src/Pure/proofterm.ML
author wenzelm
Tue Jul 19 17:21:52 2005 +0200 (2005-07-19 ago)
changeset 16880 411d91d104c4
parent 16787 b6b6e2faaa41
child 16940 d14ec6f2d29b
permissions -rw-r--r--
tuned instantiate interface;
Logic.incr_tvar;
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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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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
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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 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
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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 * sort) 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 * sort) * typ) list * ((indexname * typ) * term) list
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    -> 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 : theory -> 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
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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.tsig -> (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_data: theory -> theory
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end
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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;
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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) = Library.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 (MinProof prfs) = Library.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) = Library.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;
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(** proof objects with different levels of detail **)
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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);
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fun infer_derivs' f = infer_derivs (K f) (false, MinProof []);
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fun (prf %> t) = prf % SOME t;
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val proof_combt = Library.foldl (op %>);
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val proof_combt' = Library.foldl (op %);
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val proof_combP = Library.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 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 % Option.map 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)
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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 a Ts
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  | fold_proof_terms _ g (a, PAxm (_, prop, SOME Ts)) = foldr g a Ts
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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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fun maxidx_of_proof prf = fold_proof_terms
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  (Int.max o apfst maxidx_of_term) (Int.max o apfst maxidx_of_typ) (~1, prf); 
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fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
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  | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
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  | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
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  | size_of_proof (prf % _) = 1 + size_of_proof prf
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  | size_of_proof _ = 1;
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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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(***** 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 = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
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   288
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   289
(*Abstraction of a proof term over its occurrences of v, 
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   290
    which must contain no loose bound variables.
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   291
  The resulting proof term is ready to become the body of an Abst.*)
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   292
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   293
fun prf_abstract_over v =
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  let
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   295
    fun abst' lev u = if v aconv u then Bound lev else
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   296
      (case u of
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   297
         Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
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   298
       | f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t)
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   299
       | _ => raise SAME)
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   300
    and absth' lev t = (abst' lev t handle SAME => t);
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   301
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   302
    fun abst lev (AbsP (a, t, prf)) =
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   303
          (AbsP (a, apsome' (abst' lev) t, absth lev prf)
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   304
           handle SAME => AbsP (a, t, abst lev prf))
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   305
      | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
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   306
      | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
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   307
          handle SAME => prf1 %% abst lev prf2)
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   308
      | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
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   309
          handle SAME => prf % apsome' (abst' lev) t)
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   310
      | abst _ _ = raise SAME
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   311
    and absth lev prf = (abst lev prf handle SAME => prf)
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   312
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   313
  in absth 0 end;
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   314
berghofe@11519
   315
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   316
(*increments a proof term's non-local bound variables
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   317
  required when moving a proof term within abstractions
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   318
     inc is  increment for bound variables
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   319
     lev is  level at which a bound variable is considered 'loose'*)
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   320
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   321
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
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   322
berghofe@11715
   323
fun prf_incr_bv' incP inct Plev tlev (PBound i) =
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   324
      if i >= Plev then PBound (i+incP) else raise SAME 
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   325
  | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
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   326
      (AbsP (a, apsome' (same (incr_bv' inct tlev)) t,
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   327
         prf_incr_bv incP inct (Plev+1) tlev body) handle SAME =>
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   328
           AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
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   329
  | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
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   330
      Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
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   331
  | prf_incr_bv' incP inct Plev tlev (prf %% prf') = 
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   332
      (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
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   333
       handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
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   334
  | prf_incr_bv' incP inct Plev tlev (prf % t) = 
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   335
      (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
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   336
       handle SAME => prf % apsome' (same (incr_bv' inct tlev)) t)
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   337
  | prf_incr_bv' _ _ _ _ _ = raise SAME
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   338
and prf_incr_bv incP inct Plev tlev prf =
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   339
      (prf_incr_bv' incP inct Plev tlev prf handle SAME => prf);
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   340
berghofe@11519
   341
fun incr_pboundvars  0 0 prf = prf
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   342
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   343
berghofe@11519
   344
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   345
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
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   346
  | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
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   347
  | prf_loose_bvar1 (_ % NONE) _ = true
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   348
  | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
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   349
  | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
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   350
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
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   351
  | prf_loose_bvar1 _ _ = false;
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   352
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   353
fun prf_loose_Pbvar1 (PBound i) k = i = k
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   354
  | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
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   355
  | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   356
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
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   357
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
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   358
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   359
berghofe@12279
   360
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
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   361
      if i < plev then (is, js) else ((i-plev) ins is, js)
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   362
  | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
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   363
      prf_add_loose_bnos plev tlev prf2
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   364
        (prf_add_loose_bnos plev tlev prf1 p)
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   365
  | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
berghofe@12279
   366
      prf_add_loose_bnos plev tlev prf (case opt of
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   367
          NONE => (is, ~1 ins js)
skalberg@15531
   368
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
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   369
  | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
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   370
      prf_add_loose_bnos (plev+1) tlev prf (case opt of
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   371
          NONE => (is, ~1 ins js)
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   372
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   373
  | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
berghofe@12279
   374
      prf_add_loose_bnos plev (tlev+1) prf p
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   375
  | prf_add_loose_bnos _ _ _ _ = ([], []);
berghofe@12279
   376
berghofe@11519
   377
berghofe@11519
   378
(**** substitutions ****)
berghofe@11519
   379
berghofe@11519
   380
fun norm_proof env =
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   381
  let
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   382
    val envT = type_env env;
wenzelm@12497
   383
    fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same envT) T, normh prf)
berghofe@11519
   384
          handle SAME => Abst (s, T, norm prf))
berghofe@11519
   385
      | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf)
berghofe@11519
   386
          handle SAME => AbsP (s, t, norm prf))
skalberg@15570
   387
      | norm (prf % t) = (norm prf % Option.map (norm_term env) t
berghofe@11615
   388
          handle SAME => prf % apsome' (norm_term_same env) t)
berghofe@11615
   389
      | norm (prf1 %% prf2) = (norm prf1 %% normh prf2
berghofe@11615
   390
          handle SAME => prf1 %% norm prf2)
wenzelm@12497
   391
      | norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same envT) Ts)
wenzelm@12497
   392
      | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same envT) Ts)
berghofe@11519
   393
      | norm _ = raise SAME
berghofe@11519
   394
    and normh prf = (norm prf handle SAME => prf);
berghofe@11519
   395
  in normh end;
berghofe@11519
   396
berghofe@11519
   397
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   398
berghofe@11519
   399
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   400
  | remove_types (t $ u) = remove_types t $ remove_types u
berghofe@11519
   401
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   402
  | remove_types t = t;
berghofe@11519
   403
berghofe@11519
   404
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
berghofe@15797
   405
  Envir.Envir {iTs = iTs, asol = Vartab.map (apsnd remove_types) asol,
berghofe@15797
   406
    maxidx = maxidx};
berghofe@11519
   407
berghofe@11519
   408
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   409
berghofe@11519
   410
(**** substitution of bound variables ****)
berghofe@11519
   411
berghofe@11519
   412
fun prf_subst_bounds args prf =
berghofe@11519
   413
  let
berghofe@11519
   414
    val n = length args;
berghofe@11519
   415
    fun subst' lev (Bound i) =
berghofe@11519
   416
         (if i<lev then raise SAME    (*var is locally bound*)
berghofe@11519
   417
          else  incr_boundvars lev (List.nth (args, i-lev))
berghofe@11519
   418
                  handle Subscript => Bound (i-n)  (*loose: change it*))
berghofe@11519
   419
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   420
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
berghofe@11519
   421
          handle SAME => f $ subst' lev t)
berghofe@11519
   422
      | subst' _ _ = raise SAME
berghofe@11519
   423
    and substh' lev t = (subst' lev t handle SAME => t);
berghofe@11519
   424
berghofe@11519
   425
    fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
berghofe@11519
   426
          handle SAME => AbsP (a, t, subst lev body))
berghofe@11519
   427
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11615
   428
      | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
berghofe@11615
   429
          handle SAME => prf %% subst lev prf')
skalberg@15570
   430
      | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
berghofe@11615
   431
          handle SAME => prf % apsome' (subst' lev) t)
berghofe@11519
   432
      | subst _ _ = raise SAME
berghofe@11519
   433
    and substh lev prf = (subst lev prf handle SAME => prf)
berghofe@11519
   434
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   435
berghofe@11519
   436
fun prf_subst_pbounds args prf =
berghofe@11519
   437
  let
berghofe@11519
   438
    val n = length args;
berghofe@11519
   439
    fun subst (PBound i) Plev tlev =
berghofe@11519
   440
 	 (if i < Plev then raise SAME    (*var is locally bound*)
berghofe@11519
   441
          else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
berghofe@11519
   442
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   443
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   444
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11615
   445
      | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
berghofe@11615
   446
          handle SAME => prf %% subst prf' Plev tlev)
berghofe@11615
   447
      | subst (prf % t) Plev tlev = subst prf Plev tlev % t
berghofe@11519
   448
      | subst  prf _ _ = raise SAME
berghofe@11519
   449
    and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
berghofe@11519
   450
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   451
berghofe@11519
   452
berghofe@11519
   453
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   454
berghofe@11519
   455
fun frzT names =
skalberg@15570
   456
  map_type_tvar (fn (ixn, xs) => TFree (valOf (assoc (names, ixn)), xs));
berghofe@11519
   457
berghofe@11519
   458
fun thawT names =
berghofe@11519
   459
  map_type_tfree (fn (s, xs) => case assoc (names, s) of
skalberg@15531
   460
      NONE => TFree (s, xs)
skalberg@15531
   461
    | SOME ixn => TVar (ixn, xs));
berghofe@11519
   462
berghofe@11519
   463
fun freeze names names' (t $ u) =
berghofe@11519
   464
      freeze names names' t $ freeze names names' u
berghofe@11519
   465
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   466
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   467
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   468
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   469
  | freeze names names' (Var (ixn, T)) =
skalberg@15570
   470
      Free (valOf (assoc (names, ixn)), frzT names' T)
berghofe@11519
   471
  | freeze names names' t = t;
berghofe@11519
   472
berghofe@11519
   473
fun thaw names names' (t $ u) =
berghofe@11519
   474
      thaw names names' t $ thaw names names' u
berghofe@11519
   475
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   476
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   477
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
berghofe@11519
   478
  | thaw names names' (Free (s, T)) = 
berghofe@11519
   479
      let val T' = thawT names' T
berghofe@11519
   480
      in case assoc (names, s) of
skalberg@15531
   481
          NONE => Free (s, T')
skalberg@15531
   482
        | SOME ixn => Var (ixn, T')
berghofe@11519
   483
      end
berghofe@11519
   484
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   485
  | thaw names names' t = t;
berghofe@11519
   486
berghofe@11519
   487
fun freeze_thaw_prf prf =
berghofe@11519
   488
  let
berghofe@11519
   489
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
berghofe@11519
   490
      (fn (t, (fs, Tfs, vs, Tvs)) =>
berghofe@11519
   491
         (add_term_frees (t, fs), add_term_tfree_names (t, Tfs),
berghofe@11519
   492
          add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))
berghofe@11519
   493
      (fn (T, (fs, Tfs, vs, Tvs)) =>
berghofe@11519
   494
         (fs, add_typ_tfree_names (T, Tfs),
berghofe@11519
   495
          vs, add_typ_ixns (Tvs, T)))
berghofe@11519
   496
            (([], [], [], []), prf);
berghofe@11519
   497
    val fs' = map (fst o dest_Free) fs;
berghofe@11519
   498
    val vs' = map (fst o dest_Var) vs;
berghofe@11519
   499
    val names = vs' ~~ variantlist (map fst vs', fs');
berghofe@11519
   500
    val names' = Tvs ~~ variantlist (map fst Tvs, Tfs);
berghofe@11519
   501
    val rnames = map swap names;
berghofe@11519
   502
    val rnames' = map swap names';
berghofe@11519
   503
  in
berghofe@11519
   504
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   505
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   506
  end;
berghofe@11519
   507
berghofe@11519
   508
berghofe@11519
   509
(***** implication introduction *****)
berghofe@11519
   510
berghofe@11519
   511
fun implies_intr_proof h prf =
berghofe@11519
   512
  let
berghofe@11715
   513
    fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME
berghofe@11519
   514
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
berghofe@11519
   515
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
berghofe@11615
   516
      | abshyp i (prf % t) = abshyp i prf % t
berghofe@11715
   517
      | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2
berghofe@11715
   518
          handle SAME => prf1 %% abshyp i prf2)
berghofe@11715
   519
      | abshyp _ _ = raise SAME
berghofe@11715
   520
    and abshyph i prf = (abshyp i prf handle SAME => prf)
berghofe@11519
   521
  in
skalberg@15531
   522
    AbsP ("H", NONE (*h*), abshyph 0 prf)
berghofe@11519
   523
  end;
berghofe@11519
   524
berghofe@11519
   525
berghofe@11519
   526
(***** forall introduction *****)
berghofe@11519
   527
skalberg@15531
   528
fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
berghofe@11519
   529
berghofe@11519
   530
berghofe@11519
   531
(***** varify *****)
berghofe@11519
   532
berghofe@11519
   533
fun varify_proof t fixed prf =
berghofe@11519
   534
  let
berghofe@15797
   535
    val fs = add_term_tfrees (t, []) \\ fixed;
berghofe@11519
   536
    val ixns = add_term_tvar_ixns (t, []);
berghofe@15797
   537
    val fmap = fs ~~ variantlist (map fst fs, map #1 ixns)
berghofe@11519
   538
    fun thaw (f as (a, S)) =
berghofe@15797
   539
      (case assoc (fmap, f) of
skalberg@15531
   540
        NONE => TFree f
skalberg@15531
   541
      | SOME b => TVar ((b, 0), S));
berghofe@11519
   542
  in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf
berghofe@11519
   543
  end;
berghofe@11519
   544
berghofe@11519
   545
berghofe@11519
   546
local
berghofe@11519
   547
berghofe@11519
   548
fun new_name (ix, (pairs,used)) =
berghofe@11519
   549
  let val v = variant used (string_of_indexname ix)
berghofe@11519
   550
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   551
berghofe@11519
   552
fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of
skalberg@15531
   553
    NONE => TVar (ix, sort)
skalberg@15531
   554
  | SOME name => TFree (name, sort));
berghofe@11519
   555
berghofe@11519
   556
in
berghofe@11519
   557
berghofe@11519
   558
fun freezeT t prf =
berghofe@11519
   559
  let
berghofe@11519
   560
    val used = it_term_types add_typ_tfree_names (t, [])
berghofe@11519
   561
    and tvars = map #1 (it_term_types add_typ_tvars (t, []));
skalberg@15574
   562
    val (alist, _) = foldr new_name ([], used) tvars;
berghofe@11519
   563
  in
berghofe@11519
   564
    (case alist of
berghofe@11519
   565
      [] => prf (*nothing to do!*)
berghofe@11519
   566
    | _ =>
berghofe@11519
   567
      let val frzT = map_type_tvar (freeze_one alist)
berghofe@11519
   568
      in map_proof_terms (map_term_types frzT) frzT prf end)
berghofe@11519
   569
  end;
berghofe@11519
   570
berghofe@11519
   571
end;
berghofe@11519
   572
berghofe@11519
   573
berghofe@11519
   574
(***** rotate assumptions *****)
berghofe@11519
   575
berghofe@11519
   576
fun rotate_proof Bs Bi m prf =
berghofe@11519
   577
  let
berghofe@11519
   578
    val params = Term.strip_all_vars Bi;
berghofe@11519
   579
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   580
    val i = length asms;
berghofe@11519
   581
    val j = length Bs;
berghofe@11519
   582
  in
berghofe@11519
   583
    mk_AbsP (j+1, proof_combP (prf, map PBound
skalberg@15574
   584
      (j downto 1) @ [mk_Abst (mk_AbsP (i,
berghofe@11519
   585
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
skalberg@15574
   586
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m)))))) params]))
berghofe@11519
   587
  end;
berghofe@11519
   588
berghofe@11519
   589
berghofe@11519
   590
(***** permute premises *****)
berghofe@11519
   591
berghofe@11519
   592
fun permute_prems_prf prems j k prf =
berghofe@11519
   593
  let val n = length prems
berghofe@11519
   594
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   595
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   596
  end;
berghofe@11519
   597
berghofe@11519
   598
berghofe@11519
   599
(***** instantiation *****)
berghofe@11519
   600
wenzelm@16880
   601
fun instantiate (instT, inst) prf =
wenzelm@16880
   602
  map_proof_terms (Term.instantiate (instT, map (apsnd remove_types) inst))
wenzelm@16880
   603
    (Term.instantiateT instT) prf;
berghofe@11519
   604
berghofe@11519
   605
berghofe@11519
   606
(***** lifting *****)
berghofe@11519
   607
berghofe@11519
   608
fun lift_proof Bi inc prop prf =
berghofe@11519
   609
  let
berghofe@11519
   610
    val (_, lift_all) = Logic.lift_fns (Bi, inc);
berghofe@11519
   611
berghofe@11519
   612
    fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   613
berghofe@11715
   614
    fun lift' Us Ts (Abst (s, T, prf)) =
wenzelm@16880
   615
          (Abst (s, apsome' (same (Logic.incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf)
berghofe@11715
   616
           handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
berghofe@11715
   617
      | lift' Us Ts (AbsP (s, t, prf)) =
berghofe@11715
   618
          (AbsP (s, apsome' (same (lift'' Us Ts)) t, lifth' Us Ts prf)
berghofe@11715
   619
           handle SAME => AbsP (s, t, lift' Us Ts prf))
skalberg@15570
   620
      | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
berghofe@11715
   621
          handle SAME => prf % apsome' (same (lift'' Us Ts)) t)
berghofe@11715
   622
      | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
berghofe@11715
   623
          handle SAME => prf1 %% lift' Us Ts prf2)
berghofe@11715
   624
      | lift' _ _ (PThm (s, prf, prop, Ts)) =
wenzelm@16880
   625
          PThm (s, prf, prop, apsome' (same (map (Logic.incr_tvar inc))) Ts)
berghofe@11715
   626
      | lift' _ _ (PAxm (s, prop, Ts)) =
wenzelm@16880
   627
          PAxm (s, prop, apsome' (same (map (Logic.incr_tvar inc))) Ts)
berghofe@11715
   628
      | lift' _ _ _ = raise SAME
berghofe@11715
   629
    and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf);
berghofe@11519
   630
berghofe@13662
   631
    val ps = map lift_all (Logic.strip_imp_prems prop);
berghofe@11519
   632
    val k = length ps;
berghofe@11519
   633
berghofe@11519
   634
    fun mk_app (b, (i, j, prf)) = 
berghofe@11615
   635
          if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
berghofe@11519
   636
berghofe@11519
   637
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
skalberg@15531
   638
	    AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
berghofe@11519
   639
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 
skalberg@15531
   640
	    Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11715
   641
      | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
skalberg@15574
   642
            map (fn k => (#3 (foldr mk_app (i-1, j-1, PBound k) bs)))
berghofe@11519
   643
              (i + k - 1 downto i));
berghofe@11519
   644
  in
berghofe@11519
   645
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   646
  end;
berghofe@11519
   647
berghofe@11519
   648
berghofe@11519
   649
(***** proof by assumption *****)
berghofe@11519
   650
skalberg@15531
   651
fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", NONE (*A*), mk_asm_prf B (i+1))
skalberg@15531
   652
  | mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, NONE (*T*), mk_asm_prf t i)
berghofe@11519
   653
  | mk_asm_prf _ i = PBound i;
berghofe@11519
   654
berghofe@11519
   655
fun assumption_proof Bs Bi n prf =
berghofe@11519
   656
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@11519
   657
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi (~n)]));
berghofe@11519
   658
berghofe@11519
   659
berghofe@11519
   660
(***** Composition of object rule with proof state *****)
berghofe@11519
   661
berghofe@11519
   662
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
skalberg@15531
   663
      AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
berghofe@11519
   664
  | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
skalberg@15531
   665
      Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
berghofe@11519
   666
  | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
berghofe@11519
   667
      map Bound (j-1 downto 0)), map PBound (i-1 downto 0 \ i-n));
berghofe@11519
   668
berghofe@11519
   669
fun bicompose_proof Bs oldAs newAs A n rprf sprf =
berghofe@11519
   670
  let
berghofe@11519
   671
    val la = length newAs;
berghofe@11519
   672
    val lb = length Bs;
berghofe@11519
   673
  in
berghofe@11519
   674
    mk_AbsP (lb+la, proof_combP (sprf,
berghofe@11615
   675
      map PBound (lb + la - 1 downto la)) %%
skalberg@15570
   676
        proof_combP (rprf, (if n>0 then [mk_asm_prf (valOf A) (~n)] else []) @
berghofe@11519
   677
          map (flatten_params_proof 0 0 n) (oldAs ~~ (la - 1 downto 0))))
berghofe@11519
   678
  end;
berghofe@11519
   679
berghofe@11519
   680
berghofe@11519
   681
(***** axioms for equality *****)
berghofe@11519
   682
wenzelm@14854
   683
val aT = TFree ("'a", []);
wenzelm@14854
   684
val bT = TFree ("'b", []);
berghofe@11519
   685
val x = Free ("x", aT);
berghofe@11519
   686
val y = Free ("y", aT);
berghofe@11519
   687
val z = Free ("z", aT);
berghofe@11519
   688
val A = Free ("A", propT);
berghofe@11519
   689
val B = Free ("B", propT);
berghofe@11519
   690
val f = Free ("f", aT --> bT);
berghofe@11519
   691
val g = Free ("g", aT --> bT);
berghofe@11519
   692
berghofe@11519
   693
local open Logic in
berghofe@11519
   694
berghofe@11519
   695
val equality_axms =
berghofe@11519
   696
  [("reflexive", mk_equals (x, x)),
berghofe@11519
   697
   ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
berghofe@11519
   698
   ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
berghofe@11519
   699
   ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
berghofe@11519
   700
   ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
berghofe@11519
   701
   ("abstract_rule", Logic.mk_implies
berghofe@11519
   702
      (all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),
berghofe@11519
   703
       equals (aT --> bT) $
berghofe@11519
   704
         Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),
berghofe@11519
   705
   ("combination", Logic.list_implies
berghofe@11519
   706
      ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],
berghofe@11519
   707
       Logic.mk_equals (f $ x, g $ y)))];
berghofe@11519
   708
berghofe@11519
   709
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   710
  equal_elim_axm, abstract_rule_axm, combination_axm] =
skalberg@15531
   711
    map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, NONE)) equality_axms;
berghofe@11519
   712
berghofe@11519
   713
end;
berghofe@11519
   714
skalberg@15531
   715
val reflexive = reflexive_axm % NONE;
berghofe@11519
   716
berghofe@11615
   717
fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) % _) = prf
skalberg@15531
   718
  | symmetric prf = symmetric_axm % NONE % NONE %% prf;
berghofe@11519
   719
berghofe@11615
   720
fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) % _) prf2 = prf2
berghofe@11615
   721
  | transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) % _) = prf1
berghofe@11519
   722
  | transitive u (Type ("prop", [])) prf1 prf2 =
skalberg@15531
   723
      transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
berghofe@11519
   724
  | transitive u T prf1 prf2 =
skalberg@15531
   725
      transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
berghofe@11519
   726
berghofe@11519
   727
fun abstract_rule x a prf =
skalberg@15531
   728
  abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
berghofe@11519
   729
berghofe@11615
   730
fun check_comb (PAxm ("ProtoPure.combination", _, _) % f % g % _ % _ %% prf %% _) =
skalberg@15570
   731
      isSome f orelse check_comb prf
berghofe@11615
   732
  | check_comb (PAxm ("ProtoPure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
berghofe@11519
   733
      check_comb prf1 andalso check_comb prf2
berghofe@11615
   734
  | check_comb (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
berghofe@11519
   735
  | check_comb _ = false;
berghofe@11519
   736
berghofe@11519
   737
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   738
  let
berghofe@11519
   739
    val f = Envir.beta_norm f;
berghofe@11519
   740
    val g = Envir.beta_norm g;
berghofe@11519
   741
    val prf =  if check_comb prf1 then
skalberg@15531
   742
        combination_axm % NONE % NONE
berghofe@11519
   743
      else (case prf1 of
berghofe@11615
   744
          PAxm ("ProtoPure.reflexive", _, _) % _ =>
skalberg@15531
   745
            combination_axm %> remove_types f % NONE
berghofe@11615
   746
        | _ => combination_axm %> remove_types f %> remove_types g)
berghofe@11519
   747
  in
berghofe@11519
   748
    (case T of
berghofe@11615
   749
       Type ("fun", _) => prf %
berghofe@11519
   750
         (case head_of f of
skalberg@15531
   751
            Abs _ => SOME (remove_types t)
skalberg@15531
   752
          | Var _ => SOME (remove_types t)
skalberg@15531
   753
          | _ => NONE) %
berghofe@11519
   754
         (case head_of g of
skalberg@15531
   755
            Abs _ => SOME (remove_types u)
skalberg@15531
   756
          | Var _ => SOME (remove_types u)
skalberg@15531
   757
          | _ => NONE) %% prf1 %% prf2
skalberg@15531
   758
     | _ => prf % NONE % NONE %% prf1 %% prf2)
berghofe@11519
   759
  end;
berghofe@11519
   760
berghofe@11519
   761
fun equal_intr A B prf1 prf2 =
berghofe@11615
   762
  equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   763
berghofe@11519
   764
fun equal_elim A B prf1 prf2 =
berghofe@11615
   765
  equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   766
berghofe@11519
   767
berghofe@11519
   768
(***** axioms and theorems *****)
berghofe@11519
   769
haftmann@16787
   770
fun vars_of t = rev (fold_aterms
haftmann@16787
   771
  (fn v as Var _ => (fn vs => v ins vs) | _ => I) t []);
berghofe@11519
   772
berghofe@11519
   773
fun test_args _ [] = true
berghofe@11519
   774
  | test_args is (Bound i :: ts) =
berghofe@11519
   775
      not (i mem is) andalso test_args (i :: is) ts
berghofe@11519
   776
  | test_args _ _ = false;
berghofe@11519
   777
berghofe@11519
   778
fun is_fun (Type ("fun", _)) = true
berghofe@11519
   779
  | is_fun (TVar _) = true
berghofe@11519
   780
  | is_fun _ = false;
berghofe@11519
   781
berghofe@11519
   782
fun add_funvars Ts (vs, t) =
berghofe@11519
   783
  if is_fun (fastype_of1 (Ts, t)) then
skalberg@15570
   784
    vs union List.mapPartial (fn Var (ixn, T) =>
skalberg@15531
   785
      if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t)
berghofe@11519
   786
  else vs;
berghofe@11519
   787
berghofe@11519
   788
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
berghofe@11519
   789
      add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
berghofe@11519
   790
  | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
berghofe@11519
   791
      add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
berghofe@12041
   792
  | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
berghofe@12041
   793
  | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
berghofe@12041
   794
and add_npvars' Ts (vs, t) = (case strip_comb t of
berghofe@11519
   795
    (Var (ixn, _), ts) => if test_args [] ts then vs
skalberg@15570
   796
      else Library.foldl (add_npvars' Ts) (overwrite (vs,
skalberg@15570
   797
        (ixn, Library.foldl (add_funvars Ts) (getOpt (assoc (vs, ixn), []), ts))), ts)
skalberg@15570
   798
  | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
skalberg@15570
   799
  | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
berghofe@11519
   800
berghofe@11519
   801
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
berghofe@11519
   802
  | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
berghofe@11519
   803
  | prop_vars t = (case strip_comb t of
berghofe@11519
   804
      (Var (ixn, _), _) => [ixn] | _ => []);
berghofe@11519
   805
berghofe@11519
   806
fun is_proj t =
berghofe@11519
   807
  let
berghofe@11519
   808
    fun is_p i t = (case strip_comb t of
berghofe@11519
   809
        (Bound j, []) => false
berghofe@11519
   810
      | (Bound j, ts) => j >= i orelse exists (is_p i) ts
berghofe@11519
   811
      | (Abs (_, _, u), _) => is_p (i+1) u
berghofe@11519
   812
      | (_, ts) => exists (is_p i) ts)
berghofe@11519
   813
  in (case strip_abs_body t of
berghofe@11519
   814
        Bound _ => true
berghofe@11519
   815
      | t' => is_p 0 t')
berghofe@11519
   816
  end;
berghofe@11519
   817
berghofe@11519
   818
fun needed_vars prop = 
skalberg@15570
   819
  Library.foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union
berghofe@11519
   820
  prop_vars prop;
berghofe@11519
   821
berghofe@11519
   822
fun gen_axm_proof c name prop =
berghofe@11519
   823
  let
berghofe@11519
   824
    val nvs = needed_vars prop;
berghofe@11519
   825
    val args = map (fn (v as Var (ixn, _)) =>
skalberg@15531
   826
        if ixn mem nvs then SOME v else NONE) (vars_of prop) @
skalberg@15531
   827
      map SOME (sort (make_ord atless) (term_frees prop));
berghofe@11519
   828
  in
skalberg@15531
   829
    proof_combt' (c (name, prop, NONE), args)
berghofe@11519
   830
  end;
berghofe@11519
   831
berghofe@11519
   832
val axm_proof = gen_axm_proof PAxm;
berghofe@11519
   833
val oracle_proof = gen_axm_proof Oracle;
berghofe@11519
   834
berghofe@11519
   835
fun shrink ls lev (prf as Abst (a, T, body)) =
berghofe@11519
   836
      let val (b, is, ch, body') = shrink ls (lev+1) body
berghofe@11519
   837
      in (b, is, ch, if ch then Abst (a, T, body') else prf) end
berghofe@11519
   838
  | shrink ls lev (prf as AbsP (a, t, body)) =
berghofe@11519
   839
      let val (b, is, ch, body') = shrink (lev::ls) lev body
skalberg@15570
   840
      in (b orelse 0 mem is, List.mapPartial (fn 0 => NONE | i => SOME (i-1)) is,
berghofe@11519
   841
        ch, if ch then AbsP (a, t, body') else prf)
berghofe@11519
   842
      end
berghofe@11519
   843
  | shrink ls lev prf =
berghofe@11519
   844
      let val (is, ch, _, prf') = shrink' ls lev [] [] prf
berghofe@11519
   845
      in (false, is, ch, prf') end
berghofe@11615
   846
and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
berghofe@11519
   847
      let
berghofe@11519
   848
        val p as (_, is', ch', prf') = shrink ls lev prf2;
berghofe@11519
   849
        val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
berghofe@11519
   850
      in (is union is', ch orelse ch', ts',
berghofe@11615
   851
          if ch orelse ch' then prf'' %% prf' else prf)
berghofe@11519
   852
      end
berghofe@11615
   853
  | shrink' ls lev ts prfs (prf as prf1 % t) =
berghofe@11519
   854
      let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
berghofe@11615
   855
      in (is, ch orelse ch', ts', if ch orelse ch' then prf' % t' else prf) end
berghofe@11519
   856
  | shrink' ls lev ts prfs (prf as PBound i) =
skalberg@15570
   857
      (if exists (fn SOME (Bound j) => lev-j <= List.nth (ls, i) | _ => true) ts
berghofe@12233
   858
         orelse not (null (duplicates
skalberg@15570
   859
           (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))))
berghofe@11519
   860
         orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
berghofe@11519
   861
  | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
berghofe@11615
   862
  | shrink' ls lev ts prfs (prf as MinProof _) =
berghofe@11615
   863
      ([], false, map (pair false) ts, prf)
berghofe@11519
   864
  | shrink' ls lev ts prfs prf =
berghofe@11519
   865
      let
berghofe@11519
   866
        val prop = (case prf of PThm (_, _, prop, _) => prop | PAxm (_, prop, _) => prop
berghofe@11519
   867
          | Oracle (_, prop, _) => prop | _ => error "shrink: proof not in normal form");
berghofe@11519
   868
        val vs = vars_of prop;
nipkow@13629
   869
        val (ts', ts'') = splitAt (length vs, ts)
skalberg@15570
   870
        val insts = Library.take (length ts', map (fst o dest_Var) vs) ~~ ts';
skalberg@15570
   871
        val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
berghofe@11519
   872
          ixn ins (case assoc (insts, ixn) of
skalberg@15531
   873
              SOME (SOME t) => if is_proj t then ixns union ixns' else ixns'
berghofe@11519
   874
            | _ => ixns union ixns'))
berghofe@11519
   875
              (needed prop ts'' prfs, add_npvars false true [] ([], prop));
berghofe@11519
   876
        val insts' = map
skalberg@15531
   877
          (fn (ixn, x as SOME _) => if ixn mem nvs then (false, x) else (true, NONE)
berghofe@11519
   878
            | (_, x) => (false, x)) insts
berghofe@11519
   879
      in ([], false, insts' @ map (pair false) ts'', prf) end
berghofe@11519
   880
and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
berghofe@11519
   881
      (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
berghofe@11519
   882
  | needed (Var (ixn, _)) (_::_) _ = [ixn]
berghofe@11519
   883
  | needed _ _ _ = [];
berghofe@11519
   884
berghofe@11519
   885
berghofe@11519
   886
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
   887
berghofe@11519
   888
exception PMatch;
berghofe@11519
   889
berghofe@11519
   890
(** see pattern.ML **)
berghofe@11519
   891
skalberg@15570
   892
fun flt (i: int) = List.filter (fn n => n < i);
berghofe@12279
   893
berghofe@12279
   894
fun fomatch Ts tymatch j =
berghofe@11519
   895
  let
berghofe@11519
   896
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
   897
        (Var (ixn, T), t)  =>
berghofe@12279
   898
          if j>0 andalso not (null (flt j (loose_bnos t)))
berghofe@12279
   899
          then raise PMatch
berghofe@12279
   900
          else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
berghofe@12279
   901
            (ixn, t) :: insts)
berghofe@11519
   902
      | (Free (a, T), Free (b, U)) =>
berghofe@12279
   903
	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   904
      | (Const (a, T), Const (b, U))  =>
berghofe@12279
   905
	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   906
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@12279
   907
      | (Bound i, Bound j) => if i=j then instsp else raise PMatch
berghofe@11519
   908
      | _ => raise PMatch
berghofe@11519
   909
  in mtch end;
berghofe@11519
   910
berghofe@12279
   911
fun match_proof Ts tymatch =
berghofe@11519
   912
  let
skalberg@15531
   913
    fun optmatch _ inst (NONE, _) = inst
skalberg@15531
   914
      | optmatch _ _ (SOME _, NONE) = raise PMatch
skalberg@15531
   915
      | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
berghofe@12279
   916
berghofe@12279
   917
    fun matcht Ts j (pinst, tinst) (t, u) =
berghofe@12279
   918
      (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
berghofe@12279
   919
    fun matchT (pinst, (tyinsts, insts)) p =
berghofe@12279
   920
      (pinst, (tymatch (tyinsts, K p), insts));
skalberg@15570
   921
    fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
berghofe@12279
   922
berghofe@12279
   923
    fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
berghofe@12279
   924
          if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
berghofe@12279
   925
          else (case apfst (flt i) (apsnd (flt j)
berghofe@12279
   926
                  (prf_add_loose_bnos 0 0 prf ([], []))) of
berghofe@12279
   927
              ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
   928
            | ([], _) => if j = 0 then
berghofe@12279
   929
                   ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
   930
                 else raise PMatch
berghofe@12279
   931
            | _ => raise PMatch)
berghofe@12279
   932
      | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
berghofe@12279
   933
          optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
berghofe@12279
   934
      | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
berghofe@12279
   935
          mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
berghofe@12279
   936
      | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
skalberg@15570
   937
          mtch (getOpt (opU,dummyT) :: Ts) i (j+1)
berghofe@12279
   938
            (optmatch matchT inst (opT, opU)) (prf1, prf2)
berghofe@12279
   939
      | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
skalberg@15570
   940
          mtch (getOpt (opU,dummyT) :: Ts) i (j+1) inst
berghofe@12279
   941
            (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
berghofe@12279
   942
      | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
berghofe@12279
   943
          mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
berghofe@12279
   944
      | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
berghofe@12279
   945
          mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
berghofe@12279
   946
      | mtch Ts i j inst (PThm ((name1, _), _, prop1, opTs),
berghofe@12279
   947
            PThm ((name2, _), _, prop2, opUs)) =
berghofe@11519
   948
          if name1=name2 andalso prop1=prop2 then
berghofe@12279
   949
            optmatch matchTs inst (opTs, opUs)
berghofe@11519
   950
          else raise PMatch
berghofe@12279
   951
      | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
berghofe@12279
   952
          if s1=s2 then optmatch matchTs inst (opTs, opUs)
berghofe@11519
   953
          else raise PMatch
berghofe@12279
   954
      | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
berghofe@12279
   955
      | mtch _ _ _ _ _ = raise PMatch
berghofe@12279
   956
  in mtch Ts 0 0 end;
berghofe@11519
   957
berghofe@11519
   958
fun prf_subst (pinst, (tyinsts, insts)) =
berghofe@11519
   959
  let
berghofe@15797
   960
    val substT = Envir.typ_subst_TVars tyinsts;
berghofe@11519
   961
berghofe@11519
   962
    fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of
skalberg@15531
   963
          NONE => t
skalberg@15531
   964
        | SOME u => incr_boundvars lev u)
berghofe@11519
   965
      | subst' lev (Const (s, T)) = Const (s, substT T)
berghofe@11519
   966
      | subst' lev (Free (s, T)) = Free (s, substT T)
berghofe@11519
   967
      | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
berghofe@11519
   968
      | subst' lev (f $ t) = subst' lev f $ subst' lev t
berghofe@11519
   969
      | subst' _ t = t;
berghofe@11519
   970
berghofe@11519
   971
    fun subst plev tlev (AbsP (a, t, body)) =
skalberg@15570
   972
          AbsP (a, Option.map (subst' tlev) t, subst (plev+1) tlev body)
berghofe@11519
   973
      | subst plev tlev (Abst (a, T, body)) =
skalberg@15570
   974
          Abst (a, Option.map substT T, subst plev (tlev+1) body)
berghofe@11615
   975
      | subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf'
skalberg@15570
   976
      | subst plev tlev (prf % t) = subst plev tlev prf % Option.map (subst' tlev) t
berghofe@11519
   977
      | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of
skalberg@15531
   978
          NONE => prf
skalberg@15531
   979
        | SOME prf' => incr_pboundvars plev tlev prf')
berghofe@11519
   980
      | subst _ _ (PThm (id, prf, prop, Ts)) =
skalberg@15570
   981
          PThm (id, prf, prop, Option.map (map substT) Ts)
berghofe@11519
   982
      | subst _ _ (PAxm (id, prop, Ts)) =
skalberg@15570
   983
          PAxm (id, prop, Option.map (map substT) Ts)
berghofe@11519
   984
      | subst _ _ t = t
berghofe@11519
   985
  in subst 0 0 end;
berghofe@11519
   986
berghofe@12871
   987
(*A fast unification filter: true unless the two terms cannot be unified. 
berghofe@12871
   988
  Terms must be NORMAL.  Treats all Vars as distinct. *)
berghofe@12871
   989
fun could_unify prf1 prf2 =
berghofe@12871
   990
  let
berghofe@12871
   991
    fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
berghofe@12871
   992
          could_unify prf2 prf2' andalso matchrands prf1 prf1'
skalberg@15531
   993
      | matchrands (prf % SOME t) (prf' % SOME t') =
berghofe@12871
   994
          Term.could_unify (t, t') andalso matchrands prf prf'
berghofe@12871
   995
      | matchrands (prf % _) (prf' % _) = matchrands prf prf'
berghofe@12871
   996
      | matchrands _ _ = true
berghofe@12871
   997
berghofe@12871
   998
    fun head_of (prf %% _) = head_of prf
berghofe@12871
   999
      | head_of (prf % _) = head_of prf
berghofe@12871
  1000
      | head_of prf = prf
berghofe@12871
  1001
berghofe@12871
  1002
  in case (head_of prf1, head_of prf2) of
berghofe@12871
  1003
        (_, Hyp (Var _)) => true
berghofe@12871
  1004
      | (Hyp (Var _), _) => true
berghofe@12871
  1005
      | (PThm ((a, _), _, propa, _), PThm ((b, _), _, propb, _)) =>
berghofe@12871
  1006
          a = b andalso propa = propb andalso matchrands prf1 prf2
berghofe@12871
  1007
      | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
berghofe@12871
  1008
      | (PBound i, PBound j) =>  i = j andalso matchrands prf1 prf2
berghofe@12871
  1009
      | (AbsP _, _) =>  true   (*because of possible eta equality*)
berghofe@12871
  1010
      | (Abst _, _) =>  true
berghofe@12871
  1011
      | (_, AbsP _) =>  true
berghofe@12871
  1012
      | (_, Abst _) =>  true
berghofe@12871
  1013
      | _ => false
berghofe@12871
  1014
  end;
berghofe@12871
  1015
berghofe@11519
  1016
(**** rewriting on proof terms ****)
berghofe@11519
  1017
berghofe@13102
  1018
val skel0 = PBound 0;
berghofe@13102
  1019
berghofe@12279
  1020
fun rewrite_prf tymatch (rules, procs) prf =
berghofe@11519
  1021
  let
skalberg@15531
  1022
    fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, skel0)
skalberg@15531
  1023
      | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, skel0)
berghofe@11519
  1024
      | rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of
skalberg@15531
  1025
          SOME prf' => SOME (prf', skel0)
skalberg@15531
  1026
        | NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
berghofe@13102
  1027
            (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
skalberg@15570
  1028
               handle PMatch => NONE) (List.filter (could_unify prf o fst) rules));
berghofe@11519
  1029
berghofe@11615
  1030
    fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
berghofe@11519
  1031
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
  1032
          else
berghofe@11519
  1033
            let val prf'' = incr_pboundvars (~1) 0 prf'
skalberg@15570
  1034
            in SOME (getOpt (rew Ts prf'', (prf'', skel0))) end
skalberg@15531
  1035
      | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
berghofe@11519
  1036
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
  1037
          else
berghofe@11519
  1038
            let val prf'' = incr_pboundvars 0 (~1) prf'
skalberg@15570
  1039
            in SOME (getOpt (rew Ts prf'', (prf'', skel0))) end
berghofe@11519
  1040
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
  1041
skalberg@15531
  1042
    fun rew1 _ (Hyp (Var _)) _ = NONE
berghofe@13102
  1043
      | rew1 Ts skel prf = (case rew2 Ts skel prf of
skalberg@15531
  1044
          SOME prf1 => (case rew0 Ts prf1 of
skalberg@15570
  1045
              SOME (prf2, skel') => SOME (getOpt (rew1 Ts skel' prf2, prf2))
skalberg@15531
  1046
            | NONE => SOME prf1)
skalberg@15531
  1047
        | NONE => (case rew0 Ts prf of
skalberg@15570
  1048
              SOME (prf1, skel') => SOME (getOpt (rew1 Ts skel' prf1, prf1))
skalberg@15531
  1049
            | NONE => NONE))
berghofe@11519
  1050
skalberg@15531
  1051
    and rew2 Ts skel (prf % SOME t) = (case prf of
berghofe@11519
  1052
            Abst (_, _, body) =>
berghofe@11519
  1053
              let val prf' = prf_subst_bounds [t] body
skalberg@15570
  1054
              in SOME (getOpt (rew2 Ts skel0 prf', prf')) end
berghofe@13102
  1055
          | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf of
skalberg@15531
  1056
              SOME prf' => SOME (prf' % SOME t)
skalberg@15531
  1057
            | NONE => NONE))
skalberg@15570
  1058
      | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
berghofe@13102
  1059
          (rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf)
berghofe@13102
  1060
      | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
berghofe@11519
  1061
            AbsP (_, _, body) =>
berghofe@11519
  1062
              let val prf' = prf_subst_pbounds [prf2] body
skalberg@15570
  1063
              in SOME (getOpt (rew2 Ts skel0 prf', prf')) end
berghofe@13102
  1064
          | _ =>
berghofe@13102
  1065
            let val (skel1, skel2) = (case skel of
berghofe@13102
  1066
                skel1 %% skel2 => (skel1, skel2)
berghofe@13102
  1067
              | _ => (skel0, skel0))
berghofe@13102
  1068
            in case rew1 Ts skel1 prf1 of
skalberg@15531
  1069
                SOME prf1' => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1070
                    SOME prf2' => SOME (prf1' %% prf2')
skalberg@15531
  1071
                  | NONE => SOME (prf1' %% prf2))
skalberg@15531
  1072
              | NONE => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1073
                    SOME prf2' => SOME (prf1 %% prf2')
skalberg@15531
  1074
                  | NONE => NONE)
berghofe@13102
  1075
            end)
skalberg@15570
  1076
      | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (getOpt (T,dummyT) :: Ts)
berghofe@13102
  1077
              (case skel of Abst (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1078
            SOME prf' => SOME (Abst (s, T, prf'))
skalberg@15531
  1079
          | NONE => NONE)
berghofe@13102
  1080
      | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
berghofe@13102
  1081
              (case skel of AbsP (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1082
            SOME prf' => SOME (AbsP (s, t, prf'))
skalberg@15531
  1083
          | NONE => NONE)
skalberg@15531
  1084
      | rew2 _ _ _ = NONE
berghofe@11519
  1085
skalberg@15570
  1086
  in getOpt (rew1 [] skel0 prf, prf) end;
berghofe@11519
  1087
berghofe@11519
  1088
fun rewrite_proof tsig = rewrite_prf (fn (tab, f) =>
berghofe@11519
  1089
  Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
  1090
berghofe@11715
  1091
fun rewrite_proof_notypes rews = rewrite_prf fst rews;
berghofe@11615
  1092
berghofe@11519
  1093
(**** theory data ****)
berghofe@11519
  1094
berghofe@11519
  1095
(* data kind 'Pure/proof' *)
berghofe@11519
  1096
wenzelm@16458
  1097
structure ProofData = TheoryDataFun
wenzelm@16458
  1098
(struct
berghofe@11519
  1099
  val name = "Pure/proof";
berghofe@11519
  1100
  type T = ((proof * proof) list *
berghofe@12233
  1101
    (string * (typ list -> proof -> proof option)) list);
berghofe@11519
  1102
berghofe@12233
  1103
  val empty = ([], []);
berghofe@12233
  1104
  val copy = I;
wenzelm@16458
  1105
  val extend = I;
wenzelm@16458
  1106
  fun merge _ ((rules1, procs1), (rules2, procs2)) =
wenzelm@12293
  1107
    (merge_lists rules1 rules2, merge_alists procs1 procs2);
berghofe@11519
  1108
  fun print _ _ = ();
wenzelm@16458
  1109
end);
berghofe@11519
  1110
wenzelm@16536
  1111
val init_data = ProofData.init;
berghofe@11519
  1112
berghofe@12233
  1113
fun add_prf_rrules rs thy =
berghofe@11519
  1114
  let val r = ProofData.get thy
berghofe@12233
  1115
  in ProofData.put (rs @ fst r, snd r) thy end;
berghofe@11519
  1116
berghofe@12233
  1117
fun add_prf_rprocs ps thy =
berghofe@11519
  1118
  let val r = ProofData.get thy
berghofe@12233
  1119
  in ProofData.put (fst r, ps @ snd r) thy end;
berghofe@11519
  1120
wenzelm@16458
  1121
fun thm_proof thy (name, tags) hyps prop prf =
berghofe@11519
  1122
  let
wenzelm@12923
  1123
    val prop = Logic.list_implies (hyps, prop);
berghofe@11519
  1124
    val nvs = needed_vars prop;
berghofe@11519
  1125
    val args = map (fn (v as Var (ixn, _)) =>
skalberg@15531
  1126
        if ixn mem nvs then SOME v else NONE) (vars_of prop) @
skalberg@15531
  1127
      map SOME (sort (make_ord atless) (term_frees prop));
wenzelm@11543
  1128
    val opt_prf = if ! proofs = 2 then
wenzelm@16458
  1129
        #4 (shrink [] 0 (rewrite_prf fst (ProofData.get thy)
skalberg@15574
  1130
          (foldr (uncurry implies_intr_proof) prf hyps)))
berghofe@11519
  1131
      else MinProof (mk_min_proof ([], prf));
berghofe@12233
  1132
    val head = (case strip_combt (fst (strip_combP prf)) of
skalberg@15531
  1133
        (PThm ((old_name, _), prf', prop', NONE), args') =>
berghofe@11519
  1134
          if (old_name="" orelse old_name=name) andalso
berghofe@11519
  1135
             prop = prop' andalso args = args' then
skalberg@15531
  1136
            PThm ((name, tags), prf', prop, NONE)
berghofe@11519
  1137
          else
skalberg@15531
  1138
            PThm ((name, tags), opt_prf, prop, NONE)
skalberg@15531
  1139
      | _ => PThm ((name, tags), opt_prf, prop, NONE))
berghofe@11519
  1140
  in
wenzelm@12923
  1141
    proof_combP (proof_combt' (head, args), map Hyp hyps)
berghofe@11519
  1142
  end;
berghofe@11519
  1143
wenzelm@12923
  1144
fun get_name_tags hyps prop prf =
wenzelm@12923
  1145
  let val prop = Logic.list_implies (hyps, prop) in
wenzelm@12923
  1146
    (case strip_combt (fst (strip_combP prf)) of
berghofe@11519
  1147
      (PThm ((name, tags), _, prop', _), _) =>
berghofe@11519
  1148
        if prop=prop' then (name, tags) else ("", [])
berghofe@11519
  1149
    | (PAxm (name, prop', _), _) =>
berghofe@11519
  1150
        if prop=prop' then (name, []) else ("", [])
wenzelm@12923
  1151
    | _ => ("", []))
wenzelm@12923
  1152
  end;
berghofe@11519
  1153
berghofe@11519
  1154
end;
berghofe@11519
  1155
berghofe@11519
  1156
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
berghofe@11519
  1157
open BasicProofterm;