author  berghofe 
Tue, 10 Dec 2002 10:40:32 +0100  
changeset 13744  2241191a3c54 
parent 13662  1f8ddc4b371e 
child 13749  6844c38d74df 
permissions  rwrr 
11519  1 
(* Title: Pure/proofterm.ML 
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ID: $Id$ 

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Author: Stefan Berghofer, TU Muenchen 
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License: GPL (GNU GENERAL PUBLIC LICENSE) 

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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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val proofs: int ref 
11519  14 

15 
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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 % of proof * term option 
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 %% 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 
11519  28 
end; 
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signature PROOFTERM = 

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sig 

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include BASIC_PROOFTERM 

33 

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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) 

36 

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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 maxidx_of_proof : proof > int 
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val size_of_proof : proof > int 
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val change_type : typ list option > proof > proof 
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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 prf_add_loose_bnos : int > int > proof > 
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int list * int list > int list * int list 

11519  59 
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 list > term > proof > string * (string * string list) list 
11519  102 

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(** rewriting on proof terms **) 

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val add_prf_rrules : (proof * proof) list > theory > theory 
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val add_prf_rprocs : (string * (Term.typ list > proof > proof option)) list > 

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theory > theory 

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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 rewrite_proof_notypes : (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 

114 

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structure Proofterm : PROOFTERM = 

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struct 

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open Envir; 
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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; 

131 

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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 

140 
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 

146 
in 

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

148 
end; 

149 

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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 (MinProof prfs) = foldl (uncurry thms_of_proof) (tab, prfs) 
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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 (MinProof prfs) = foldl (uncurry axms_of_proof) (tab, prfs) 
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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; 

181 

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

183 

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val proofs = ref 2; 
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fun err_illegal_level i = 
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error ("Illegal level of detail for proof objects: " ^ string_of_int i); 
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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 !proofs of 
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2 => f prf1 prf2 
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 1 => MinProof (mk_min_proof (mk_min_proof ([], prf1), prf2)) 
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 0 => MinProof (if_ora ora2 (if_ora ora1 [] prf1) prf2) 
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 i => err_illegal_level i); 
11519  198 

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fun infer_derivs' f (ora, prf) = 

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(ora, 

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case !proofs of 
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2 => f prf 
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 1 => MinProof (mk_min_proof ([], prf)) 
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 0 => MinProof (if_ora ora [] prf) 
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 i => err_illegal_level i); 
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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; 

229 

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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 same f x = 
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let val x' = f x 
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in if x = x' then raise SAME else x' end; 
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fun map_proof_terms f g = 
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let 
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fun mapp (Abst (s, T, prf)) = (Abst (s, apsome' (same g) T, mapph prf) 
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handle SAME => Abst (s, T, mapp prf)) 
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 mapp (AbsP (s, t, prf)) = (AbsP (s, apsome' (same f) t, mapph prf) 
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handle SAME => AbsP (s, t, mapp prf)) 
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 mapp (prf % t) = (mapp prf % apsome f t 
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handle SAME => prf % apsome' (same f) t) 
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 mapp (prf1 %% prf2) = (mapp prf1 %% mapph prf2 
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handle SAME => prf1 %% mapp prf2) 
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 mapp (PThm (a, prf, prop, Some Ts)) = 
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PThm (a, prf, prop, Some (same (map g) Ts)) 
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 mapp (PAxm (a, prop, Some Ts)) = 
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PAxm (a, prop, Some (same (map g) Ts)) 
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 mapp _ = raise SAME 
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and mapph prf = (mapp prf handle SAME => prf) 
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in mapph end; 
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fun fold_proof_terms f g (a, Abst (_, Some T, prf)) = fold_proof_terms f g (g (T, a), prf) 

257 
 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) 

259 
 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 

11519  263 
(fold_proof_terms f g (a, prf1), prf2) 
264 
 fold_proof_terms _ g (a, PThm (_, _, _, Some Ts)) = foldr g (Ts, a) 

265 
 fold_proof_terms _ g (a, PAxm (_, prop, Some Ts)) = foldr g (Ts, a) 

266 
 fold_proof_terms _ _ (a, _) = a; 

267 

268 
val add_prf_names = fold_proof_terms add_term_names ((uncurry K) o swap); 

269 
val add_prf_tfree_names = fold_proof_terms add_term_tfree_names add_typ_tfree_names; 

270 
val add_prf_tvar_ixns = fold_proof_terms add_term_tvar_ixns (add_typ_ixns o swap); 

271 

12868  272 
fun maxidx_of_proof prf = fold_proof_terms 
273 
(Int.max o apfst maxidx_of_term) (Int.max o apfst maxidx_of_typ) (~1, prf); 

274 

13744  275 
fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf 
276 
 size_of_proof (AbsP (_, t, prf)) = 

277 
if_none (apsome size_of_term t) 1 + size_of_proof prf 

278 
 size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2 

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 size_of_proof (prf % t) = 

280 
if_none (apsome size_of_term t) 1 + size_of_proof prf 

281 
 size_of_proof _ = 1; 

282 

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fun change_type opTs (PThm (name, prf, prop, _)) = PThm (name, prf, prop, opTs) 
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 change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs) 
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 change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs) 
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 change_type _ prf = prf; 
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11519  288 

289 
(***** utilities *****) 

290 

291 
fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t 

292 
 strip_abs _ t = t; 

293 

294 
fun mk_abs Ts t = foldl (fn (t', T) => Abs ("", T, t')) (t, Ts); 

295 

296 

297 
(*Abstraction of a proof term over its occurrences of v, 

298 
which must contain no loose bound variables. 

299 
The resulting proof term is ready to become the body of an Abst.*) 

300 

301 
fun prf_abstract_over v = 

302 
let 

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fun abst' lev u = if v aconv u then Bound lev else 
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(case u of 
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Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t) 
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 f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t) 
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 _ => raise SAME) 
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308 
and absth' lev t = (abst' lev t handle SAME => t); 
11519  309 

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310 
fun abst lev (AbsP (a, t, prf)) = 
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311 
(AbsP (a, apsome' (abst' lev) t, absth lev prf) 
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312 
handle SAME => AbsP (a, t, abst lev prf)) 
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313 
 abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf) 
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314 
 abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2 
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315 
handle SAME => prf1 %% abst lev prf2) 
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316 
 abst lev (prf % t) = (abst lev prf % apsome (absth' lev) t 
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317 
handle SAME => prf % apsome' (abst' lev) t) 
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318 
 abst _ _ = raise SAME 
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319 
and absth lev prf = (abst lev prf handle SAME => prf) 
11519  320 

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321 
in absth 0 end; 
11519  322 

323 

324 
(*increments a proof term's nonlocal bound variables 

325 
required when moving a proof term within abstractions 

326 
inc is increment for bound variables 

327 
lev is level at which a bound variable is considered 'loose'*) 

328 

329 
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t); 

330 

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331 
fun prf_incr_bv' incP inct Plev tlev (PBound i) = 
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332 
if i >= Plev then PBound (i+incP) else raise SAME 
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333 
 prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) = 
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334 
(AbsP (a, apsome' (same (incr_bv' inct tlev)) t, 
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335 
prf_incr_bv incP inct (Plev+1) tlev body) handle SAME => 
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336 
AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body)) 
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337 
 prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) = 
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338 
Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body) 
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339 
 prf_incr_bv' incP inct Plev tlev (prf %% prf') = 
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340 
(prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf' 
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341 
handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf') 
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342 
 prf_incr_bv' incP inct Plev tlev (prf % t) = 
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343 
(prf_incr_bv' incP inct Plev tlev prf % apsome (incr_bv' inct tlev) t 
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344 
handle SAME => prf % apsome' (same (incr_bv' inct tlev)) t) 
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345 
 prf_incr_bv' _ _ _ _ _ = raise SAME 
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346 
and prf_incr_bv incP inct Plev tlev prf = 
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347 
(prf_incr_bv' incP inct Plev tlev prf handle SAME => prf); 
11519  348 

349 
fun incr_pboundvars 0 0 prf = prf 

350 
 incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf; 

351 

352 

11615  353 
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k 
354 
 prf_loose_bvar1 (prf % Some t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k) 

355 
 prf_loose_bvar1 (_ % None) _ = true 

11519  356 
 prf_loose_bvar1 (AbsP (_, Some t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k 
357 
 prf_loose_bvar1 (AbsP (_, None, _)) k = true 

358 
 prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1) 

359 
 prf_loose_bvar1 _ _ = false; 

360 

361 
fun prf_loose_Pbvar1 (PBound i) k = i = k 

11615  362 
 prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k 
363 
 prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k 

11519  364 
 prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1) 
365 
 prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k 

366 
 prf_loose_Pbvar1 _ _ = false; 

367 

12279  368 
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) = 
369 
if i < plev then (is, js) else ((iplev) ins is, js) 

370 
 prf_add_loose_bnos plev tlev (prf1 %% prf2) p = 

371 
prf_add_loose_bnos plev tlev prf2 

372 
(prf_add_loose_bnos plev tlev prf1 p) 

373 
 prf_add_loose_bnos plev tlev (prf % opt) (is, js) = 

374 
prf_add_loose_bnos plev tlev prf (case opt of 

375 
None => (is, ~1 ins js) 

376 
 Some t => (is, add_loose_bnos (t, tlev, js))) 

377 
 prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) = 

378 
prf_add_loose_bnos (plev+1) tlev prf (case opt of 

379 
None => (is, ~1 ins js) 

380 
 Some t => (is, add_loose_bnos (t, tlev, js))) 

381 
 prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p = 

382 
prf_add_loose_bnos plev (tlev+1) prf p 

383 
 prf_add_loose_bnos _ _ _ _ = ([], []); 

384 

11519  385 

386 
(**** substitutions ****) 

387 

388 
fun norm_proof env = 

389 
let 

12497  390 
val envT = type_env env; 
391 
fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same envT) T, normh prf) 

11519  392 
handle SAME => Abst (s, T, norm prf)) 
393 
 norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf) 

394 
handle SAME => AbsP (s, t, norm prf)) 

11615  395 
 norm (prf % t) = (norm prf % apsome (norm_term env) t 
396 
handle SAME => prf % apsome' (norm_term_same env) t) 

397 
 norm (prf1 %% prf2) = (norm prf1 %% normh prf2 

398 
handle SAME => prf1 %% norm prf2) 

12497  399 
 norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same envT) Ts) 
400 
 norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same envT) Ts) 

11519  401 
 norm _ = raise SAME 
402 
and normh prf = (norm prf handle SAME => prf); 

403 
in normh end; 

404 

405 
(***** Remove some types in proof term (to save space) *****) 

406 

407 
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t) 

408 
 remove_types (t $ u) = remove_types t $ remove_types u 

409 
 remove_types (Const (s, _)) = Const (s, dummyT) 

410 
 remove_types t = t; 

411 

412 
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) = 

413 
Envir.Envir {iTs = iTs, asol = Vartab.map remove_types asol, maxidx = maxidx}; 

414 

415 
fun norm_proof' env prf = norm_proof (remove_types_env env) prf; 

416 

417 
(**** substitution of bound variables ****) 

418 

419 
fun prf_subst_bounds args prf = 

420 
let 

421 
val n = length args; 

422 
fun subst' lev (Bound i) = 

423 
(if i<lev then raise SAME (*var is locally bound*) 

424 
else incr_boundvars lev (List.nth (args, ilev)) 

425 
handle Subscript => Bound (in) (*loose: change it*)) 

426 
 subst' lev (Abs (a, T, body)) = Abs (a, T, subst' (lev+1) body) 

427 
 subst' lev (f $ t) = (subst' lev f $ substh' lev t 

428 
handle SAME => f $ subst' lev t) 

429 
 subst' _ _ = raise SAME 

430 
and substh' lev t = (subst' lev t handle SAME => t); 

431 

432 
fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body) 

433 
handle SAME => AbsP (a, t, subst lev body)) 

434 
 subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body) 

11615  435 
 subst lev (prf %% prf') = (subst lev prf %% substh lev prf' 
436 
handle SAME => prf %% subst lev prf') 

437 
 subst lev (prf % t) = (subst lev prf % apsome (substh' lev) t 

438 
handle SAME => prf % apsome' (subst' lev) t) 

11519  439 
 subst _ _ = raise SAME 
440 
and substh lev prf = (subst lev prf handle SAME => prf) 

441 
in case args of [] => prf  _ => substh 0 prf end; 

442 

443 
fun prf_subst_pbounds args prf = 

444 
let 

445 
val n = length args; 

446 
fun subst (PBound i) Plev tlev = 

447 
(if i < Plev then raise SAME (*var is locally bound*) 

448 
else incr_pboundvars Plev tlev (List.nth (args, iPlev)) 

449 
handle Subscript => PBound (in) (*loose: change it*)) 

450 
 subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev) 

451 
 subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1)) 

11615  452 
 subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev 
453 
handle SAME => prf %% subst prf' Plev tlev) 

454 
 subst (prf % t) Plev tlev = subst prf Plev tlev % t 

11519  455 
 subst prf _ _ = raise SAME 
456 
and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf) 

457 
in case args of [] => prf  _ => substh prf 0 0 end; 

458 

459 

460 
(**** Freezing and thawing of variables in proof terms ****) 

461 

462 
fun frzT names = 

463 
map_type_tvar (fn (ixn, xs) => TFree (the (assoc (names, ixn)), xs)); 

464 

465 
fun thawT names = 

466 
map_type_tfree (fn (s, xs) => case assoc (names, s) of 

467 
None => TFree (s, xs) 

468 
 Some ixn => TVar (ixn, xs)); 

469 

470 
fun freeze names names' (t $ u) = 

471 
freeze names names' t $ freeze names names' u 

472 
 freeze names names' (Abs (s, T, t)) = 

473 
Abs (s, frzT names' T, freeze names names' t) 

474 
 freeze names names' (Const (s, T)) = Const (s, frzT names' T) 

475 
 freeze names names' (Free (s, T)) = Free (s, frzT names' T) 

476 
 freeze names names' (Var (ixn, T)) = 

477 
Free (the (assoc (names, ixn)), frzT names' T) 

478 
 freeze names names' t = t; 

479 

480 
fun thaw names names' (t $ u) = 

481 
thaw names names' t $ thaw names names' u 

482 
 thaw names names' (Abs (s, T, t)) = 

483 
Abs (s, thawT names' T, thaw names names' t) 

484 
 thaw names names' (Const (s, T)) = Const (s, thawT names' T) 

485 
 thaw names names' (Free (s, T)) = 

486 
let val T' = thawT names' T 

487 
in case assoc (names, s) of 

488 
None => Free (s, T') 

489 
 Some ixn => Var (ixn, T') 

490 
end 

491 
 thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T) 

492 
 thaw names names' t = t; 

493 

494 
fun freeze_thaw_prf prf = 

495 
let 

496 
val (fs, Tfs, vs, Tvs) = fold_proof_terms 

497 
(fn (t, (fs, Tfs, vs, Tvs)) => 

498 
(add_term_frees (t, fs), add_term_tfree_names (t, Tfs), 

499 
add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs))) 

500 
(fn (T, (fs, Tfs, vs, Tvs)) => 

501 
(fs, add_typ_tfree_names (T, Tfs), 

502 
vs, add_typ_ixns (Tvs, T))) 

503 
(([], [], [], []), prf); 

504 
val fs' = map (fst o dest_Free) fs; 

505 
val vs' = map (fst o dest_Var) vs; 

506 
val names = vs' ~~ variantlist (map fst vs', fs'); 

507 
val names' = Tvs ~~ variantlist (map fst Tvs, Tfs); 

508 
val rnames = map swap names; 

509 
val rnames' = map swap names'; 

510 
in 

511 
(map_proof_terms (freeze names names') (frzT names') prf, 

512 
map_proof_terms (thaw rnames rnames') (thawT rnames')) 

513 
end; 

514 

515 

516 
(***** implication introduction *****) 

517 

518 
fun implies_intr_proof h prf = 

519 
let 

11715
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520 
fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME 
11519  521 
 abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf) 
522 
 abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf) 

11615  523 
 abshyp i (prf % t) = abshyp i prf % t 
11715
592923615f77
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524 
 abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2 
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525 
handle SAME => prf1 %% abshyp i prf2) 
592923615f77
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changeset

526 
 abshyp _ _ = raise SAME 
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527 
and abshyph i prf = (abshyp i prf handle SAME => prf) 
11519  528 
in 
11715
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529 
AbsP ("H", None (*h*), abshyph 0 prf) 
11519  530 
end; 
531 

532 

533 
(***** forall introduction *****) 

534 

535 
fun forall_intr_proof x a prf = Abst (a, None, prf_abstract_over x prf); 

536 

537 

538 
(***** varify *****) 

539 

540 
fun varify_proof t fixed prf = 

541 
let 

542 
val fs = add_term_tfree_names (t, []) \\ fixed; 

543 
val ixns = add_term_tvar_ixns (t, []); 

544 
val fmap = fs ~~ variantlist (fs, map #1 ixns) 

545 
fun thaw (f as (a, S)) = 

546 
(case assoc (fmap, a) of 

547 
None => TFree f 

548 
 Some b => TVar ((b, 0), S)); 

549 
in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf 

550 
end; 

551 

552 

553 
local 

554 

555 
fun new_name (ix, (pairs,used)) = 

556 
let val v = variant used (string_of_indexname ix) 

557 
in ((ix, v) :: pairs, v :: used) end; 

558 

559 
fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of 

560 
None => TVar (ix, sort) 

561 
 Some name => TFree (name, sort)); 

562 

563 
in 

564 

565 
fun freezeT t prf = 

566 
let 

567 
val used = it_term_types add_typ_tfree_names (t, []) 

568 
and tvars = map #1 (it_term_types add_typ_tvars (t, [])); 

569 
val (alist, _) = foldr new_name (tvars, ([], used)); 

570 
in 

571 
(case alist of 

572 
[] => prf (*nothing to do!*) 

573 
 _ => 

574 
let val frzT = map_type_tvar (freeze_one alist) 

575 
in map_proof_terms (map_term_types frzT) frzT prf end) 

576 
end; 

577 

578 
end; 

579 

580 

581 
(***** rotate assumptions *****) 

582 

583 
fun rotate_proof Bs Bi m prf = 

584 
let 

585 
val params = Term.strip_all_vars Bi; 

586 
val asms = Logic.strip_imp_prems (Term.strip_all_body Bi); 

587 
val i = length asms; 

588 
val j = length Bs; 

589 
in 

590 
mk_AbsP (j+1, proof_combP (prf, map PBound 

591 
(j downto 1) @ [mk_Abst (params, mk_AbsP (i, 

592 
proof_combP (proof_combt (PBound i, map Bound ((length params  1) downto 0)), 

593 
map PBound (((im1) downto 0) @ ((i1) downto (im))))))])) 

594 
end; 

595 

596 

597 
(***** permute premises *****) 

598 

599 
fun permute_prems_prf prems j k prf = 

600 
let val n = length prems 

601 
in mk_AbsP (n, proof_combP (prf, 

602 
map PBound ((n1 downto nj) @ (k1 downto 0) @ (nj1 downto k)))) 

603 
end; 

604 

605 

606 
(***** instantiation *****) 

607 

608 
fun instantiate vTs tpairs = 

609 
map_proof_terms (subst_atomic (map (apsnd remove_types) tpairs) o 

610 
subst_TVars vTs) (typ_subst_TVars vTs); 

611 

612 

613 
(***** lifting *****) 

614 

615 
fun lift_proof Bi inc prop prf = 

616 
let 

617 
val (_, lift_all) = Logic.lift_fns (Bi, inc); 

618 

619 
fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t)); 

620 

11715
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changeset

621 
fun lift' Us Ts (Abst (s, T, prf)) = 
592923615f77
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diff
changeset

622 
(Abst (s, apsome' (same (incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
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11652
diff
changeset

623 
handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf)) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

624 
 lift' Us Ts (AbsP (s, t, prf)) = 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

625 
(AbsP (s, apsome' (same (lift'' Us Ts)) t, lifth' Us Ts prf) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

626 
handle SAME => AbsP (s, t, lift' Us Ts prf)) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
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11652
diff
changeset

627 
 lift' Us Ts (prf % t) = (lift' Us Ts prf % apsome (lift'' Us Ts) t 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

628 
handle SAME => prf % apsome' (same (lift'' Us Ts)) t) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

629 
 lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

630 
handle SAME => prf1 %% lift' Us Ts prf2) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

631 
 lift' _ _ (PThm (s, prf, prop, Ts)) = 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
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diff
changeset

632 
PThm (s, prf, prop, apsome' (same (map (incr_tvar inc))) Ts) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

633 
 lift' _ _ (PAxm (s, prop, Ts)) = 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

634 
PAxm (s, prop, apsome' (same (map (incr_tvar inc))) Ts) 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

635 
 lift' _ _ _ = raise SAME 
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

636 
and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf); 
11519  637 

13662  638 
val ps = map lift_all (Logic.strip_imp_prems prop); 
11519  639 
val k = length ps; 
640 

641 
fun mk_app (b, (i, j, prf)) = 

11615  642 
if b then (i1, j, prf %% PBound i) else (i, j1, prf %> Bound j); 
11519  643 

644 
fun lift Us bs i j (Const ("==>", _) $ A $ B) = 

645 
AbsP ("H", None (*A*), lift Us (true::bs) (i+1) j B) 

646 
 lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 

647 
Abst (a, None (*T*), lift (T::Us) (false::bs) i (j+1) t) 

11715
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

648 
 lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf, 
11519  649 
map (fn k => (#3 (foldr mk_app (bs, (i1, j1, PBound k))))) 
650 
(i + k  1 downto i)); 

651 
in 

652 
mk_AbsP (k, lift [] [] 0 0 Bi) 

653 
end; 

654 

655 

656 
(***** proof by assumption *****) 

657 

658 
fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", None (*A*), mk_asm_prf B (i+1)) 

659 
 mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, None (*T*), mk_asm_prf t i) 

660 
 mk_asm_prf _ i = PBound i; 

661 

662 
fun assumption_proof Bs Bi n prf = 

663 
mk_AbsP (length Bs, proof_combP (prf, 

664 
map PBound (length Bs  1 downto 0) @ [mk_asm_prf Bi (~n)])); 

665 

666 

667 
(***** Composition of object rule with proof state *****) 

668 

669 
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) = 

670 
AbsP ("H", None (*A*), flatten_params_proof (i+1) j n (B, k)) 

671 
 flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) = 

672 
Abst (a, None (*T*), flatten_params_proof i (j+1) n (t, k)) 

673 
 flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i), 

674 
map Bound (j1 downto 0)), map PBound (i1 downto 0 \ in)); 

675 

676 
fun bicompose_proof Bs oldAs newAs A n rprf sprf = 

677 
let 

678 
val la = length newAs; 

679 
val lb = length Bs; 

680 
in 

681 
mk_AbsP (lb+la, proof_combP (sprf, 

11615  682 
map PBound (lb + la  1 downto la)) %% 
11519  683 
proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @ 
684 
map (flatten_params_proof 0 0 n) (oldAs ~~ (la  1 downto 0)))) 

685 
end; 

686 

687 

688 
(***** axioms for equality *****) 

689 

690 
val aT = TFree ("'a", ["logic"]); 

691 
val bT = TFree ("'b", ["logic"]); 

692 
val x = Free ("x", aT); 

693 
val y = Free ("y", aT); 

694 
val z = Free ("z", aT); 

695 
val A = Free ("A", propT); 

696 
val B = Free ("B", propT); 

697 
val f = Free ("f", aT > bT); 

698 
val g = Free ("g", aT > bT); 

699 

700 
local open Logic in 

701 

702 
val equality_axms = 

703 
[("reflexive", mk_equals (x, x)), 

704 
("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))), 

705 
("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))), 

706 
("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))), 

707 
("equal_elim", list_implies ([mk_equals (A, B), A], B)), 

708 
("abstract_rule", Logic.mk_implies 

709 
(all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)), 

710 
equals (aT > bT) $ 

711 
Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))), 

712 
("combination", Logic.list_implies 

713 
([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], 

714 
Logic.mk_equals (f $ x, g $ y)))]; 

715 

716 
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm, 

717 
equal_elim_axm, abstract_rule_axm, combination_axm] = 

718 
map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, None)) equality_axms; 

719 

720 
end; 

721 

11615  722 
val reflexive = reflexive_axm % None; 
11519  723 

11615  724 
fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) % _) = prf 
725 
 symmetric prf = symmetric_axm % None % None %% prf; 

11519  726 

11615  727 
fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) % _) prf2 = prf2 
728 
 transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) % _) = prf1 

11519  729 
 transitive u (Type ("prop", [])) prf1 prf2 = 
11615  730 
transitive_axm % None % Some (remove_types u) % None %% prf1 %% prf2 
11519  731 
 transitive u T prf1 prf2 = 
11615  732 
transitive_axm % None % None % None %% prf1 %% prf2; 
11519  733 

734 
fun abstract_rule x a prf = 

11615  735 
abstract_rule_axm % None % None %% forall_intr_proof x a prf; 
11519  736 

11615  737 
fun check_comb (PAxm ("ProtoPure.combination", _, _) % f % g % _ % _ %% prf %% _) = 
11519  738 
is_some f orelse check_comb prf 
11615  739 
 check_comb (PAxm ("ProtoPure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) = 
11519  740 
check_comb prf1 andalso check_comb prf2 
11615  741 
 check_comb (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf) = check_comb prf 
11519  742 
 check_comb _ = false; 
743 

744 
fun combination f g t u (Type (_, [T, U])) prf1 prf2 = 

745 
let 

746 
val f = Envir.beta_norm f; 

747 
val g = Envir.beta_norm g; 

748 
val prf = if check_comb prf1 then 

11615  749 
combination_axm % None % None 
11519  750 
else (case prf1 of 
11615  751 
PAxm ("ProtoPure.reflexive", _, _) % _ => 
752 
combination_axm %> remove_types f % None 

753 
 _ => combination_axm %> remove_types f %> remove_types g) 

11519  754 
in 
755 
(case T of 

11615  756 
Type ("fun", _) => prf % 
11519  757 
(case head_of f of 
758 
Abs _ => Some (remove_types t) 

759 
 Var _ => Some (remove_types t) 

11615  760 
 _ => None) % 
11519  761 
(case head_of g of 
762 
Abs _ => Some (remove_types u) 

763 
 Var _ => Some (remove_types u) 

11615  764 
 _ => None) %% prf1 %% prf2 
765 
 _ => prf % None % None %% prf1 %% prf2) 

11519  766 
end; 
767 

768 
fun equal_intr A B prf1 prf2 = 

11615  769 
equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2; 
11519  770 

771 
fun equal_elim A B prf1 prf2 = 

11615  772 
equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2; 
11519  773 

774 

775 
(***** axioms and theorems *****) 

776 

777 
fun vars_of t = rev (foldl_aterms 

778 
(fn (vs, v as Var _) => v ins vs  (vs, _) => vs) ([], t)); 

779 

780 
fun test_args _ [] = true 

781 
 test_args is (Bound i :: ts) = 

782 
not (i mem is) andalso test_args (i :: is) ts 

783 
 test_args _ _ = false; 

784 

785 
fun is_fun (Type ("fun", _)) = true 

786 
 is_fun (TVar _) = true 

787 
 is_fun _ = false; 

788 

789 
fun add_funvars Ts (vs, t) = 

790 
if is_fun (fastype_of1 (Ts, t)) then 

791 
vs union mapfilter (fn Var (ixn, T) => 

792 
if is_fun T then Some ixn else None  _ => None) (vars_of t) 

793 
else vs; 

794 

795 
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) = 

796 
add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u) 

797 
 add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) = 

798 
add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t) 

12041  799 
 add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t) 
800 
 add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t) 

801 
and add_npvars' Ts (vs, t) = (case strip_comb t of 

11519  802 
(Var (ixn, _), ts) => if test_args [] ts then vs 
12041  803 
else foldl (add_npvars' Ts) (overwrite (vs, 
11519  804 
(ixn, foldl (add_funvars Ts) (if_none (assoc (vs, ixn)) [], ts))), ts) 
12041  805 
 (Abs (_, T, u), ts) => foldl (add_npvars' (T::Ts)) (vs, u :: ts) 
806 
 (_, ts) => foldl (add_npvars' Ts) (vs, ts)); 

11519  807 

808 
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q 

809 
 prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t 

810 
 prop_vars t = (case strip_comb t of 

811 
(Var (ixn, _), _) => [ixn]  _ => []); 

812 

813 
fun is_proj t = 

814 
let 

815 
fun is_p i t = (case strip_comb t of 

816 
(Bound j, []) => false 

817 
 (Bound j, ts) => j >= i orelse exists (is_p i) ts 

818 
 (Abs (_, _, u), _) => is_p (i+1) u 

819 
 (_, ts) => exists (is_p i) ts) 

820 
in (case strip_abs_body t of 

821 
Bound _ => true 

822 
 t' => is_p 0 t') 

823 
end; 

824 

825 
fun needed_vars prop = 

826 
foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union 

827 
prop_vars prop; 

828 

829 
fun gen_axm_proof c name prop = 

830 
let 

831 
val nvs = needed_vars prop; 

832 
val args = map (fn (v as Var (ixn, _)) => 

833 
if ixn mem nvs then Some v else None) (vars_of prop) @ 

834 
map Some (sort (make_ord atless) (term_frees prop)); 

835 
in 

836 
proof_combt' (c (name, prop, None), args) 

837 
end; 

838 

839 
val axm_proof = gen_axm_proof PAxm; 

840 
val oracle_proof = gen_axm_proof Oracle; 

841 

842 
fun shrink ls lev (prf as Abst (a, T, body)) = 

843 
let val (b, is, ch, body') = shrink ls (lev+1) body 

844 
in (b, is, ch, if ch then Abst (a, T, body') else prf) end 

845 
 shrink ls lev (prf as AbsP (a, t, body)) = 

846 
let val (b, is, ch, body') = shrink (lev::ls) lev body 

847 
in (b orelse 0 mem is, mapfilter (fn 0 => None  i => Some (i1)) is, 

848 
ch, if ch then AbsP (a, t, body') else prf) 

849 
end 

850 
 shrink ls lev prf = 

851 
let val (is, ch, _, prf') = shrink' ls lev [] [] prf 

852 
in (false, is, ch, prf') end 

11615  853 
and shrink' ls lev ts prfs (prf as prf1 %% prf2) = 
11519  854 
let 
855 
val p as (_, is', ch', prf') = shrink ls lev prf2; 

856 
val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1 

857 
in (is union is', ch orelse ch', ts', 

11615  858 
if ch orelse ch' then prf'' %% prf' else prf) 
11519  859 
end 
11615  860 
 shrink' ls lev ts prfs (prf as prf1 % t) = 
11519  861 
let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1 
11615  862 
in (is, ch orelse ch', ts', if ch orelse ch' then prf' % t' else prf) end 
11519  863 
 shrink' ls lev ts prfs (prf as PBound i) = 
864 
(if exists (fn Some (Bound j) => levj <= nth_elem (i, ls)  _ => true) ts 

12233  865 
orelse not (null (duplicates 
866 
(foldl (fn (js, Some (Bound j)) => j :: js  (js, _) => js) ([], ts)))) 

11519  867 
orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf) 
868 
 shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf) 

11615  869 
 shrink' ls lev ts prfs (prf as MinProof _) = 
870 
([], false, map (pair false) ts, prf) 

11519  871 
 shrink' ls lev ts prfs prf = 
872 
let 

873 
val prop = (case prf of PThm (_, _, prop, _) => prop  PAxm (_, prop, _) => prop 

874 
 Oracle (_, prop, _) => prop  _ => error "shrink: proof not in normal form"); 

875 
val vs = vars_of prop; 

13629  876 
val (ts', ts'') = splitAt (length vs, ts) 
11519  877 
val insts = take (length ts', map (fst o dest_Var) vs) ~~ ts'; 
878 
val nvs = foldl (fn (ixns', (ixn, ixns)) => 

879 
ixn ins (case assoc (insts, ixn) of 

880 
Some (Some t) => if is_proj t then ixns union ixns' else ixns' 

881 
 _ => ixns union ixns')) 

882 
(needed prop ts'' prfs, add_npvars false true [] ([], prop)); 

883 
val insts' = map 

884 
(fn (ixn, x as Some _) => if ixn mem nvs then (false, x) else (true, None) 

885 
 (_, x) => (false, x)) insts 

886 
in ([], false, insts' @ map (pair false) ts'', prf) end 

887 
and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) = 

888 
(if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs 

889 
 needed (Var (ixn, _)) (_::_) _ = [ixn] 

890 
 needed _ _ _ = []; 

891 

892 

893 
(**** Simple first order matching functions for terms and proofs ****) 

894 

895 
exception PMatch; 

896 

897 
(** see pattern.ML **) 

898 

12923  899 
fun flt (i: int) = filter (fn n => n < i); 
12279  900 

901 
fun fomatch Ts tymatch j = 

11519  902 
let 
903 
fun mtch (instsp as (tyinsts, insts)) = fn 

904 
(Var (ixn, T), t) => 

12279  905 
if j>0 andalso not (null (flt j (loose_bnos t))) 
906 
then raise PMatch 

907 
else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))), 

908 
(ixn, t) :: insts) 

11519  909 
 (Free (a, T), Free (b, U)) => 
12279  910 
if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch 
11519  911 
 (Const (a, T), Const (b, U)) => 
12279  912 
if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch 
11519  913 
 (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u) 
12279  914 
 (Bound i, Bound j) => if i=j then instsp else raise PMatch 
11519  915 
 _ => raise PMatch 
916 
in mtch end; 

917 

12279  918 
fun match_proof Ts tymatch = 
11519  919 
let 
12279  920 
fun optmatch _ inst (None, _) = inst 
921 
 optmatch _ _ (Some _, None) = raise PMatch 

922 
 optmatch mtch inst (Some x, Some y) = mtch inst (x, y) 

923 

924 
fun matcht Ts j (pinst, tinst) (t, u) = 

925 
(pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u)); 

926 
fun matchT (pinst, (tyinsts, insts)) p = 

927 
(pinst, (tymatch (tyinsts, K p), insts)); 

928 
fun matchTs inst (Ts, Us) = foldl (uncurry matchT) (inst, Ts ~~ Us); 

929 

930 
fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) = 

931 
if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst) 

932 
else (case apfst (flt i) (apsnd (flt j) 

933 
(prf_add_loose_bnos 0 0 prf ([], []))) of 

934 
([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst) 

935 
 ([], _) => if j = 0 then 

936 
((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst) 

937 
else raise PMatch 

938 
 _ => raise PMatch) 

939 
 mtch Ts i j inst (prf1 % opt1, prf2 % opt2) = 

940 
optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2) 

941 
 mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') = 

942 
mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2') 

943 
 mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) = 

944 
mtch (if_none opU dummyT :: Ts) i (j+1) 

945 
(optmatch matchT inst (opT, opU)) (prf1, prf2) 

946 
 mtch Ts i j inst (prf1, Abst (_, opU, prf2)) = 

947 
mtch (if_none opU dummyT :: Ts) i (j+1) inst 

948 
(incr_pboundvars 0 1 prf1 %> Bound 0, prf2) 

949 
 mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) = 

950 
mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2) 

951 
 mtch Ts i j inst (prf1, AbsP (_, _, prf2)) = 

952 
mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2) 

953 
 mtch Ts i j inst (PThm ((name1, _), _, prop1, opTs), 

954 
PThm ((name2, _), _, prop2, opUs)) = 

11519  955 
if name1=name2 andalso prop1=prop2 then 
12279  956 
optmatch matchTs inst (opTs, opUs) 
11519  957 
else raise PMatch 
12279  958 
 mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) = 
959 
if s1=s2 then optmatch matchTs inst (opTs, opUs) 

11519  960 
else raise PMatch 
12279  961 
 mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch 
962 
 mtch _ _ _ _ _ = raise PMatch 

963 
in mtch Ts 0 0 end; 

11519  964 

965 
fun prf_subst (pinst, (tyinsts, insts)) = 

966 
let 

967 
val substT = typ_subst_TVars_Vartab tyinsts; 

968 

969 
fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of 

970 
None => t 

971 
 Some u => incr_boundvars lev u) 

972 
 subst' lev (Const (s, T)) = Const (s, substT T) 

973 
 subst' lev (Free (s, T)) = Free (s, substT T) 

974 
 subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body) 

975 
 subst' lev (f $ t) = subst' lev f $ subst' lev t 

976 
 subst' _ t = t; 

977 

978 
fun subst plev tlev (AbsP (a, t, body)) = 

979 
AbsP (a, apsome (subst' tlev) t, subst (plev+1) tlev body) 

980 
 subst plev tlev (Abst (a, T, body)) = 

981 
Abst (a, apsome substT T, subst plev (tlev+1) body) 

11615  982 
 subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf' 
983 
 subst plev tlev (prf % t) = subst plev tlev prf % apsome (subst' tlev) t 

11519  984 
 subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of 
985 
None => prf 

986 
 Some prf' => incr_pboundvars plev tlev prf') 

987 
 subst _ _ (PThm (id, prf, prop, Ts)) = 

988 
PThm (id, prf, prop, apsome (map substT) Ts) 

989 
 subst _ _ (PAxm (id, prop, Ts)) = 

990 
PAxm (id, prop, apsome (map substT) Ts) 

991 
 subst _ _ t = t 

992 
in subst 0 0 end; 

993 

12871
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

994 
(*A fast unification filter: true unless the two terms cannot be unified. 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

995 
Terms must be NORMAL. Treats all Vars as distinct. *) 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

996 
fun could_unify prf1 prf2 = 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

997 
let 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

998 
fun matchrands (prf1 %% prf2) (prf1' %% prf2') = 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

999 
could_unify prf2 prf2' andalso matchrands prf1 prf1' 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1000 
 matchrands (prf % Some t) (prf' % Some t') = 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1001 
Term.could_unify (t, t') andalso matchrands prf prf' 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1002 
 matchrands (prf % _) (prf' % _) = matchrands prf prf' 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1003 
 matchrands _ _ = true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1004 

21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1005 
fun head_of (prf %% _) = head_of prf 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1006 
 head_of (prf % _) = head_of prf 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1007 
 head_of prf = prf 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1008 

21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1009 
in case (head_of prf1, head_of prf2) of 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1010 
(_, Hyp (Var _)) => true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1011 
 (Hyp (Var _), _) => true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1012 
 (PThm ((a, _), _, propa, _), PThm ((b, _), _, propb, _)) => 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1013 
a = b andalso propa = propb andalso matchrands prf1 prf2 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1014 
 (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1015 
 (PBound i, PBound j) => i = j andalso matchrands prf1 prf2 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1016 
 (AbsP _, _) => true (*because of possible eta equality*) 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1017 
 (Abst _, _) => true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1018 
 (_, AbsP _) => true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1019 
 (_, Abst _) => true 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1020 
 _ => false 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1021 
end; 
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1022 

11519  1023 
(**** rewriting on proof terms ****) 
1024 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1025 
val skel0 = PBound 0; 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1026 

12279  1027 
fun rewrite_prf tymatch (rules, procs) prf = 
11519  1028 
let 
13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1029 
fun rew _ (Abst (_, _, body) % Some t) = Some (prf_subst_bounds [t] body, skel0) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1030 
 rew _ (AbsP (_, _, body) %% prf) = Some (prf_subst_pbounds [prf] body, skel0) 
11519  1031 
 rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of 
13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1032 
Some prf' => Some (prf', skel0) 
11519  1033 
 None => get_first (fn (prf1, prf2) => Some (prf_subst 
13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1034 
(match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2) 
12871
21486a0557d1
Added function could_unify to speed up rewriting of proof terms.
berghofe
parents:
12868
diff
changeset

1035 
handle PMatch => None) (filter (could_unify prf o fst) rules)); 
11519  1036 

11615  1037 
fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) = 
11519  1038 
if prf_loose_Pbvar1 prf' 0 then rew Ts prf 
1039 
else 

1040 
let val prf'' = incr_pboundvars (~1) 0 prf' 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1041 
in Some (if_none (rew Ts prf'') (prf'', skel0)) end 
11615  1042 
 rew0 Ts (prf as Abst (_, _, prf' % Some (Bound 0))) = 
11519  1043 
if prf_loose_bvar1 prf' 0 then rew Ts prf 
1044 
else 

1045 
let val prf'' = incr_pboundvars 0 (~1) prf' 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1046 
in Some (if_none (rew Ts prf'') (prf'', skel0)) end 
11519  1047 
 rew0 Ts prf = rew Ts prf; 
1048 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1049 
fun rew1 _ (Hyp (Var _)) _ = None 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1050 
 rew1 Ts skel prf = (case rew2 Ts skel prf of 
11519  1051 
Some prf1 => (case rew0 Ts prf1 of 
13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1052 
Some (prf2, skel') => Some (if_none (rew1 Ts skel' prf2) prf2) 
11519  1053 
 None => Some prf1) 
1054 
 None => (case rew0 Ts prf of 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1055 
Some (prf1, skel') => Some (if_none (rew1 Ts skel' prf1) prf1) 
11519  1056 
 None => None)) 
1057 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1058 
and rew2 Ts skel (prf % Some t) = (case prf of 
11519  1059 
Abst (_, _, body) => 
1060 
let val prf' = prf_subst_bounds [t] body 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1061 
in Some (if_none (rew2 Ts skel0 prf') prf') end 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1062 
 _ => (case rew1 Ts (case skel of skel' % _ => skel'  _ => skel0) prf of 
11615  1063 
Some prf' => Some (prf' % Some t) 
11519  1064 
 None => None)) 
13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1065 
 rew2 Ts skel (prf % None) = apsome (fn prf' => prf' % None) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1066 
(rew1 Ts (case skel of skel' % _ => skel'  _ => skel0) prf) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1067 
 rew2 Ts skel (prf1 %% prf2) = (case prf1 of 
11519  1068 
AbsP (_, _, body) => 
1069 
let val prf' = prf_subst_pbounds [prf2] body 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1070 
in Some (if_none (rew2 Ts skel0 prf') prf') end 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1071 
 _ => 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1072 
let val (skel1, skel2) = (case skel of 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1073 
skel1 %% skel2 => (skel1, skel2) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1074 
 _ => (skel0, skel0)) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1075 
in case rew1 Ts skel1 prf1 of 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1076 
Some prf1' => (case rew1 Ts skel2 prf2 of 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1077 
Some prf2' => Some (prf1' %% prf2') 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1078 
 None => Some (prf1' %% prf2)) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1079 
 None => (case rew1 Ts skel2 prf2 of 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1080 
Some prf2' => Some (prf1 %% prf2') 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1081 
 None => None) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1082 
end) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1083 
 rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (if_none T dummyT :: Ts) 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1084 
(case skel of Abst (_, _, skel') => skel'  _ => skel0) prf of 
11519  1085 
Some prf' => Some (Abst (s, T, prf')) 
1086 
 None => None) 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1087 
 rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts 
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1088 
(case skel of AbsP (_, _, skel') => skel'  _ => skel0) prf of 
11519  1089 
Some prf' => Some (AbsP (s, t, prf')) 
1090 
 None => None) 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1091 
 rew2 _ _ _ = None 
11519  1092 

13102
b6f8aae5f152
Added skeletons to speed up rewriting on proof terms.
berghofe
parents:
12923
diff
changeset

1093 
in if_none (rew1 [] skel0 prf) prf end; 
11519  1094 

1095 
fun rewrite_proof tsig = rewrite_prf (fn (tab, f) => 

1096 
Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch); 

1097 

11715
592923615f77
Tuned several functions to improve sharing of unchanged subproofs.
berghofe
parents:
11652
diff
changeset

1098 
fun rewrite_proof_notypes rews = rewrite_prf fst rews; 
11615  1099 

11519  1100 
(**** theory data ****) 
1101 

1102 
(* data kind 'Pure/proof' *) 

1103 

1104 
structure ProofArgs = 

1105 
struct 

1106 
val name = "Pure/proof"; 

1107 
type T = ((proof * proof) list * 

12233  1108 
(string * (typ list > proof > proof option)) list); 
11519  1109 

12233  1110 
val empty = ([], []); 
1111 
val copy = I; 

1112 
val prep_ext = I; 

1113 
fun merge ((rules1, procs1), (rules2, procs2)) = 

12293  1114 
(merge_lists rules1 rules2, merge_alists procs1 procs2); 
11519  1115 
fun print _ _ = (); 
1116 
end; 

1117 

1118 
structure ProofData = TheoryDataFun(ProofArgs); 

1119 

1120 
val init = ProofData.init; 

1121 

12233  1122 
fun add_prf_rrules rs thy = 
11519  1123 
let val r = ProofData.get thy 
12233  1124 
in ProofData.put (rs @ fst r, snd r) thy end; 
11519  1125 

12233  1126 
fun add_prf_rprocs ps thy = 
11519  1127 
let val r = ProofData.get thy 
12233  1128 
in ProofData.put (fst r, ps @ snd r) thy end; 
11519  1129 

1130 
fun thm_proof sign (name, tags) hyps prop prf = 

1131 
let 

12923  1132 
val prop = Logic.list_implies (hyps, prop); 
11519  1133 
val nvs = needed_vars prop; 
1134 
val args = map (fn (v as Var (ixn, _)) => 

1135 
if ixn mem nvs then Some v else None) (vars_of prop) @ 

1136 
map Some (sort (make_ord atless) (term_frees prop)); 

11543
d61b913431c5
renamed `keep_derivs' to `proofs', and made an integer;
wenzelm
parents:
11540
diff
changeset

1137 
val opt_prf = if ! proofs = 2 then 
12233  1138 
#4 (shrink [] 0 (rewrite_prf fst (ProofData.get_sg sign) 
12923  1139 
(foldr (uncurry implies_intr_proof) (hyps, prf)))) 
11519  1140 
else MinProof (mk_min_proof ([], prf)); 
12233  1141 
val head = (case strip_combt (fst (strip_combP prf)) of 
11519  1142 
(PThm ((old_name, _), prf', prop', None), args') => 
1143 
if (old_name="" orelse old_name=name) andalso 

1144 
prop = prop' andalso args = args' then 

1145 
PThm ((name, tags), prf', prop, None) 

1146 
else 

1147 
PThm ((name, tags), opt_prf, prop, None) 

1148 
 _ => PThm ((name, tags), opt_prf, prop, None)) 

1149 
in 

12923  1150 
proof_combP (proof_combt' (head, args), map Hyp hyps) 
11519  1151 
end; 
1152 

12923  1153 
fun get_name_tags hyps prop prf = 
1154 
let val prop = Logic.list_implies (hyps, prop) in 

1155 
(case strip_combt (fst (strip_combP prf)) of 

11519  1156 
(PThm ((name, tags), _, prop', _), _) => 
1157 
if prop=prop' then (name, tags) else ("", []) 

1158 
 (PAxm (name, prop', _), _) => 

1159 
if prop=prop' then (name, []) else ("", []) 

12923  1160 
 _ => ("", [])) 
1161 
end; 

11519  1162 

1163 
end; 

1164 

1165 
structure BasicProofterm : BASIC_PROOFTERM = Proofterm; 

1166 
open BasicProofterm; 