11519

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(* Title: Pure/proofterm.ML


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ID: $Id$


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Author: Stefan Berghofer


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Copyright 2000 TU Muenchen


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LF style proof terms


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*)


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infix 8 % %% %%%;


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signature BASIC_PROOFTERM =


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sig


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datatype deriv_kind = MinDeriv  ThmDeriv  FullDeriv;


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val keep_derivs : deriv_kind ref


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datatype proof =


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PBound of int


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 Abst of string * typ option * proof


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 AbsP of string * term option * proof


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 op %% of proof * term option


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 op % of proof * proof


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 Hyp of term


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 PThm of (string * (string * string list) list) * proof * term * typ list option


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 PAxm of string * term * typ list option


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 Oracle of string * term * typ list option


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 MinProof of proof list;


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val %%% : proof * term > proof


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end;


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signature PROOFTERM =


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sig


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include BASIC_PROOFTERM


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val infer_derivs : (proof > proof > proof) > bool * proof > bool * proof > bool * proof


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val infer_derivs' : (proof > proof) > (bool * proof > bool * proof)


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(** primitive operations **)


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val proof_combt : proof * term list > proof


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val proof_combt' : proof * term option list > proof


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val proof_combP : proof * proof list > proof


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val strip_combt : proof > proof * term option list


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val strip_combP : proof > proof * proof list


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val strip_thm : proof > proof


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val map_proof_terms : (term > term) > (typ > typ) > proof > proof


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val fold_proof_terms : (term * 'a > 'a) > (typ * 'a > 'a) > 'a * proof > 'a


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val add_prf_names : string list * proof > string list


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val add_prf_tfree_names : string list * proof > string list


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val add_prf_tvar_ixns : indexname list * proof > indexname list


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val prf_abstract_over : term > proof > proof


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val prf_incr_bv : int > int > int > int > proof > proof


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val incr_pboundvars : int > int > proof > proof


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val prf_loose_bvar1 : proof > int > bool


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val prf_loose_Pbvar1 : proof > int > bool


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val norm_proof : Envir.env > proof > proof


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val norm_proof' : Envir.env > proof > proof


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val prf_subst_bounds : term list > proof > proof


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val prf_subst_pbounds : proof list > proof > proof


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val freeze_thaw_prf : proof > proof * (proof > proof)


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val thms_of_proof : (term * proof) list Symtab.table > proof >


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(term * proof) list Symtab.table


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val axms_of_proof : proof Symtab.table > proof > proof Symtab.table


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val oracles_of_proof : proof list > proof > proof list


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(** proof terms for specific inference rules **)


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val implies_intr_proof : term > proof > proof


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val forall_intr_proof : term > string > proof > proof


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val varify_proof : term > string list > proof > proof


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val freezeT : term > proof > proof


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val rotate_proof : term list > term > int > proof > proof


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val permute_prems_prf : term list > int > int > proof > proof


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val instantiate : (indexname * typ) list > (term * term) list > proof > proof


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val lift_proof : term > int > term > proof > proof


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val assumption_proof : term list > term > int > proof > proof


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val bicompose_proof : term list > term list > term list > term option >


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int > proof > proof > proof


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val equality_axms : (string * term) list


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val reflexive_axm : proof


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val symmetric_axm : proof


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val transitive_axm : proof


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val equal_intr_axm : proof


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val equal_elim_axm : proof


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val abstract_rule_axm : proof


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val combination_axm : proof


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val reflexive : proof


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val symmetric : proof > proof


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val transitive : term > typ > proof > proof > proof


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val abstract_rule : term > string > proof > proof


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val combination : term > term > term > term > typ > proof > proof > proof


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val equal_intr : term > term > proof > proof > proof


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val equal_elim : term > term > proof > proof > proof


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val axm_proof : string > term > proof


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val oracle_proof : string > term > proof


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val thm_proof : Sign.sg > string * (string * string list) list >


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term list > term > proof > proof


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val get_name_tags : term > proof > string * (string * string list) list


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(** rewriting on proof terms **)


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val add_prf_rrules : theory > (proof * proof) list > unit


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val add_prf_rprocs : theory >


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(string * (Term.typ list > proof > proof option)) list > unit


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val rewrite_proof : Type.type_sig > (proof * proof) list *


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(string * (typ list > proof > proof option)) list > proof > proof


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val init : theory > theory


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end


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structure Proofterm : PROOFTERM =


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struct


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datatype proof =


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PBound of int


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 Abst of string * typ option * proof


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 AbsP of string * term option * proof


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 op %% of proof * term option


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 op % of proof * proof


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 Hyp of term


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 PThm of (string * (string * string list) list) * proof * term * typ list option


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 PAxm of string * term * typ list option


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 Oracle of string * term * typ list option


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 MinProof of proof list;


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fun oracles_of_proof prfs prf =


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let


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fun oras_of (tabs, Abst (_, _, prf)) = oras_of (tabs, prf)


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 oras_of (tabs, AbsP (_, _, prf)) = oras_of (tabs, prf)


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 oras_of (tabs, prf %% _) = oras_of (tabs, prf)


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 oras_of (tabs, prf1 % prf2) = oras_of (oras_of (tabs, prf1), prf2)


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 oras_of (tabs as (thms, oras), PThm ((name, _), prf, prop, _)) =


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(case Symtab.lookup (thms, name) of


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None => oras_of ((Symtab.update ((name, [prop]), thms), oras), prf)


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 Some ps => if prop mem ps then tabs else


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oras_of ((Symtab.update ((name, prop::ps), thms), oras), prf))


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 oras_of ((thms, oras), prf as Oracle _) = (thms, prf ins oras)


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 oras_of (tabs, MinProof prfs) = foldl oras_of (tabs, prfs)


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 oras_of (tabs, _) = tabs


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in


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snd (oras_of ((Symtab.empty, prfs), prf))


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end;


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fun thms_of_proof tab (Abst (_, _, prf)) = thms_of_proof tab prf


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 thms_of_proof tab (AbsP (_, _, prf)) = thms_of_proof tab prf


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 thms_of_proof tab (prf1 % prf2) = thms_of_proof (thms_of_proof tab prf1) prf2


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 thms_of_proof tab (prf %% _) = thms_of_proof tab prf


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 thms_of_proof tab (prf' as PThm ((s, _), prf, prop, _)) =


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(case Symtab.lookup (tab, s) of


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None => thms_of_proof (Symtab.update ((s, [(prop, prf')]), tab)) prf


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 Some ps => if exists (equal prop o fst) ps then tab else


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thms_of_proof (Symtab.update ((s, (prop, prf')::ps), tab)) prf)


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 thms_of_proof tab _ = tab;


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fun axms_of_proof tab (Abst (_, _, prf)) = axms_of_proof tab prf


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 axms_of_proof tab (AbsP (_, _, prf)) = axms_of_proof tab prf


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 axms_of_proof tab (prf1 % prf2) = axms_of_proof (axms_of_proof tab prf1) prf2


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 axms_of_proof tab (prf %% _) = axms_of_proof tab prf


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 axms_of_proof tab (prf as PAxm (s, _, _)) = Symtab.update ((s, prf), tab)


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 axms_of_proof tab _ = tab;


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(** collect all theorems, axioms and oracles **)


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fun mk_min_proof (prfs, Abst (_, _, prf)) = mk_min_proof (prfs, prf)


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 mk_min_proof (prfs, AbsP (_, _, prf)) = mk_min_proof (prfs, prf)


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 mk_min_proof (prfs, prf %% _) = mk_min_proof (prfs, prf)


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 mk_min_proof (prfs, prf1 % prf2) = mk_min_proof (mk_min_proof (prfs, prf1), prf2)


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 mk_min_proof (prfs, prf as PThm _) = prf ins prfs


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 mk_min_proof (prfs, prf as PAxm _) = prf ins prfs


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 mk_min_proof (prfs, prf as Oracle _) = prf ins prfs


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 mk_min_proof (prfs, MinProof prfs') = prfs union prfs'


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 mk_min_proof (prfs, _) = prfs;


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(** proof objects with different levels of detail **)


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datatype deriv_kind = MinDeriv  ThmDeriv  FullDeriv;


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val keep_derivs = ref FullDeriv;


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fun if_ora b = if b then oracles_of_proof else K;


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fun infer_derivs f (ora1, prf1) (ora2, prf2) =


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(ora1 orelse ora2,


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case !keep_derivs of


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FullDeriv => f prf1 prf2


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 ThmDeriv => MinProof (mk_min_proof (mk_min_proof ([], prf1), prf2))


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 MinDeriv => MinProof (if_ora ora2 (if_ora ora1 [] prf1) prf2));


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fun infer_derivs' f (ora, prf) =


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(ora,


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case !keep_derivs of


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FullDeriv => f prf


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 ThmDeriv => MinProof (mk_min_proof ([], prf))


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 MinDeriv => MinProof (if_ora ora [] prf));


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fun (prf %%% t) = prf %% Some t;


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val proof_combt = foldl (op %%%);


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val proof_combt' = foldl (op %%);


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val proof_combP = foldl (op %);


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fun strip_combt prf =


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let fun stripc (prf %% t, ts) = stripc (prf, t::ts)


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 stripc x = x


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in stripc (prf, []) end;


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fun strip_combP prf =


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let fun stripc (prf % prf', prfs) = stripc (prf, prf'::prfs)


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 stripc x = x


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in stripc (prf, []) end;


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fun strip_thm prf = (case strip_combt (fst (strip_combP prf)) of


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(PThm (_, prf', _, _), _) => prf'


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 _ => prf);


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val mk_Abst = foldr (fn ((s, T:typ), prf) => Abst (s, None, prf));


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fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", None, prf)) prf;


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fun map_proof_terms f g (Abst (s, T, prf)) = Abst (s, apsome g T, map_proof_terms f g prf)


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 map_proof_terms f g (AbsP (s, t, prf)) = AbsP (s, apsome f t, map_proof_terms f g prf)


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 map_proof_terms f g (prf %% t) = map_proof_terms f g prf %% apsome f t


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 map_proof_terms f g (prf1 % prf2) = map_proof_terms f g prf1 % map_proof_terms f g prf2


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 map_proof_terms _ g (PThm (a, prf, prop, Some Ts)) = PThm (a, prf, prop, Some (map g Ts))


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 map_proof_terms _ g (PAxm (a, prop, Some Ts)) = PAxm (a, prop, Some (map g Ts))


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 map_proof_terms _ _ prf = prf;


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fun fold_proof_terms f g (a, Abst (_, Some T, prf)) = fold_proof_terms f g (g (T, a), prf)


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 fold_proof_terms f g (a, Abst (_, None, prf)) = fold_proof_terms f g (a, prf)


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 fold_proof_terms f g (a, AbsP (_, Some t, prf)) = fold_proof_terms f g (f (t, a), prf)


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 fold_proof_terms f g (a, AbsP (_, None, prf)) = fold_proof_terms f g (a, prf)


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 fold_proof_terms f g (a, prf %% Some t) = f (t, fold_proof_terms f g (a, prf))


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 fold_proof_terms f g (a, prf %% None) = fold_proof_terms f g (a, prf)


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 fold_proof_terms f g (a, prf1 % prf2) = fold_proof_terms f g


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(fold_proof_terms f g (a, prf1), prf2)


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 fold_proof_terms _ g (a, PThm (_, _, _, Some Ts)) = foldr g (Ts, a)


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 fold_proof_terms _ g (a, PAxm (_, prop, Some Ts)) = foldr g (Ts, a)


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 fold_proof_terms _ _ (a, _) = a;


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val add_prf_names = fold_proof_terms add_term_names ((uncurry K) o swap);


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val add_prf_tfree_names = fold_proof_terms add_term_tfree_names add_typ_tfree_names;


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val add_prf_tvar_ixns = fold_proof_terms add_term_tvar_ixns (add_typ_ixns o swap);


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(***** utilities *****)


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fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t


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 strip_abs _ t = t;


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fun mk_abs Ts t = foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);


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(*Abstraction of a proof term over its occurrences of v,


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which must contain no loose bound variables.


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The resulting proof term is ready to become the body of an Abst.*)


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fun prf_abstract_over v =


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let


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fun abst' Ts t = strip_abs Ts (abstract_over (v, mk_abs Ts t));


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fun abst Ts (AbsP (a, t, prf)) = AbsP (a, apsome (abst' Ts) t, abst Ts prf)


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 abst Ts (Abst (a, T, prf)) = Abst (a, T, abst (dummyT::Ts) prf)


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 abst Ts (prf1 % prf2) = abst Ts prf1 % abst Ts prf2


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 abst Ts (prf %% t) = abst Ts prf %% apsome (abst' Ts) t


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 abst _ prf = prf


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in abst [] end;


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(*increments a proof term's nonlocal bound variables


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required when moving a proof term within abstractions


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inc is increment for bound variables


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lev is level at which a bound variable is considered 'loose'*)


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fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);


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fun prf_incr_bv incP inct Plev tlev (u as PBound i) = if i>=Plev then PBound(i+incP) else u


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 prf_incr_bv incP inct Plev tlev (AbsP (a, t, body)) =


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AbsP (a, apsome (incr_bv' inct tlev) t, prf_incr_bv incP inct (Plev+1) tlev body)


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 prf_incr_bv incP inct Plev tlev (Abst (a, T, body)) =


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Abst (a, T, prf_incr_bv incP inct Plev (tlev+1) body)


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 prf_incr_bv incP inct Plev tlev (prf % prf') =


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prf_incr_bv incP inct Plev tlev prf % prf_incr_bv incP inct Plev tlev prf'


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 prf_incr_bv incP inct Plev tlev (prf %% t) =


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prf_incr_bv incP inct Plev tlev prf %% apsome (incr_bv' inct tlev) t


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 prf_incr_bv _ _ _ _ prf = prf;


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fun incr_pboundvars 0 0 prf = prf


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 incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;


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fun prf_loose_bvar1 (prf1 % prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k


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 prf_loose_bvar1 (prf %% Some t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)


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 prf_loose_bvar1 (_ %% None) _ = true


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 prf_loose_bvar1 (AbsP (_, Some t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k


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 prf_loose_bvar1 (AbsP (_, None, _)) k = true


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 prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)


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 prf_loose_bvar1 _ _ = false;


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fun prf_loose_Pbvar1 (PBound i) k = i = k


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 prf_loose_Pbvar1 (prf1 % prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k


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 prf_loose_Pbvar1 (prf %% _) k = prf_loose_Pbvar1 prf k


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 prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)


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 prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k


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 prf_loose_Pbvar1 _ _ = false;


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(**** substitutions ****)


306 


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local open Envir in


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fun apsome' f None = raise SAME


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 apsome' f (Some x) = Some (f x);


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fun norm_proof env =


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let


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fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same env) T, normh prf)


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handle SAME => Abst (s, T, norm prf))


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 norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf)


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handle SAME => AbsP (s, t, norm prf))


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 norm (prf %% t) = (norm prf %% apsome (norm_term env) t


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handle SAME => prf %% apsome' (norm_term_same env) t)


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 norm (prf1 % prf2) = (norm prf1 % normh prf2


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handle SAME => prf1 % norm prf2)


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 norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same env) Ts)


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 norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same env) Ts)


324 
 norm _ = raise SAME


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and normh prf = (norm prf handle SAME => prf);


326 
in normh end;


327 


328 
(***** Remove some types in proof term (to save space) *****)


329 


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fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)


331 
 remove_types (t $ u) = remove_types t $ remove_types u


332 
 remove_types (Const (s, _)) = Const (s, dummyT)


333 
 remove_types t = t;


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335 
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =


336 
Envir.Envir {iTs = iTs, asol = Vartab.map remove_types asol, maxidx = maxidx};


337 


338 
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;


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340 
(**** substitution of bound variables ****)


341 


342 
fun prf_subst_bounds args prf =


343 
let


344 
val n = length args;


345 
fun subst' lev (Bound i) =


346 
(if i<lev then raise SAME (*var is locally bound*)


347 
else incr_boundvars lev (List.nth (args, ilev))


348 
handle Subscript => Bound (in) (*loose: change it*))


349 
 subst' lev (Abs (a, T, body)) = Abs (a, T, subst' (lev+1) body)


350 
 subst' lev (f $ t) = (subst' lev f $ substh' lev t


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handle SAME => f $ subst' lev t)


352 
 subst' _ _ = raise SAME


353 
and substh' lev t = (subst' lev t handle SAME => t);


354 


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fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)


356 
handle SAME => AbsP (a, t, subst lev body))


357 
 subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)


358 
 subst lev (prf % prf') = (subst lev prf % substh lev prf'


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handle SAME => prf % subst lev prf')


360 
 subst lev (prf %% t) = (subst lev prf %% apsome (substh' lev) t


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handle SAME => prf %% apsome' (subst' lev) t)


362 
 subst _ _ = raise SAME


363 
and substh lev prf = (subst lev prf handle SAME => prf)


364 
in case args of [] => prf  _ => substh 0 prf end;


365 


366 
fun prf_subst_pbounds args prf =


367 
let


368 
val n = length args;


369 
fun subst (PBound i) Plev tlev =


370 
(if i < Plev then raise SAME (*var is locally bound*)


371 
else incr_pboundvars Plev tlev (List.nth (args, iPlev))


372 
handle Subscript => PBound (in) (*loose: change it*))


373 
 subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)


374 
 subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))


375 
 subst (prf % prf') Plev tlev = (subst prf Plev tlev % substh prf' Plev tlev


376 
handle SAME => prf % subst prf' Plev tlev)


377 
 subst (prf %% t) Plev tlev = subst prf Plev tlev %% t


378 
 subst prf _ _ = raise SAME


379 
and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)


380 
in case args of [] => prf  _ => substh prf 0 0 end;


381 


382 
end;


383 


384 


385 
(**** Freezing and thawing of variables in proof terms ****)


386 


387 
fun frzT names =


388 
map_type_tvar (fn (ixn, xs) => TFree (the (assoc (names, ixn)), xs));


389 


390 
fun thawT names =


391 
map_type_tfree (fn (s, xs) => case assoc (names, s) of


392 
None => TFree (s, xs)


393 
 Some ixn => TVar (ixn, xs));


394 


395 
fun freeze names names' (t $ u) =


396 
freeze names names' t $ freeze names names' u


397 
 freeze names names' (Abs (s, T, t)) =


398 
Abs (s, frzT names' T, freeze names names' t)


399 
 freeze names names' (Const (s, T)) = Const (s, frzT names' T)


400 
 freeze names names' (Free (s, T)) = Free (s, frzT names' T)


401 
 freeze names names' (Var (ixn, T)) =


402 
Free (the (assoc (names, ixn)), frzT names' T)


403 
 freeze names names' t = t;


404 


405 
fun thaw names names' (t $ u) =


406 
thaw names names' t $ thaw names names' u


407 
 thaw names names' (Abs (s, T, t)) =


408 
Abs (s, thawT names' T, thaw names names' t)


409 
 thaw names names' (Const (s, T)) = Const (s, thawT names' T)


410 
 thaw names names' (Free (s, T)) =


411 
let val T' = thawT names' T


412 
in case assoc (names, s) of


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None => Free (s, T')


414 
 Some ixn => Var (ixn, T')


415 
end


416 
 thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)


417 
 thaw names names' t = t;


418 


419 
fun freeze_thaw_prf prf =


420 
let


421 
val (fs, Tfs, vs, Tvs) = fold_proof_terms


422 
(fn (t, (fs, Tfs, vs, Tvs)) =>


423 
(add_term_frees (t, fs), add_term_tfree_names (t, Tfs),


424 
add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))


425 
(fn (T, (fs, Tfs, vs, Tvs)) =>


426 
(fs, add_typ_tfree_names (T, Tfs),


427 
vs, add_typ_ixns (Tvs, T)))


428 
(([], [], [], []), prf);


429 
val fs' = map (fst o dest_Free) fs;


430 
val vs' = map (fst o dest_Var) vs;


431 
val names = vs' ~~ variantlist (map fst vs', fs');


432 
val names' = Tvs ~~ variantlist (map fst Tvs, Tfs);


433 
val rnames = map swap names;


434 
val rnames' = map swap names';


435 
in


436 
(map_proof_terms (freeze names names') (frzT names') prf,


437 
map_proof_terms (thaw rnames rnames') (thawT rnames'))


438 
end;


439 


440 


441 
(***** implication introduction *****)


442 


443 
fun implies_intr_proof h prf =


444 
let


445 
fun abshyp i (Hyp t) = if h aconv t then PBound i else Hyp t


446 
 abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)


447 
 abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)


448 
 abshyp i (prf %% t) = abshyp i prf %% t


449 
 abshyp i (prf1 % prf2) = abshyp i prf1 % abshyp i prf2


450 
 abshyp _ prf = prf;


451 
in


452 
AbsP ("H", None (*h*), abshyp 0 prf)


453 
end;


454 


455 


456 
(***** forall introduction *****)


457 


458 
fun forall_intr_proof x a prf = Abst (a, None, prf_abstract_over x prf);


459 


460 


461 
(***** varify *****)


462 


463 
fun varify_proof t fixed prf =


464 
let


465 
val fs = add_term_tfree_names (t, []) \\ fixed;


466 
val ixns = add_term_tvar_ixns (t, []);


467 
val fmap = fs ~~ variantlist (fs, map #1 ixns)


468 
fun thaw (f as (a, S)) =


469 
(case assoc (fmap, a) of


470 
None => TFree f


471 
 Some b => TVar ((b, 0), S));


472 
in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf


473 
end;


474 


475 


476 
local


477 


478 
fun new_name (ix, (pairs,used)) =


479 
let val v = variant used (string_of_indexname ix)


480 
in ((ix, v) :: pairs, v :: used) end;


481 


482 
fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of


483 
None => TVar (ix, sort)


484 
 Some name => TFree (name, sort));


485 


486 
in


487 


488 
fun freezeT t prf =


489 
let


490 
val used = it_term_types add_typ_tfree_names (t, [])


491 
and tvars = map #1 (it_term_types add_typ_tvars (t, []));


492 
val (alist, _) = foldr new_name (tvars, ([], used));


493 
in


494 
(case alist of


495 
[] => prf (*nothing to do!*)


496 
 _ =>


497 
let val frzT = map_type_tvar (freeze_one alist)


498 
in map_proof_terms (map_term_types frzT) frzT prf end)


499 
end;


500 


501 
end;


502 


503 


504 
(***** rotate assumptions *****)


505 


506 
fun rotate_proof Bs Bi m prf =


507 
let


508 
val params = Term.strip_all_vars Bi;


509 
val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);


510 
val i = length asms;


511 
val j = length Bs;


512 
in


513 
mk_AbsP (j+1, proof_combP (prf, map PBound


514 
(j downto 1) @ [mk_Abst (params, mk_AbsP (i,


515 
proof_combP (proof_combt (PBound i, map Bound ((length params  1) downto 0)),


516 
map PBound (((im1) downto 0) @ ((i1) downto (im))))))]))


517 
end;


518 


519 


520 
(***** permute premises *****)


521 


522 
fun permute_prems_prf prems j k prf =


523 
let val n = length prems


524 
in mk_AbsP (n, proof_combP (prf,


525 
map PBound ((n1 downto nj) @ (k1 downto 0) @ (nj1 downto k))))


526 
end;


527 


528 


529 
(***** instantiation *****)


530 


531 
fun instantiate vTs tpairs =


532 
map_proof_terms (subst_atomic (map (apsnd remove_types) tpairs) o


533 
subst_TVars vTs) (typ_subst_TVars vTs);


534 


535 


536 
(***** lifting *****)


537 


538 
fun lift_proof Bi inc prop prf =


539 
let


540 
val (_, lift_all) = Logic.lift_fns (Bi, inc);


541 


542 
fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));


543 


544 
fun lift' Us Ts (Abst (s, T, prf)) = Abst (s, apsome (incr_tvar inc) T, lift' Us (dummyT::Ts) prf)


545 
 lift' Us Ts (AbsP (s, t, prf)) = AbsP (s, apsome (lift'' Us Ts) t, lift' Us Ts prf)


546 
 lift' Us Ts (prf %% t) = lift' Us Ts prf %% apsome (lift'' Us Ts) t


547 
 lift' Us Ts (prf1 % prf2) = lift' Us Ts prf1 % lift' Us Ts prf2


548 
 lift' _ _ (PThm (s, prf, prop, Ts)) = PThm (s, prf, prop, apsome (map (incr_tvar inc)) Ts)


549 
 lift' _ _ (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome (map (incr_tvar inc)) Ts)


550 
 lift' _ _ prf = prf;


551 


552 
val ps = map lift_all (Logic.strip_imp_prems (snd (Logic.strip_flexpairs prop)));


553 
val k = length ps;


554 


555 
fun mk_app (b, (i, j, prf)) =


556 
if b then (i1, j, prf % PBound i) else (i, j1, prf %%% Bound j);


557 


558 
fun lift Us bs i j (Const ("==>", _) $ A $ B) =


559 
AbsP ("H", None (*A*), lift Us (true::bs) (i+1) j B)


560 
 lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =


561 
Abst (a, None (*T*), lift (T::Us) (false::bs) i (j+1) t)


562 
 lift Us bs i j _ = proof_combP (lift' (rev Us) [] prf,


563 
map (fn k => (#3 (foldr mk_app (bs, (i1, j1, PBound k)))))


564 
(i + k  1 downto i));


565 
in


566 
mk_AbsP (k, lift [] [] 0 0 Bi)


567 
end;


568 


569 


570 
(***** proof by assumption *****)


571 


572 
fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", None (*A*), mk_asm_prf B (i+1))


573 
 mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, None (*T*), mk_asm_prf t i)


574 
 mk_asm_prf _ i = PBound i;


575 


576 
fun assumption_proof Bs Bi n prf =


577 
mk_AbsP (length Bs, proof_combP (prf,


578 
map PBound (length Bs  1 downto 0) @ [mk_asm_prf Bi (~n)]));


579 


580 


581 
(***** Composition of object rule with proof state *****)


582 


583 
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =


584 
AbsP ("H", None (*A*), flatten_params_proof (i+1) j n (B, k))


585 
 flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =


586 
Abst (a, None (*T*), flatten_params_proof i (j+1) n (t, k))


587 
 flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),


588 
map Bound (j1 downto 0)), map PBound (i1 downto 0 \ in));


589 


590 
fun bicompose_proof Bs oldAs newAs A n rprf sprf =


591 
let


592 
val la = length newAs;


593 
val lb = length Bs;


594 
in


595 
mk_AbsP (lb+la, proof_combP (sprf,


596 
map PBound (lb + la  1 downto la)) %


597 
proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @


598 
map (flatten_params_proof 0 0 n) (oldAs ~~ (la  1 downto 0))))


599 
end;


600 


601 


602 
(***** axioms for equality *****)


603 


604 
val aT = TFree ("'a", ["logic"]);


605 
val bT = TFree ("'b", ["logic"]);


606 
val x = Free ("x", aT);


607 
val y = Free ("y", aT);


608 
val z = Free ("z", aT);


609 
val A = Free ("A", propT);


610 
val B = Free ("B", propT);


611 
val f = Free ("f", aT > bT);


612 
val g = Free ("g", aT > bT);


613 


614 
local open Logic in


615 


616 
val equality_axms =


617 
[("reflexive", mk_equals (x, x)),


618 
("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),


619 
("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),


620 
("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),


621 
("equal_elim", list_implies ([mk_equals (A, B), A], B)),


622 
("abstract_rule", Logic.mk_implies


623 
(all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),


624 
equals (aT > bT) $


625 
Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),


626 
("combination", Logic.list_implies


627 
([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],


628 
Logic.mk_equals (f $ x, g $ y)))];


629 


630 
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,


631 
equal_elim_axm, abstract_rule_axm, combination_axm] =


632 
map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, None)) equality_axms;


633 


634 
end;


635 


636 
val reflexive = reflexive_axm %% None;


637 


638 
fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) %% _) = prf


639 
 symmetric prf = symmetric_axm %% None %% None % prf;


640 


641 
fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) %% _) prf2 = prf2


642 
 transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) %% _) = prf1


643 
 transitive u (Type ("prop", [])) prf1 prf2 =


644 
transitive_axm %% None %% Some (remove_types u) %% None % prf1 % prf2


645 
 transitive u T prf1 prf2 =


646 
transitive_axm %% None %% None %% None % prf1 % prf2;


647 


648 
fun abstract_rule x a prf =


649 
abstract_rule_axm %% None %% None % forall_intr_proof x a prf;


650 


651 
fun check_comb (PAxm ("ProtoPure.combination", _, _) %% f %% g %% _ %% _ % prf % _) =


652 
is_some f orelse check_comb prf


653 
 check_comb (PAxm ("ProtoPure.transitive", _, _) %% _ %% _ %% _ % prf1 % prf2) =


654 
check_comb prf1 andalso check_comb prf2


655 
 check_comb (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % prf) = check_comb prf


656 
 check_comb _ = false;


657 


658 
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =


659 
let


660 
val f = Envir.beta_norm f;


661 
val g = Envir.beta_norm g;


662 
val prf = if check_comb prf1 then


663 
combination_axm %% None %% None


664 
else (case prf1 of


665 
PAxm ("ProtoPure.reflexive", _, _) %% _ =>


666 
combination_axm %%% remove_types f %% None


667 
 _ => combination_axm %%% remove_types f %%% remove_types g)


668 
in


669 
(case T of


670 
Type ("fun", _) => prf %%


671 
(case head_of f of


672 
Abs _ => Some (remove_types t)


673 
 Var _ => Some (remove_types t)


674 
 _ => None) %%


675 
(case head_of g of


676 
Abs _ => Some (remove_types u)


677 
 Var _ => Some (remove_types u)


678 
 _ => None) % prf1 % prf2


679 
 _ => prf %% None %% None % prf1 % prf2)


680 
end;


681 


682 
fun equal_intr A B prf1 prf2 =


683 
equal_intr_axm %%% remove_types A %%% remove_types B % prf1 % prf2;


684 


685 
fun equal_elim A B prf1 prf2 =


686 
equal_elim_axm %%% remove_types A %%% remove_types B % prf1 % prf2;


687 


688 


689 
(***** axioms and theorems *****)


690 


691 
fun vars_of t = rev (foldl_aterms


692 
(fn (vs, v as Var _) => v ins vs  (vs, _) => vs) ([], t));


693 


694 
fun test_args _ [] = true


695 
 test_args is (Bound i :: ts) =


696 
not (i mem is) andalso test_args (i :: is) ts


697 
 test_args _ _ = false;


698 


699 
fun is_fun (Type ("fun", _)) = true


700 
 is_fun (TVar _) = true


701 
 is_fun _ = false;


702 


703 
fun add_funvars Ts (vs, t) =


704 
if is_fun (fastype_of1 (Ts, t)) then


705 
vs union mapfilter (fn Var (ixn, T) =>


706 
if is_fun T then Some ixn else None  _ => None) (vars_of t)


707 
else vs;


708 


709 
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =


710 
add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)


711 
 add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =


712 
add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)


713 
 add_npvars q p Ts (vs, t) = (case strip_comb t of


714 
(Var (ixn, _), ts) => if test_args [] ts then vs


715 
else foldl (add_npvars q p Ts) (overwrite (vs,


716 
(ixn, foldl (add_funvars Ts) (if_none (assoc (vs, ixn)) [], ts))), ts)


717 
 (Abs (_, T, u), ts) => foldl (add_npvars q p (T::Ts)) (vs, u :: ts)


718 
 (_, ts) => foldl (add_npvars q p Ts) (vs, ts));


719 


720 
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q


721 
 prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t


722 
 prop_vars t = (case strip_comb t of


723 
(Var (ixn, _), _) => [ixn]  _ => []);


724 


725 
fun is_proj t =


726 
let


727 
fun is_p i t = (case strip_comb t of


728 
(Bound j, []) => false


729 
 (Bound j, ts) => j >= i orelse exists (is_p i) ts


730 
 (Abs (_, _, u), _) => is_p (i+1) u


731 
 (_, ts) => exists (is_p i) ts)


732 
in (case strip_abs_body t of


733 
Bound _ => true


734 
 t' => is_p 0 t')


735 
end;


736 


737 
fun needed_vars prop =


738 
foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union


739 
prop_vars prop;


740 


741 
fun gen_axm_proof c name prop =


742 
let


743 
val nvs = needed_vars prop;


744 
val args = map (fn (v as Var (ixn, _)) =>


745 
if ixn mem nvs then Some v else None) (vars_of prop) @


746 
map Some (sort (make_ord atless) (term_frees prop));


747 
in


748 
proof_combt' (c (name, prop, None), args)


749 
end;


750 


751 
val axm_proof = gen_axm_proof PAxm;


752 
val oracle_proof = gen_axm_proof Oracle;


753 


754 
fun shrink ls lev (prf as Abst (a, T, body)) =


755 
let val (b, is, ch, body') = shrink ls (lev+1) body


756 
in (b, is, ch, if ch then Abst (a, T, body') else prf) end


757 
 shrink ls lev (prf as AbsP (a, t, body)) =


758 
let val (b, is, ch, body') = shrink (lev::ls) lev body


759 
in (b orelse 0 mem is, mapfilter (fn 0 => None  i => Some (i1)) is,


760 
ch, if ch then AbsP (a, t, body') else prf)


761 
end


762 
 shrink ls lev prf =


763 
let val (is, ch, _, prf') = shrink' ls lev [] [] prf


764 
in (false, is, ch, prf') end


765 
and shrink' ls lev ts prfs (prf as prf1 % prf2) =


766 
let


767 
val p as (_, is', ch', prf') = shrink ls lev prf2;


768 
val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1


769 
in (is union is', ch orelse ch', ts',


770 
if ch orelse ch' then prf'' % prf' else prf)


771 
end


772 
 shrink' ls lev ts prfs (prf as prf1 %% t) =


773 
let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1


774 
in (is, ch orelse ch', ts', if ch orelse ch' then prf' %% t' else prf) end


775 
 shrink' ls lev ts prfs (prf as PBound i) =


776 
(if exists (fn Some (Bound j) => levj <= nth_elem (i, ls)  _ => true) ts


777 
orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)


778 
 shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)


779 
 shrink' ls lev ts prfs prf =


780 
let


781 
val prop = (case prf of PThm (_, _, prop, _) => prop  PAxm (_, prop, _) => prop


782 
 Oracle (_, prop, _) => prop  _ => error "shrink: proof not in normal form");


783 
val vs = vars_of prop;


784 
val ts' = take (length vs, ts)


785 
val ts'' = drop (length vs, ts)


786 
val insts = take (length ts', map (fst o dest_Var) vs) ~~ ts';


787 
val nvs = foldl (fn (ixns', (ixn, ixns)) =>


788 
ixn ins (case assoc (insts, ixn) of


789 
Some (Some t) => if is_proj t then ixns union ixns' else ixns'


790 
 _ => ixns union ixns'))


791 
(needed prop ts'' prfs, add_npvars false true [] ([], prop));


792 
val insts' = map


793 
(fn (ixn, x as Some _) => if ixn mem nvs then (false, x) else (true, None)


794 
 (_, x) => (false, x)) insts


795 
in ([], false, insts' @ map (pair false) ts'', prf) end


796 
and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =


797 
(if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs


798 
 needed (Var (ixn, _)) (_::_) _ = [ixn]


799 
 needed _ _ _ = [];


800 


801 


802 
(**** Simple first order matching functions for terms and proofs ****)


803 


804 
exception PMatch;


805 


806 
(** see pattern.ML **)


807 


808 
fun fomatch Ts tmatch =


809 
let


810 
fun mtch (instsp as (tyinsts, insts)) = fn


811 
(Var (ixn, T), t) =>


812 
(tmatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))), (ixn, t)::insts)


813 
 (Free (a, T), Free (b, U)) =>


814 
if a=b then (tmatch (tyinsts, K (T, U)), insts) else raise PMatch


815 
 (Const (a, T), Const (b, U)) =>


816 
if a=b then (tmatch (tyinsts, K (T, U)), insts) else raise PMatch


817 
 (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)


818 
 _ => raise PMatch


819 
in mtch end;


820 


821 
fun match_proof Ts tmatch =


822 
let


823 
fun mtch (inst as (pinst, tinst as (tyinsts, insts))) = fn


824 
(Hyp (Var (ixn, _)), prf) => ((ixn, prf)::pinst, tinst)


825 
 (prf1 %% opt1, prf2 %% opt2) =>


826 
let val inst' as (pinst, tinst) = mtch inst (prf1, prf2)


827 
in (case (opt1, opt2) of


828 
(None, _) => inst'


829 
 (Some _, None) => raise PMatch


830 
 (Some t, Some u) => (pinst, fomatch Ts tmatch tinst (t, Envir.beta_norm u)))


831 
end


832 
 (prf1 % prf2, prf1' % prf2') =>


833 
mtch (mtch inst (prf1, prf1')) (prf2, prf2')


834 
 (PThm ((name1, _), _, prop1, None), PThm ((name2, _), _, prop2, _)) =>


835 
if name1=name2 andalso prop1=prop2 then inst else raise PMatch


836 
 (PThm ((name1, _), _, prop1, Some Ts), PThm ((name2, _), _, prop2, Some Us)) =>


837 
if name1=name2 andalso prop1=prop2 then


838 
(pinst, (foldl (tmatch o apsnd K) (tyinsts, Ts ~~ Us), insts))


839 
else raise PMatch


840 
 (PAxm (s1, _, None), PAxm (s2, _, _)) =>


841 
if s1=s2 then inst else raise PMatch


842 
 (PAxm (s1, _, Some Ts), PAxm (s2, _, Some Us)) =>


843 
if s1=s2 then


844 
(pinst, (foldl (tmatch o apsnd K) (tyinsts, Ts ~~ Us), insts))


845 
else raise PMatch


846 
 _ => raise PMatch


847 
in mtch end;


848 


849 
fun prf_subst (pinst, (tyinsts, insts)) =


850 
let


851 
val substT = typ_subst_TVars_Vartab tyinsts;


852 


853 
fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of


854 
None => t


855 
 Some u => incr_boundvars lev u)


856 
 subst' lev (Const (s, T)) = Const (s, substT T)


857 
 subst' lev (Free (s, T)) = Free (s, substT T)


858 
 subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)


859 
 subst' lev (f $ t) = subst' lev f $ subst' lev t


860 
 subst' _ t = t;


861 


862 
fun subst plev tlev (AbsP (a, t, body)) =


863 
AbsP (a, apsome (subst' tlev) t, subst (plev+1) tlev body)


864 
 subst plev tlev (Abst (a, T, body)) =


865 
Abst (a, apsome substT T, subst plev (tlev+1) body)


866 
 subst plev tlev (prf % prf') = subst plev tlev prf % subst plev tlev prf'


867 
 subst plev tlev (prf %% t) = subst plev tlev prf %% apsome (subst' tlev) t


868 
 subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of


869 
None => prf


870 
 Some prf' => incr_pboundvars plev tlev prf')


871 
 subst _ _ (PThm (id, prf, prop, Ts)) =


872 
PThm (id, prf, prop, apsome (map substT) Ts)


873 
 subst _ _ (PAxm (id, prop, Ts)) =


874 
PAxm (id, prop, apsome (map substT) Ts)


875 
 subst _ _ t = t


876 
in subst 0 0 end;


877 


878 
(**** rewriting on proof terms ****)


879 


880 
fun rewrite_prf tmatch (rules, procs) prf =


881 
let


882 
fun rew _ (Abst (_, _, body) %% Some t) = Some (prf_subst_bounds [t] body)


883 
 rew _ (AbsP (_, _, body) % prf) = Some (prf_subst_pbounds [prf] body)


884 
 rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of


885 
Some prf' => Some prf'


886 
 None => get_first (fn (prf1, prf2) => Some (prf_subst


887 
(match_proof Ts tmatch ([], (Vartab.empty, [])) (prf1, prf)) prf2)


888 
handle PMatch => None) rules);


889 


890 
fun rew0 Ts (prf as AbsP (_, _, prf' % PBound 0)) =


891 
if prf_loose_Pbvar1 prf' 0 then rew Ts prf


892 
else


893 
let val prf'' = incr_pboundvars (~1) 0 prf'


894 
in Some (if_none (rew Ts prf'') prf'') end


895 
 rew0 Ts (prf as Abst (_, _, prf' %% Some (Bound 0))) =


896 
if prf_loose_bvar1 prf' 0 then rew Ts prf


897 
else


898 
let val prf'' = incr_pboundvars 0 (~1) prf'


899 
in Some (if_none (rew Ts prf'') prf'') end


900 
 rew0 Ts prf = rew Ts prf;


901 


902 
fun rew1 Ts prf = (case rew2 Ts prf of


903 
Some prf1 => (case rew0 Ts prf1 of


904 
Some prf2 => Some (if_none (rew1 Ts prf2) prf2)


905 
 None => Some prf1)


906 
 None => (case rew0 Ts prf of


907 
Some prf1 => Some (if_none (rew1 Ts prf1) prf1)


908 
 None => None))


909 


910 
and rew2 Ts (prf %% Some t) = (case prf of


911 
Abst (_, _, body) =>


912 
let val prf' = prf_subst_bounds [t] body


913 
in Some (if_none (rew2 Ts prf') prf') end


914 
 _ => (case rew1 Ts prf of


915 
Some prf' => Some (prf' %% Some t)


916 
 None => None))


917 
 rew2 Ts (prf %% None) = apsome (fn prf' => prf' %% None) (rew1 Ts prf)


918 
 rew2 Ts (prf1 % prf2) = (case prf1 of


919 
AbsP (_, _, body) =>


920 
let val prf' = prf_subst_pbounds [prf2] body


921 
in Some (if_none (rew2 Ts prf') prf') end


922 
 _ => (case rew1 Ts prf1 of


923 
Some prf1' => (case rew1 Ts prf2 of


924 
Some prf2' => Some (prf1' % prf2')


925 
 None => Some (prf1' % prf2))


926 
 None => (case rew1 Ts prf2 of


927 
Some prf2' => Some (prf1 % prf2')


928 
 None => None)))


929 
 rew2 Ts (Abst (s, T, prf)) = (case rew1 (if_none T dummyT :: Ts) prf of


930 
Some prf' => Some (Abst (s, T, prf'))


931 
 None => None)


932 
 rew2 Ts (AbsP (s, t, prf)) = (case rew1 Ts prf of


933 
Some prf' => Some (AbsP (s, t, prf'))


934 
 None => None)


935 
 rew2 _ _ = None


936 


937 
in if_none (rew1 [] prf) prf end;


938 


939 
fun rewrite_proof tsig = rewrite_prf (fn (tab, f) =>


940 
Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch);


941 


942 
(**** theory data ****)


943 


944 
(* data kind 'Pure/proof' *)


945 


946 
structure ProofArgs =


947 
struct


948 
val name = "Pure/proof";


949 
type T = ((proof * proof) list *


950 
(string * (typ list > proof > proof option)) list) ref;


951 


952 
val empty = (ref ([], [])): T;


953 
fun copy (ref rews) = (ref rews): T; (*create new reference!*)


954 
val prep_ext = copy;


955 
fun merge (ref (rules1, procs1), ref (rules2, procs2)) = ref


956 
(merge_lists rules1 rules2,


957 
generic_merge (uncurry equal o pairself fst) I I procs1 procs2);


958 
fun print _ _ = ();


959 
end;


960 


961 
structure ProofData = TheoryDataFun(ProofArgs);


962 


963 
val init = ProofData.init;


964 


965 
fun add_prf_rrules thy rs =


966 
let val r = ProofData.get thy


967 
in r := (rs @ fst (!r), snd (!r)) end;


968 


969 
fun add_prf_rprocs thy ps =


970 
let val r = ProofData.get thy


971 
in r := (fst (!r), ps @ snd (!r)) end;


972 


973 
fun thm_proof sign (name, tags) hyps prop prf =


974 
let


975 
val hyps' = gen_distinct op aconv hyps;


976 
val prop = Logic.list_implies (hyps', prop);


977 
val nvs = needed_vars prop;


978 
val args = map (fn (v as Var (ixn, _)) =>


979 
if ixn mem nvs then Some v else None) (vars_of prop) @


980 
map Some (sort (make_ord atless) (term_frees prop));


981 
val opt_prf = if !keep_derivs=FullDeriv then


982 
#4 (shrink [] 0 (rewrite_prf fst (!(ProofData.get_sg sign))


983 
(foldr (uncurry implies_intr_proof) (hyps', prf))))


984 
else MinProof (mk_min_proof ([], prf));


985 
val head = (case strip_combt (fst (strip_combP prf)) of


986 
(PThm ((old_name, _), prf', prop', None), args') =>


987 
if (old_name="" orelse old_name=name) andalso


988 
prop = prop' andalso args = args' then


989 
PThm ((name, tags), prf', prop, None)


990 
else


991 
PThm ((name, tags), opt_prf, prop, None)


992 
 _ => PThm ((name, tags), opt_prf, prop, None))


993 
in


994 
proof_combP (proof_combt' (head, args), map Hyp hyps')


995 
end;


996 


997 
fun get_name_tags prop prf = (case strip_combt (fst (strip_combP prf)) of


998 
(PThm ((name, tags), _, prop', _), _) =>


999 
if prop=prop' then (name, tags) else ("", [])


1000 
 (PAxm (name, prop', _), _) =>


1001 
if prop=prop' then (name, []) else ("", [])


1002 
 _ => ("", []));


1003 


1004 
end;


1005 


1006 
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;


1007 
open BasicProofterm;
