src/Pure/proofterm.ML
author wenzelm
Fri Aug 31 22:44:44 2001 +0200 (2001-08-31)
changeset 11540 23794728cdb7
parent 11519 0c96830636a1
child 11543 d61b913431c5
permissions -rw-r--r--
fixed header;
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(*  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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  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 non-local 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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   283
  | prf_incr_bv _ _ _ _ prf = prf;
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   284
berghofe@11519
   285
fun incr_pboundvars  0 0 prf = prf
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   286
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   287
berghofe@11519
   288
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   289
fun prf_loose_bvar1 (prf1 % prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
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   290
  | prf_loose_bvar1 (prf %% Some t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
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   291
  | prf_loose_bvar1 (_ %% None) _ = true
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   292
  | prf_loose_bvar1 (AbsP (_, Some t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
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   293
  | prf_loose_bvar1 (AbsP (_, None, _)) k = true
berghofe@11519
   294
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
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   295
  | prf_loose_bvar1 _ _ = false;
berghofe@11519
   296
berghofe@11519
   297
fun prf_loose_Pbvar1 (PBound i) k = i = k
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   298
  | prf_loose_Pbvar1 (prf1 % prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
berghofe@11519
   299
  | prf_loose_Pbvar1 (prf %% _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   300
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
berghofe@11519
   301
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
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   302
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   303
berghofe@11519
   304
berghofe@11519
   305
(**** substitutions ****)
berghofe@11519
   306
berghofe@11519
   307
local open Envir in
berghofe@11519
   308
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   309
fun apsome' f None = raise SAME
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   310
  | apsome' f (Some x) = Some (f x);
berghofe@11519
   311
berghofe@11519
   312
fun norm_proof env =
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   313
  let
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   314
    fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same env) T, normh prf)
berghofe@11519
   315
          handle SAME => Abst (s, T, norm prf))
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   316
      | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf)
berghofe@11519
   317
          handle SAME => AbsP (s, t, norm prf))
berghofe@11519
   318
      | norm (prf %% t) = (norm prf %% apsome (norm_term env) t
berghofe@11519
   319
          handle SAME => prf %% apsome' (norm_term_same env) t)
berghofe@11519
   320
      | norm (prf1 % prf2) = (norm prf1 % normh prf2
berghofe@11519
   321
          handle SAME => prf1 % norm prf2)
berghofe@11519
   322
      | norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same env) Ts)
berghofe@11519
   323
      | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same env) Ts)
berghofe@11519
   324
      | norm _ = raise SAME
berghofe@11519
   325
    and normh prf = (norm prf handle SAME => prf);
berghofe@11519
   326
  in normh end;
berghofe@11519
   327
berghofe@11519
   328
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   329
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   330
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   331
  | remove_types (t $ u) = remove_types t $ remove_types u
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   332
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   333
  | remove_types t = t;
berghofe@11519
   334
berghofe@11519
   335
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
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   336
  Envir.Envir {iTs = iTs, asol = Vartab.map remove_types asol, maxidx = maxidx};
berghofe@11519
   337
berghofe@11519
   338
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   339
berghofe@11519
   340
(**** substitution of bound variables ****)
berghofe@11519
   341
berghofe@11519
   342
fun prf_subst_bounds args prf =
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   343
  let
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   344
    val n = length args;
berghofe@11519
   345
    fun subst' lev (Bound i) =
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   346
         (if i<lev then raise SAME    (*var is locally bound*)
berghofe@11519
   347
          else  incr_boundvars lev (List.nth (args, i-lev))
berghofe@11519
   348
                  handle Subscript => Bound (i-n)  (*loose: change it*))
berghofe@11519
   349
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   350
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
berghofe@11519
   351
          handle SAME => f $ subst' lev t)
berghofe@11519
   352
      | subst' _ _ = raise SAME
berghofe@11519
   353
    and substh' lev t = (subst' lev t handle SAME => t);
berghofe@11519
   354
berghofe@11519
   355
    fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
berghofe@11519
   356
          handle SAME => AbsP (a, t, subst lev body))
berghofe@11519
   357
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11519
   358
      | subst lev (prf % prf') = (subst lev prf % substh lev prf'
berghofe@11519
   359
          handle SAME => prf % subst lev prf')
berghofe@11519
   360
      | subst lev (prf %% t) = (subst lev prf %% apsome (substh' lev) t
berghofe@11519
   361
          handle SAME => prf %% apsome' (subst' lev) t)
berghofe@11519
   362
      | subst _ _ = raise SAME
berghofe@11519
   363
    and substh lev prf = (subst lev prf handle SAME => prf)
berghofe@11519
   364
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   365
berghofe@11519
   366
fun prf_subst_pbounds args prf =
berghofe@11519
   367
  let
berghofe@11519
   368
    val n = length args;
berghofe@11519
   369
    fun subst (PBound i) Plev tlev =
berghofe@11519
   370
 	 (if i < Plev then raise SAME    (*var is locally bound*)
berghofe@11519
   371
          else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
berghofe@11519
   372
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   373
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   374
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11519
   375
      | subst (prf % prf') Plev tlev = (subst prf Plev tlev % substh prf' Plev tlev
berghofe@11519
   376
          handle SAME => prf % subst prf' Plev tlev)
berghofe@11519
   377
      | subst (prf %% t) Plev tlev = subst prf Plev tlev %% t
berghofe@11519
   378
      | subst  prf _ _ = raise SAME
berghofe@11519
   379
    and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
berghofe@11519
   380
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   381
berghofe@11519
   382
end;
berghofe@11519
   383
berghofe@11519
   384
berghofe@11519
   385
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   386
berghofe@11519
   387
fun frzT names =
berghofe@11519
   388
  map_type_tvar (fn (ixn, xs) => TFree (the (assoc (names, ixn)), xs));
berghofe@11519
   389
berghofe@11519
   390
fun thawT names =
berghofe@11519
   391
  map_type_tfree (fn (s, xs) => case assoc (names, s) of
berghofe@11519
   392
      None => TFree (s, xs)
berghofe@11519
   393
    | Some ixn => TVar (ixn, xs));
berghofe@11519
   394
berghofe@11519
   395
fun freeze names names' (t $ u) =
berghofe@11519
   396
      freeze names names' t $ freeze names names' u
berghofe@11519
   397
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   398
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   399
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   400
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   401
  | freeze names names' (Var (ixn, T)) =
berghofe@11519
   402
      Free (the (assoc (names, ixn)), frzT names' T)
berghofe@11519
   403
  | freeze names names' t = t;
berghofe@11519
   404
berghofe@11519
   405
fun thaw names names' (t $ u) =
berghofe@11519
   406
      thaw names names' t $ thaw names names' u
berghofe@11519
   407
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   408
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   409
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
berghofe@11519
   410
  | thaw names names' (Free (s, T)) = 
berghofe@11519
   411
      let val T' = thawT names' T
berghofe@11519
   412
      in case assoc (names, s) of
berghofe@11519
   413
          None => Free (s, T')
berghofe@11519
   414
        | Some ixn => Var (ixn, T')
berghofe@11519
   415
      end
berghofe@11519
   416
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   417
  | thaw names names' t = t;
berghofe@11519
   418
berghofe@11519
   419
fun freeze_thaw_prf prf =
berghofe@11519
   420
  let
berghofe@11519
   421
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
berghofe@11519
   422
      (fn (t, (fs, Tfs, vs, Tvs)) =>
berghofe@11519
   423
         (add_term_frees (t, fs), add_term_tfree_names (t, Tfs),
berghofe@11519
   424
          add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))
berghofe@11519
   425
      (fn (T, (fs, Tfs, vs, Tvs)) =>
berghofe@11519
   426
         (fs, add_typ_tfree_names (T, Tfs),
berghofe@11519
   427
          vs, add_typ_ixns (Tvs, T)))
berghofe@11519
   428
            (([], [], [], []), prf);
berghofe@11519
   429
    val fs' = map (fst o dest_Free) fs;
berghofe@11519
   430
    val vs' = map (fst o dest_Var) vs;
berghofe@11519
   431
    val names = vs' ~~ variantlist (map fst vs', fs');
berghofe@11519
   432
    val names' = Tvs ~~ variantlist (map fst Tvs, Tfs);
berghofe@11519
   433
    val rnames = map swap names;
berghofe@11519
   434
    val rnames' = map swap names';
berghofe@11519
   435
  in
berghofe@11519
   436
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   437
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   438
  end;
berghofe@11519
   439
berghofe@11519
   440
berghofe@11519
   441
(***** implication introduction *****)
berghofe@11519
   442
berghofe@11519
   443
fun implies_intr_proof h prf =
berghofe@11519
   444
  let
berghofe@11519
   445
    fun abshyp i (Hyp t) = if h aconv t then PBound i else Hyp t
berghofe@11519
   446
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
berghofe@11519
   447
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
berghofe@11519
   448
      | abshyp i (prf %% t) = abshyp i prf %% t
berghofe@11519
   449
      | abshyp i (prf1 % prf2) = abshyp i prf1 % abshyp i prf2
berghofe@11519
   450
      | abshyp _ prf = prf;
berghofe@11519
   451
  in
berghofe@11519
   452
    AbsP ("H", None (*h*), abshyp 0 prf)
berghofe@11519
   453
  end;
berghofe@11519
   454
berghofe@11519
   455
berghofe@11519
   456
(***** forall introduction *****)
berghofe@11519
   457
berghofe@11519
   458
fun forall_intr_proof x a prf = Abst (a, None, prf_abstract_over x prf);
berghofe@11519
   459
berghofe@11519
   460
berghofe@11519
   461
(***** varify *****)
berghofe@11519
   462
berghofe@11519
   463
fun varify_proof t fixed prf =
berghofe@11519
   464
  let
berghofe@11519
   465
    val fs = add_term_tfree_names (t, []) \\ fixed;
berghofe@11519
   466
    val ixns = add_term_tvar_ixns (t, []);
berghofe@11519
   467
    val fmap = fs ~~ variantlist (fs, map #1 ixns)
berghofe@11519
   468
    fun thaw (f as (a, S)) =
berghofe@11519
   469
      (case assoc (fmap, a) of
berghofe@11519
   470
        None => TFree f
berghofe@11519
   471
      | Some b => TVar ((b, 0), S));
berghofe@11519
   472
  in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf
berghofe@11519
   473
  end;
berghofe@11519
   474
berghofe@11519
   475
berghofe@11519
   476
local
berghofe@11519
   477
berghofe@11519
   478
fun new_name (ix, (pairs,used)) =
berghofe@11519
   479
  let val v = variant used (string_of_indexname ix)
berghofe@11519
   480
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   481
berghofe@11519
   482
fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of
berghofe@11519
   483
    None => TVar (ix, sort)
berghofe@11519
   484
  | Some name => TFree (name, sort));
berghofe@11519
   485
berghofe@11519
   486
in
berghofe@11519
   487
berghofe@11519
   488
fun freezeT t prf =
berghofe@11519
   489
  let
berghofe@11519
   490
    val used = it_term_types add_typ_tfree_names (t, [])
berghofe@11519
   491
    and tvars = map #1 (it_term_types add_typ_tvars (t, []));
berghofe@11519
   492
    val (alist, _) = foldr new_name (tvars, ([], used));
berghofe@11519
   493
  in
berghofe@11519
   494
    (case alist of
berghofe@11519
   495
      [] => prf (*nothing to do!*)
berghofe@11519
   496
    | _ =>
berghofe@11519
   497
      let val frzT = map_type_tvar (freeze_one alist)
berghofe@11519
   498
      in map_proof_terms (map_term_types frzT) frzT prf end)
berghofe@11519
   499
  end;
berghofe@11519
   500
berghofe@11519
   501
end;
berghofe@11519
   502
berghofe@11519
   503
berghofe@11519
   504
(***** rotate assumptions *****)
berghofe@11519
   505
berghofe@11519
   506
fun rotate_proof Bs Bi m prf =
berghofe@11519
   507
  let
berghofe@11519
   508
    val params = Term.strip_all_vars Bi;
berghofe@11519
   509
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   510
    val i = length asms;
berghofe@11519
   511
    val j = length Bs;
berghofe@11519
   512
  in
berghofe@11519
   513
    mk_AbsP (j+1, proof_combP (prf, map PBound
berghofe@11519
   514
      (j downto 1) @ [mk_Abst (params, mk_AbsP (i,
berghofe@11519
   515
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
berghofe@11519
   516
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
berghofe@11519
   517
  end;
berghofe@11519
   518
berghofe@11519
   519
berghofe@11519
   520
(***** permute premises *****)
berghofe@11519
   521
berghofe@11519
   522
fun permute_prems_prf prems j k prf =
berghofe@11519
   523
  let val n = length prems
berghofe@11519
   524
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   525
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   526
  end;
berghofe@11519
   527
berghofe@11519
   528
berghofe@11519
   529
(***** instantiation *****)
berghofe@11519
   530
berghofe@11519
   531
fun instantiate vTs tpairs =
berghofe@11519
   532
  map_proof_terms (subst_atomic (map (apsnd remove_types) tpairs) o
berghofe@11519
   533
    subst_TVars vTs) (typ_subst_TVars vTs);
berghofe@11519
   534
berghofe@11519
   535
berghofe@11519
   536
(***** lifting *****)
berghofe@11519
   537
berghofe@11519
   538
fun lift_proof Bi inc prop prf =
berghofe@11519
   539
  let
berghofe@11519
   540
    val (_, lift_all) = Logic.lift_fns (Bi, inc);
berghofe@11519
   541
berghofe@11519
   542
    fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   543
berghofe@11519
   544
    fun lift' Us Ts (Abst (s, T, prf)) = Abst (s, apsome (incr_tvar inc) T, lift' Us (dummyT::Ts) prf)
berghofe@11519
   545
      | lift' Us Ts (AbsP (s, t, prf)) = AbsP (s, apsome (lift'' Us Ts) t, lift' Us Ts prf)
berghofe@11519
   546
      | lift' Us Ts (prf %% t) = lift' Us Ts prf %% apsome (lift'' Us Ts) t
berghofe@11519
   547
      | lift' Us Ts (prf1 % prf2) = lift' Us Ts prf1 % lift' Us Ts prf2
berghofe@11519
   548
      | lift' _ _ (PThm (s, prf, prop, Ts)) = PThm (s, prf, prop, apsome (map (incr_tvar inc)) Ts)
berghofe@11519
   549
      | lift' _ _ (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome (map (incr_tvar inc)) Ts)
berghofe@11519
   550
      | lift' _ _ prf = prf;
berghofe@11519
   551
berghofe@11519
   552
    val ps = map lift_all (Logic.strip_imp_prems (snd (Logic.strip_flexpairs prop)));
berghofe@11519
   553
    val k = length ps;
berghofe@11519
   554
berghofe@11519
   555
    fun mk_app (b, (i, j, prf)) = 
berghofe@11519
   556
          if b then (i-1, j, prf % PBound i) else (i, j-1, prf %%% Bound j);
berghofe@11519
   557
berghofe@11519
   558
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
berghofe@11519
   559
	    AbsP ("H", None (*A*), lift Us (true::bs) (i+1) j B)
berghofe@11519
   560
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 
berghofe@11519
   561
	    Abst (a, None (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11519
   562
      | lift Us bs i j _ = proof_combP (lift' (rev Us) [] prf,
berghofe@11519
   563
            map (fn k => (#3 (foldr mk_app (bs, (i-1, j-1, PBound k)))))
berghofe@11519
   564
              (i + k - 1 downto i));
berghofe@11519
   565
  in
berghofe@11519
   566
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   567
  end;
berghofe@11519
   568
berghofe@11519
   569
berghofe@11519
   570
(***** proof by assumption *****)
berghofe@11519
   571
berghofe@11519
   572
fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", None (*A*), mk_asm_prf B (i+1))
berghofe@11519
   573
  | mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, None (*T*), mk_asm_prf t i)
berghofe@11519
   574
  | mk_asm_prf _ i = PBound i;
berghofe@11519
   575
berghofe@11519
   576
fun assumption_proof Bs Bi n prf =
berghofe@11519
   577
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@11519
   578
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi (~n)]));
berghofe@11519
   579
berghofe@11519
   580
berghofe@11519
   581
(***** Composition of object rule with proof state *****)
berghofe@11519
   582
berghofe@11519
   583
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
berghofe@11519
   584
      AbsP ("H", None (*A*), flatten_params_proof (i+1) j n (B, k))
berghofe@11519
   585
  | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
berghofe@11519
   586
      Abst (a, None (*T*), flatten_params_proof i (j+1) n (t, k))
berghofe@11519
   587
  | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
berghofe@11519
   588
      map Bound (j-1 downto 0)), map PBound (i-1 downto 0 \ i-n));
berghofe@11519
   589
berghofe@11519
   590
fun bicompose_proof Bs oldAs newAs A n rprf sprf =
berghofe@11519
   591
  let
berghofe@11519
   592
    val la = length newAs;
berghofe@11519
   593
    val lb = length Bs;
berghofe@11519
   594
  in
berghofe@11519
   595
    mk_AbsP (lb+la, proof_combP (sprf,
berghofe@11519
   596
      map PBound (lb + la - 1 downto la)) %
berghofe@11519
   597
        proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @
berghofe@11519
   598
          map (flatten_params_proof 0 0 n) (oldAs ~~ (la - 1 downto 0))))
berghofe@11519
   599
  end;
berghofe@11519
   600
berghofe@11519
   601
berghofe@11519
   602
(***** axioms for equality *****)
berghofe@11519
   603
berghofe@11519
   604
val aT = TFree ("'a", ["logic"]);
berghofe@11519
   605
val bT = TFree ("'b", ["logic"]);
berghofe@11519
   606
val x = Free ("x", aT);
berghofe@11519
   607
val y = Free ("y", aT);
berghofe@11519
   608
val z = Free ("z", aT);
berghofe@11519
   609
val A = Free ("A", propT);
berghofe@11519
   610
val B = Free ("B", propT);
berghofe@11519
   611
val f = Free ("f", aT --> bT);
berghofe@11519
   612
val g = Free ("g", aT --> bT);
berghofe@11519
   613
berghofe@11519
   614
local open Logic in
berghofe@11519
   615
berghofe@11519
   616
val equality_axms =
berghofe@11519
   617
  [("reflexive", mk_equals (x, x)),
berghofe@11519
   618
   ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
berghofe@11519
   619
   ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
berghofe@11519
   620
   ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
berghofe@11519
   621
   ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
berghofe@11519
   622
   ("abstract_rule", Logic.mk_implies
berghofe@11519
   623
      (all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),
berghofe@11519
   624
       equals (aT --> bT) $
berghofe@11519
   625
         Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),
berghofe@11519
   626
   ("combination", Logic.list_implies
berghofe@11519
   627
      ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],
berghofe@11519
   628
       Logic.mk_equals (f $ x, g $ y)))];
berghofe@11519
   629
berghofe@11519
   630
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   631
  equal_elim_axm, abstract_rule_axm, combination_axm] =
berghofe@11519
   632
    map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, None)) equality_axms;
berghofe@11519
   633
berghofe@11519
   634
end;
berghofe@11519
   635
berghofe@11519
   636
val reflexive = reflexive_axm %% None;
berghofe@11519
   637
berghofe@11519
   638
fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) %% _) = prf
berghofe@11519
   639
  | symmetric prf = symmetric_axm %% None %% None % prf;
berghofe@11519
   640
berghofe@11519
   641
fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) %% _) prf2 = prf2
berghofe@11519
   642
  | transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) %% _) = prf1
berghofe@11519
   643
  | transitive u (Type ("prop", [])) prf1 prf2 =
berghofe@11519
   644
      transitive_axm %% None %% Some (remove_types u) %% None % prf1 % prf2
berghofe@11519
   645
  | transitive u T prf1 prf2 =
berghofe@11519
   646
      transitive_axm %% None %% None %% None % prf1 % prf2;
berghofe@11519
   647
berghofe@11519
   648
fun abstract_rule x a prf =
berghofe@11519
   649
  abstract_rule_axm %% None %% None % forall_intr_proof x a prf;
berghofe@11519
   650
berghofe@11519
   651
fun check_comb (PAxm ("ProtoPure.combination", _, _) %% f %% g %% _ %% _ % prf % _) =
berghofe@11519
   652
      is_some f orelse check_comb prf
berghofe@11519
   653
  | check_comb (PAxm ("ProtoPure.transitive", _, _) %% _ %% _ %% _ % prf1 % prf2) =
berghofe@11519
   654
      check_comb prf1 andalso check_comb prf2
berghofe@11519
   655
  | check_comb (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % prf) = check_comb prf
berghofe@11519
   656
  | check_comb _ = false;
berghofe@11519
   657
berghofe@11519
   658
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   659
  let
berghofe@11519
   660
    val f = Envir.beta_norm f;
berghofe@11519
   661
    val g = Envir.beta_norm g;
berghofe@11519
   662
    val prf =  if check_comb prf1 then
berghofe@11519
   663
        combination_axm %% None %% None
berghofe@11519
   664
      else (case prf1 of
berghofe@11519
   665
          PAxm ("ProtoPure.reflexive", _, _) %% _ =>
berghofe@11519
   666
            combination_axm %%% remove_types f %% None
berghofe@11519
   667
        | _ => combination_axm %%% remove_types f %%% remove_types g)
berghofe@11519
   668
  in
berghofe@11519
   669
    (case T of
berghofe@11519
   670
       Type ("fun", _) => prf %%
berghofe@11519
   671
         (case head_of f of
berghofe@11519
   672
            Abs _ => Some (remove_types t)
berghofe@11519
   673
          | Var _ => Some (remove_types t)
berghofe@11519
   674
          | _ => None) %%
berghofe@11519
   675
         (case head_of g of
berghofe@11519
   676
            Abs _ => Some (remove_types u)
berghofe@11519
   677
          | Var _ => Some (remove_types u)
berghofe@11519
   678
          | _ => None) % prf1 % prf2
berghofe@11519
   679
     | _ => prf %% None %% None % prf1 % prf2)
berghofe@11519
   680
  end;
berghofe@11519
   681
berghofe@11519
   682
fun equal_intr A B prf1 prf2 =
berghofe@11519
   683
  equal_intr_axm %%% remove_types A %%% remove_types B % prf1 % prf2;
berghofe@11519
   684
berghofe@11519
   685
fun equal_elim A B prf1 prf2 =
berghofe@11519
   686
  equal_elim_axm %%% remove_types A %%% remove_types B % prf1 % prf2;
berghofe@11519
   687
berghofe@11519
   688
berghofe@11519
   689
(***** axioms and theorems *****)
berghofe@11519
   690
berghofe@11519
   691
fun vars_of t = rev (foldl_aterms
berghofe@11519
   692
  (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t));
berghofe@11519
   693
berghofe@11519
   694
fun test_args _ [] = true
berghofe@11519
   695
  | test_args is (Bound i :: ts) =
berghofe@11519
   696
      not (i mem is) andalso test_args (i :: is) ts
berghofe@11519
   697
  | test_args _ _ = false;
berghofe@11519
   698
berghofe@11519
   699
fun is_fun (Type ("fun", _)) = true
berghofe@11519
   700
  | is_fun (TVar _) = true
berghofe@11519
   701
  | is_fun _ = false;
berghofe@11519
   702
berghofe@11519
   703
fun add_funvars Ts (vs, t) =
berghofe@11519
   704
  if is_fun (fastype_of1 (Ts, t)) then
berghofe@11519
   705
    vs union mapfilter (fn Var (ixn, T) =>
berghofe@11519
   706
      if is_fun T then Some ixn else None | _ => None) (vars_of t)
berghofe@11519
   707
  else vs;
berghofe@11519
   708
berghofe@11519
   709
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
berghofe@11519
   710
      add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
berghofe@11519
   711
  | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
berghofe@11519
   712
      add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
berghofe@11519
   713
  | add_npvars q p Ts (vs, t) = (case strip_comb t of
berghofe@11519
   714
    (Var (ixn, _), ts) => if test_args [] ts then vs
berghofe@11519
   715
      else foldl (add_npvars q p Ts) (overwrite (vs,
berghofe@11519
   716
        (ixn, foldl (add_funvars Ts) (if_none (assoc (vs, ixn)) [], ts))), ts)
berghofe@11519
   717
  | (Abs (_, T, u), ts) => foldl (add_npvars q p (T::Ts)) (vs, u :: ts)
berghofe@11519
   718
  | (_, ts) => foldl (add_npvars q p Ts) (vs, ts));
berghofe@11519
   719
berghofe@11519
   720
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
berghofe@11519
   721
  | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
berghofe@11519
   722
  | prop_vars t = (case strip_comb t of
berghofe@11519
   723
      (Var (ixn, _), _) => [ixn] | _ => []);
berghofe@11519
   724
berghofe@11519
   725
fun is_proj t =
berghofe@11519
   726
  let
berghofe@11519
   727
    fun is_p i t = (case strip_comb t of
berghofe@11519
   728
        (Bound j, []) => false
berghofe@11519
   729
      | (Bound j, ts) => j >= i orelse exists (is_p i) ts
berghofe@11519
   730
      | (Abs (_, _, u), _) => is_p (i+1) u
berghofe@11519
   731
      | (_, ts) => exists (is_p i) ts)
berghofe@11519
   732
  in (case strip_abs_body t of
berghofe@11519
   733
        Bound _ => true
berghofe@11519
   734
      | t' => is_p 0 t')
berghofe@11519
   735
  end;
berghofe@11519
   736
berghofe@11519
   737
fun needed_vars prop = 
berghofe@11519
   738
  foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union
berghofe@11519
   739
  prop_vars prop;
berghofe@11519
   740
berghofe@11519
   741
fun gen_axm_proof c name prop =
berghofe@11519
   742
  let
berghofe@11519
   743
    val nvs = needed_vars prop;
berghofe@11519
   744
    val args = map (fn (v as Var (ixn, _)) =>
berghofe@11519
   745
        if ixn mem nvs then Some v else None) (vars_of prop) @
berghofe@11519
   746
      map Some (sort (make_ord atless) (term_frees prop));
berghofe@11519
   747
  in
berghofe@11519
   748
    proof_combt' (c (name, prop, None), args)
berghofe@11519
   749
  end;
berghofe@11519
   750
berghofe@11519
   751
val axm_proof = gen_axm_proof PAxm;
berghofe@11519
   752
val oracle_proof = gen_axm_proof Oracle;
berghofe@11519
   753
berghofe@11519
   754
fun shrink ls lev (prf as Abst (a, T, body)) =
berghofe@11519
   755
      let val (b, is, ch, body') = shrink ls (lev+1) body
berghofe@11519
   756
      in (b, is, ch, if ch then Abst (a, T, body') else prf) end
berghofe@11519
   757
  | shrink ls lev (prf as AbsP (a, t, body)) =
berghofe@11519
   758
      let val (b, is, ch, body') = shrink (lev::ls) lev body
berghofe@11519
   759
      in (b orelse 0 mem is, mapfilter (fn 0 => None | i => Some (i-1)) is,
berghofe@11519
   760
        ch, if ch then AbsP (a, t, body') else prf)
berghofe@11519
   761
      end
berghofe@11519
   762
  | shrink ls lev prf =
berghofe@11519
   763
      let val (is, ch, _, prf') = shrink' ls lev [] [] prf
berghofe@11519
   764
      in (false, is, ch, prf') end
berghofe@11519
   765
and shrink' ls lev ts prfs (prf as prf1 % prf2) =
berghofe@11519
   766
      let
berghofe@11519
   767
        val p as (_, is', ch', prf') = shrink ls lev prf2;
berghofe@11519
   768
        val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
berghofe@11519
   769
      in (is union is', ch orelse ch', ts',
berghofe@11519
   770
          if ch orelse ch' then prf'' % prf' else prf)
berghofe@11519
   771
      end
berghofe@11519
   772
  | shrink' ls lev ts prfs (prf as prf1 %% t) =
berghofe@11519
   773
      let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
berghofe@11519
   774
      in (is, ch orelse ch', ts', if ch orelse ch' then prf' %% t' else prf) end
berghofe@11519
   775
  | shrink' ls lev ts prfs (prf as PBound i) =
berghofe@11519
   776
      (if exists (fn Some (Bound j) => lev-j <= nth_elem (i, ls) | _ => true) ts
berghofe@11519
   777
         orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
berghofe@11519
   778
  | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
berghofe@11519
   779
  | shrink' ls lev ts prfs prf =
berghofe@11519
   780
      let
berghofe@11519
   781
        val prop = (case prf of PThm (_, _, prop, _) => prop | PAxm (_, prop, _) => prop
berghofe@11519
   782
          | Oracle (_, prop, _) => prop | _ => error "shrink: proof not in normal form");
berghofe@11519
   783
        val vs = vars_of prop;
berghofe@11519
   784
        val ts' = take (length vs, ts)
berghofe@11519
   785
        val ts'' = drop (length vs, ts)
berghofe@11519
   786
        val insts = take (length ts', map (fst o dest_Var) vs) ~~ ts';
berghofe@11519
   787
        val nvs = foldl (fn (ixns', (ixn, ixns)) =>
berghofe@11519
   788
          ixn ins (case assoc (insts, ixn) of
berghofe@11519
   789
              Some (Some t) => if is_proj t then ixns union ixns' else ixns'
berghofe@11519
   790
            | _ => ixns union ixns'))
berghofe@11519
   791
              (needed prop ts'' prfs, add_npvars false true [] ([], prop));
berghofe@11519
   792
        val insts' = map
berghofe@11519
   793
          (fn (ixn, x as Some _) => if ixn mem nvs then (false, x) else (true, None)
berghofe@11519
   794
            | (_, x) => (false, x)) insts
berghofe@11519
   795
      in ([], false, insts' @ map (pair false) ts'', prf) end
berghofe@11519
   796
and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
berghofe@11519
   797
      (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
berghofe@11519
   798
  | needed (Var (ixn, _)) (_::_) _ = [ixn]
berghofe@11519
   799
  | needed _ _ _ = [];
berghofe@11519
   800
berghofe@11519
   801
berghofe@11519
   802
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
   803
berghofe@11519
   804
exception PMatch;
berghofe@11519
   805
berghofe@11519
   806
(** see pattern.ML **)
berghofe@11519
   807
berghofe@11519
   808
fun fomatch Ts tmatch =
berghofe@11519
   809
  let
berghofe@11519
   810
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
   811
        (Var (ixn, T), t)  =>
berghofe@11519
   812
	  (tmatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))), (ixn, t)::insts)
berghofe@11519
   813
      | (Free (a, T), Free (b, U)) =>
berghofe@11519
   814
	  if a=b then (tmatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   815
      | (Const (a, T), Const (b, U))  =>
berghofe@11519
   816
	  if a=b then (tmatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   817
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@11519
   818
      | _ => raise PMatch
berghofe@11519
   819
  in mtch end;
berghofe@11519
   820
berghofe@11519
   821
fun match_proof Ts tmatch =
berghofe@11519
   822
  let
berghofe@11519
   823
    fun mtch (inst as (pinst, tinst as (tyinsts, insts))) = fn
berghofe@11519
   824
        (Hyp (Var (ixn, _)), prf) => ((ixn, prf)::pinst, tinst)
berghofe@11519
   825
      | (prf1 %% opt1, prf2 %% opt2) =>
berghofe@11519
   826
          let val inst' as (pinst, tinst) = mtch inst (prf1, prf2)
berghofe@11519
   827
          in (case (opt1, opt2) of
berghofe@11519
   828
                (None, _) => inst'
berghofe@11519
   829
              | (Some _, None) => raise PMatch
berghofe@11519
   830
              | (Some t, Some u) => (pinst, fomatch Ts tmatch tinst (t, Envir.beta_norm u)))
berghofe@11519
   831
          end
berghofe@11519
   832
      | (prf1 % prf2, prf1' % prf2') =>
berghofe@11519
   833
          mtch (mtch inst (prf1, prf1')) (prf2, prf2')
berghofe@11519
   834
      | (PThm ((name1, _), _, prop1, None), PThm ((name2, _), _, prop2, _)) =>
berghofe@11519
   835
          if name1=name2 andalso prop1=prop2 then inst else raise PMatch
berghofe@11519
   836
      | (PThm ((name1, _), _, prop1, Some Ts), PThm ((name2, _), _, prop2, Some Us)) =>
berghofe@11519
   837
          if name1=name2 andalso prop1=prop2 then
berghofe@11519
   838
            (pinst, (foldl (tmatch o apsnd K) (tyinsts, Ts ~~ Us), insts))
berghofe@11519
   839
          else raise PMatch
berghofe@11519
   840
      | (PAxm (s1, _, None), PAxm (s2, _, _)) =>
berghofe@11519
   841
          if s1=s2 then inst else raise PMatch
berghofe@11519
   842
      | (PAxm (s1, _, Some Ts), PAxm (s2, _, Some Us)) =>
berghofe@11519
   843
          if s1=s2 then
berghofe@11519
   844
            (pinst, (foldl (tmatch o apsnd K) (tyinsts, Ts ~~ Us), insts))
berghofe@11519
   845
          else raise PMatch
berghofe@11519
   846
      | _ => raise PMatch
berghofe@11519
   847
  in mtch end;
berghofe@11519
   848
berghofe@11519
   849
fun prf_subst (pinst, (tyinsts, insts)) =
berghofe@11519
   850
  let
berghofe@11519
   851
    val substT = typ_subst_TVars_Vartab tyinsts;
berghofe@11519
   852
berghofe@11519
   853
    fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of
berghofe@11519
   854
          None => t
berghofe@11519
   855
        | Some u => incr_boundvars lev u)
berghofe@11519
   856
      | subst' lev (Const (s, T)) = Const (s, substT T)
berghofe@11519
   857
      | subst' lev (Free (s, T)) = Free (s, substT T)
berghofe@11519
   858
      | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
berghofe@11519
   859
      | subst' lev (f $ t) = subst' lev f $ subst' lev t
berghofe@11519
   860
      | subst' _ t = t;
berghofe@11519
   861
berghofe@11519
   862
    fun subst plev tlev (AbsP (a, t, body)) =
berghofe@11519
   863
          AbsP (a, apsome (subst' tlev) t, subst (plev+1) tlev body)
berghofe@11519
   864
      | subst plev tlev (Abst (a, T, body)) =
berghofe@11519
   865
          Abst (a, apsome substT T, subst plev (tlev+1) body)
berghofe@11519
   866
      | subst plev tlev (prf % prf') = subst plev tlev prf % subst plev tlev prf'
berghofe@11519
   867
      | subst plev tlev (prf %% t) = subst plev tlev prf %% apsome (subst' tlev) t
berghofe@11519
   868
      | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of
berghofe@11519
   869
          None => prf
berghofe@11519
   870
        | Some prf' => incr_pboundvars plev tlev prf')
berghofe@11519
   871
      | subst _ _ (PThm (id, prf, prop, Ts)) =
berghofe@11519
   872
          PThm (id, prf, prop, apsome (map substT) Ts)
berghofe@11519
   873
      | subst _ _ (PAxm (id, prop, Ts)) =
berghofe@11519
   874
          PAxm (id, prop, apsome (map substT) Ts)
berghofe@11519
   875
      | subst _ _ t = t
berghofe@11519
   876
  in subst 0 0 end;
berghofe@11519
   877
berghofe@11519
   878
(**** rewriting on proof terms ****)
berghofe@11519
   879
berghofe@11519
   880
fun rewrite_prf tmatch (rules, procs) prf =
berghofe@11519
   881
  let
berghofe@11519
   882
    fun rew _ (Abst (_, _, body) %% Some t) = Some (prf_subst_bounds [t] body)
berghofe@11519
   883
      | rew _ (AbsP (_, _, body) % prf) = Some (prf_subst_pbounds [prf] body)
berghofe@11519
   884
      | rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of
berghofe@11519
   885
          Some prf' => Some prf'
berghofe@11519
   886
        | None => get_first (fn (prf1, prf2) => Some (prf_subst
berghofe@11519
   887
            (match_proof Ts tmatch ([], (Vartab.empty, [])) (prf1, prf)) prf2)
berghofe@11519
   888
               handle PMatch => None) rules);
berghofe@11519
   889
berghofe@11519
   890
    fun rew0 Ts (prf as AbsP (_, _, prf' % PBound 0)) =
berghofe@11519
   891
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
   892
          else
berghofe@11519
   893
            let val prf'' = incr_pboundvars (~1) 0 prf'
berghofe@11519
   894
            in Some (if_none (rew Ts prf'') prf'') end
berghofe@11519
   895
      | rew0 Ts (prf as Abst (_, _, prf' %% Some (Bound 0))) =
berghofe@11519
   896
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
   897
          else
berghofe@11519
   898
            let val prf'' = incr_pboundvars 0 (~1) prf'
berghofe@11519
   899
            in Some (if_none (rew Ts prf'') prf'') end
berghofe@11519
   900
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
   901
berghofe@11519
   902
    fun rew1 Ts prf = (case rew2 Ts prf of
berghofe@11519
   903
          Some prf1 => (case rew0 Ts prf1 of
berghofe@11519
   904
              Some prf2 => Some (if_none (rew1 Ts prf2) prf2)
berghofe@11519
   905
            | None => Some prf1)
berghofe@11519
   906
        | None => (case rew0 Ts prf of
berghofe@11519
   907
              Some prf1 => Some (if_none (rew1 Ts prf1) prf1)
berghofe@11519
   908
            | None => None))
berghofe@11519
   909
berghofe@11519
   910
    and rew2 Ts (prf %% Some t) = (case prf of
berghofe@11519
   911
            Abst (_, _, body) =>
berghofe@11519
   912
              let val prf' = prf_subst_bounds [t] body
berghofe@11519
   913
              in Some (if_none (rew2 Ts prf') prf') end
berghofe@11519
   914
          | _ => (case rew1 Ts prf of
berghofe@11519
   915
              Some prf' => Some (prf' %% Some t)
berghofe@11519
   916
            | None => None))
berghofe@11519
   917
      | rew2 Ts (prf %% None) = apsome (fn prf' => prf' %% None) (rew1 Ts prf)
berghofe@11519
   918
      | rew2 Ts (prf1 % prf2) = (case prf1 of
berghofe@11519
   919
            AbsP (_, _, body) =>
berghofe@11519
   920
              let val prf' = prf_subst_pbounds [prf2] body
berghofe@11519
   921
              in Some (if_none (rew2 Ts prf') prf') end
berghofe@11519
   922
          | _ => (case rew1 Ts prf1 of
berghofe@11519
   923
              Some prf1' => (case rew1 Ts prf2 of
berghofe@11519
   924
                  Some prf2' => Some (prf1' % prf2')
berghofe@11519
   925
                | None => Some (prf1' % prf2))
berghofe@11519
   926
            | None => (case rew1 Ts prf2 of
berghofe@11519
   927
                  Some prf2' => Some (prf1 % prf2')
berghofe@11519
   928
                | None => None)))
berghofe@11519
   929
      | rew2 Ts (Abst (s, T, prf)) = (case rew1 (if_none T dummyT :: Ts) prf of
berghofe@11519
   930
            Some prf' => Some (Abst (s, T, prf'))
berghofe@11519
   931
          | None => None)
berghofe@11519
   932
      | rew2 Ts (AbsP (s, t, prf)) = (case rew1 Ts prf of
berghofe@11519
   933
            Some prf' => Some (AbsP (s, t, prf'))
berghofe@11519
   934
          | None => None)
berghofe@11519
   935
      | rew2 _ _ = None
berghofe@11519
   936
berghofe@11519
   937
  in if_none (rew1 [] prf) prf end;
berghofe@11519
   938
berghofe@11519
   939
fun rewrite_proof tsig = rewrite_prf (fn (tab, f) =>
berghofe@11519
   940
  Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
   941
berghofe@11519
   942
(**** theory data ****)
berghofe@11519
   943
berghofe@11519
   944
(* data kind 'Pure/proof' *)
berghofe@11519
   945
berghofe@11519
   946
structure ProofArgs =
berghofe@11519
   947
struct
berghofe@11519
   948
  val name = "Pure/proof";
berghofe@11519
   949
  type T = ((proof * proof) list *
berghofe@11519
   950
    (string * (typ list -> proof -> proof option)) list) ref;
berghofe@11519
   951
berghofe@11519
   952
  val empty = (ref ([], [])): T;
berghofe@11519
   953
  fun copy (ref rews) = (ref rews): T;            (*create new reference!*)
berghofe@11519
   954
  val prep_ext = copy;
berghofe@11519
   955
  fun merge (ref (rules1, procs1), ref (rules2, procs2)) = ref
berghofe@11519
   956
    (merge_lists rules1 rules2,
berghofe@11519
   957
     generic_merge (uncurry equal o pairself fst) I I procs1 procs2);
berghofe@11519
   958
  fun print _ _ = ();
berghofe@11519
   959
end;
berghofe@11519
   960
berghofe@11519
   961
structure ProofData = TheoryDataFun(ProofArgs);
berghofe@11519
   962
berghofe@11519
   963
val init = ProofData.init;
berghofe@11519
   964
berghofe@11519
   965
fun add_prf_rrules thy rs =
berghofe@11519
   966
  let val r = ProofData.get thy
berghofe@11519
   967
  in r := (rs @ fst (!r), snd (!r)) end;
berghofe@11519
   968
berghofe@11519
   969
fun add_prf_rprocs thy ps =
berghofe@11519
   970
  let val r = ProofData.get thy
berghofe@11519
   971
  in r := (fst (!r), ps @ snd (!r)) end;
berghofe@11519
   972
berghofe@11519
   973
fun thm_proof sign (name, tags) hyps prop prf =
berghofe@11519
   974
  let
berghofe@11519
   975
    val hyps' = gen_distinct op aconv hyps;
berghofe@11519
   976
    val prop = Logic.list_implies (hyps', prop);
berghofe@11519
   977
    val nvs = needed_vars prop;
berghofe@11519
   978
    val args = map (fn (v as Var (ixn, _)) =>
berghofe@11519
   979
        if ixn mem nvs then Some v else None) (vars_of prop) @
berghofe@11519
   980
      map Some (sort (make_ord atless) (term_frees prop));
berghofe@11519
   981
    val opt_prf = if !keep_derivs=FullDeriv then
berghofe@11519
   982
        #4 (shrink [] 0 (rewrite_prf fst (!(ProofData.get_sg sign))
berghofe@11519
   983
          (foldr (uncurry implies_intr_proof) (hyps', prf))))
berghofe@11519
   984
      else MinProof (mk_min_proof ([], prf));
berghofe@11519
   985
    val head = (case strip_combt (fst (strip_combP prf)) of
berghofe@11519
   986
        (PThm ((old_name, _), prf', prop', None), args') =>
berghofe@11519
   987
          if (old_name="" orelse old_name=name) andalso
berghofe@11519
   988
             prop = prop' andalso args = args' then
berghofe@11519
   989
            PThm ((name, tags), prf', prop, None)
berghofe@11519
   990
          else
berghofe@11519
   991
            PThm ((name, tags), opt_prf, prop, None)
berghofe@11519
   992
      | _ => PThm ((name, tags), opt_prf, prop, None))
berghofe@11519
   993
  in
berghofe@11519
   994
    proof_combP (proof_combt' (head, args), map Hyp hyps')
berghofe@11519
   995
  end;
berghofe@11519
   996
berghofe@11519
   997
fun get_name_tags prop prf = (case strip_combt (fst (strip_combP prf)) of
berghofe@11519
   998
      (PThm ((name, tags), _, prop', _), _) =>
berghofe@11519
   999
        if prop=prop' then (name, tags) else ("", [])
berghofe@11519
  1000
    | (PAxm (name, prop', _), _) =>
berghofe@11519
  1001
        if prop=prop' then (name, []) else ("", [])
berghofe@11519
  1002
    | _ => ("", []));
berghofe@11519
  1003
berghofe@11519
  1004
end;
berghofe@11519
  1005
berghofe@11519
  1006
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
berghofe@11519
  1007
open BasicProofterm;