn2) + else + let val (env', cs') = decompose sg env [] tn1 tn2 + in if cs' = [(tn1, tn2)] then + apsnd (cons (false, (tn1, tn2), vs)) (search env ps) + else search env' (map (fn q => (true, q, vs)) cs' @ ps) + end + end + else apsnd (cons (false, p, vs)) (search env ps); + val Envir.Envir {maxidx, ...} = bigenv; + val (env, cs') = search (Envir.empty maxidx) cs; + in + solve sg (upd_constrs env cs') (merge_envs bigenv env) + end; + + +(******************************************************************************** + reconstruction of proofs +*********************************************************************************) + +fun reconstruct_prf sg prop cprf = + let + val (cprf' %% Some prop', thawf) = freeze_thaw_prf (cprf %% Some prop); + val _ = message "Collecting type constraints..."; + val (Tcs, cprf'', maxidx) = make_Tconstraints_cprf 0 cprf'; + val (ts, Ts) = ListPair.unzip Tcs; + val tsig = Sign.tsig_of sg; + val {classrel, arities, ...} = Type.rep_tsig tsig; + val _ = message "Solving type constraints..."; + val (ts', _, unifier) = TypeInfer.infer_types (Sign.pretty_term sg) (Sign.pretty_typ sg) + (Sign.const_type sg) classrel arities [] false (K true) ts Ts; + val env = Envir.Envir {asol = Vartab.empty, iTs = Vartab.make unifier, maxidx = maxidx}; + val _ = message "Collecting term constraints..."; + val (t, prf, cs, env, _) = make_constraints_cprf sg env ts' cprf''; + val cs' = map (fn p => (true, p, op union + (pairself (map (fst o dest_Var) o term_vars) p))) (map (pairself (Envir.norm_term env)) ((t, prop')::cs)); + val _ = message ("Solving remaining constraints (" ^ string_of_int (length cs') ^ ") ..."); + val env' = solve sg cs' env + in + thawf (norm_proof env' prf) + end; + +fun full_prf_of thm = + let val {prop, der = (_, prf), sign, ...} = rep_thm thm + in reconstruct_prf sign prop prf end; + + +(******************************************************************************** + expand and reconstruct subproofs +*********************************************************************************) + +fun full_forall_intr_proof prf x a T = Abst (a, Some T, prf_abstract_over x prf); + +fun expand_proof sg names prf = + let + fun expand prfs (AbsP (s, t, prf)) = + let val (prfs', prf') = expand prfs prf + in (prfs', AbsP (s, t, prf')) end + | expand prfs (Abst (s, T, prf)) = + let val (prfs', prf') = expand prfs prf + in (prfs', Abst (s, T, prf')) end + | expand prfs (prf1 % prf2) = + let + val (prfs', prf1') = expand prfs prf1; + val (prfs'', prf2') = expand prfs' prf2; + in (prfs'', prf1' % prf2') end + | expand prfs (prf %% t) = + let val (prfs', prf') = expand prfs prf + in (prfs', prf' %% t) end + | expand prfs (prf as PThm ((a, _), cprf, prop, Some Ts)) = + if not (a mem names) then (prfs, prf) else + let + val (prf, prfs') = (case assoc (prfs, (a, prop)) of + None => + let + val _ = message ("Reconstructing proof of " ^ a); + val _ = message (Sign.string_of_term sg prop); + val prf = reconstruct_prf sg prop cprf + in (prf, ((a, prop), prf)::prfs) end + | Some prf => (prf, prfs)); + val tvars = term_tvars prop; + val vars = vars_of prop; + val tye = map fst tvars ~~ Ts; + fun abst (t as Var ((s, _), T), prf) = full_forall_intr_proof prf t s T; + val prf' = map_proof_terms (subst_TVars tye) (typ_subst_TVars tye) prf + in + expand prfs' (foldr abst (map (subst_TVars tye) vars, prf')) + end + | expand prfs prf = (prfs, prf); + + in snd (expand [] prf) end; + +end;