Initial revision of tools for proof terms.
--- /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;
--- /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\\<Lambda>_./ _)", [0,0], 1)),
+ ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
+ ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [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;
--- /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;
+
--- /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;