src/Pure/proofterm.ML
author haftmann
Fri Nov 10 07:44:47 2006 +0100 (2006-11-10)
changeset 21286 b5e7b80caa6a
parent 20853 3ff5a2e05810
child 21646 c07b5b0e8492
permissions -rw-r--r--
introduces canonical AList functions for loop_tacs
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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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   | % of proof * term option
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   | %% of proof * proof
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   | Hyp of term
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   | PThm of (string * (string * string list) list) * proof * term * typ list option
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   | PAxm of string * term * typ list option
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   | Oracle of string * term * typ list option
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   | MinProof of ((string * term) * proof) list * (string * term) list * (string * term) 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_option : (term -> term option) -> (typ -> typ option) -> 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) -> proof -> 'a -> 'a
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  val maxidx_proof : proof -> int -> 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 proof_of_min_axm : string * term -> proof
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  val proof_of_min_thm : (string * term) * proof -> proof
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  val thms_of_proof : proof -> (term * proof) list Symtab.table ->
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    (term * proof) list Symtab.table
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  val thms_of_proof' : proof -> (term * proof) list Symtab.table ->
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    (term * proof) list Symtab.table
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  val axms_of_proof : proof -> proof Symtab.table -> proof Symtab.table
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  val oracles_of_proof : (string * term) list -> proof -> (string * term) 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 generalize: string list * string list -> 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 : bool -> 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 : theory -> (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 ((string * term) * proof) list * (string * term) list * (string * term) list;
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fun proof_of_min_axm (s, prop) = PAxm (s, prop, NONE);
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fun proof_of_min_thm ((s, prop), prf) = PThm ((s, []), prf, prop, NONE);
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val string_term_ord = prod_ord fast_string_ord Term.fast_term_ord;
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fun oracles_of_proof oras prf =
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  let
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    fun oras_of (Abst (_, _, prf)) = oras_of prf
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      | oras_of (AbsP (_, _, prf)) = oras_of prf
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      | oras_of (prf % _) = oras_of prf
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      | oras_of (prf1 %% prf2) = oras_of prf1 #> oras_of prf2
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      | oras_of (PThm ((name, _), prf, prop, _)) = (fn tabs as (thms, oras) =>
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          case Symtab.lookup thms name of
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            NONE => oras_of prf (Symtab.update (name, [prop]) thms, oras)
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          | SOME ps => if member (op =) ps prop then tabs else
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              oras_of prf (Symtab.update (name, prop::ps) thms, oras))
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      | oras_of (Oracle (s, prop, _)) =
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          apsnd (OrdList.insert string_term_ord (s, prop))
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      | oras_of (MinProof (thms, _, oras)) =
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          apsnd (OrdList.union string_term_ord oras) #>
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          fold (oras_of o proof_of_min_thm) thms
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      | oras_of _ = I
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  in
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    snd (oras_of prf (Symtab.empty, oras))
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  end;
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fun thms_of_proof (Abst (_, _, prf)) = thms_of_proof prf
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  | thms_of_proof (AbsP (_, _, prf)) = thms_of_proof prf
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  | thms_of_proof (prf1 %% prf2) = thms_of_proof prf1 #> thms_of_proof prf2
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  | thms_of_proof (prf % _) = thms_of_proof prf
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  | thms_of_proof (prf' as PThm ((s, _), prf, prop, _)) = (fn tab =>
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      case Symtab.lookup tab s of
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        NONE => thms_of_proof prf (Symtab.update (s, [(prop, prf')]) tab)
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      | SOME ps => if exists (fn (p, _) => p = prop) ps then tab else
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          thms_of_proof prf (Symtab.update (s, (prop, prf')::ps) tab))
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  | thms_of_proof (MinProof (prfs, _, _)) = fold (thms_of_proof o proof_of_min_thm) prfs
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  | thms_of_proof _ = I;
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(* this version does not recursively descend into proofs of (named) theorems *)
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fun thms_of_proof' (Abst (_, _, prf)) = thms_of_proof' prf
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  | thms_of_proof' (AbsP (_, _, prf)) = thms_of_proof' prf
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  | thms_of_proof' (prf1 %% prf2) = thms_of_proof' prf1 #> thms_of_proof' prf2
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  | thms_of_proof' (prf % _) = thms_of_proof' prf
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  | thms_of_proof' (PThm (("", _), prf, prop, _)) = thms_of_proof' prf
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  | thms_of_proof' (prf' as PThm ((s, _), _, prop, _)) = (fn tab =>
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      case Symtab.lookup tab s of
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        NONE => Symtab.update (s, [(prop, prf')]) tab
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      | SOME ps => if exists (fn (p, _) => p = prop) ps then tab else
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          Symtab.update (s, (prop, prf')::ps) tab)
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  | thms_of_proof' (MinProof (prfs, _, _)) = fold (thms_of_proof' o proof_of_min_thm) prfs
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  | thms_of_proof' _ = I;
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fun axms_of_proof (Abst (_, _, prf)) = axms_of_proof prf
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  | axms_of_proof (AbsP (_, _, prf)) = axms_of_proof prf
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  | axms_of_proof (prf1 %% prf2) = axms_of_proof prf1 #> axms_of_proof prf2
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  | axms_of_proof (prf % _) = axms_of_proof prf
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  | axms_of_proof (prf as PAxm (s, _, _)) = Symtab.update (s, prf)
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  | axms_of_proof (MinProof (_, prfs, _)) = fold (axms_of_proof o proof_of_min_axm) prfs
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  | axms_of_proof _ = I;
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(** collect all theorems, axioms and oracles **)
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fun map3 f g h (thms, axms, oras) = (f thms, g axms, h oras);
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fun mk_min_proof (Abst (_, _, prf)) = mk_min_proof prf
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  | mk_min_proof (AbsP (_, _, prf)) = mk_min_proof prf
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  | mk_min_proof (prf % _) = mk_min_proof prf
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  | mk_min_proof (prf1 %% prf2) = mk_min_proof prf1 #> mk_min_proof prf2
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  | mk_min_proof (PThm ((s, _), prf, prop, _)) =
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      map3 (OrdList.insert (string_term_ord o pairself fst) ((s, prop), prf)) I I
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  | mk_min_proof (PAxm (s, prop, _)) =
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      map3 I (OrdList.insert string_term_ord (s, prop)) I
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  | mk_min_proof (Oracle (s, prop, _)) =
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      map3 I I (OrdList.insert string_term_ord (s, prop))
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  | mk_min_proof (MinProof (thms, axms, oras)) =
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      map3 (OrdList.union (string_term_ord o pairself fst) thms)
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        (OrdList.union string_term_ord axms) (OrdList.union string_term_ord oras)
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  | mk_min_proof _ = I;
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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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val min_proof = MinProof ([], [], []);
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fun infer_derivs f (ora1, prf1) (ora2, prf2) =
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  let val ora = ora1 orelse ora2 in
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    (ora,
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      case !proofs of
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        2 => f prf1 prf2
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      | 1 => MinProof (([], [], []) |> mk_min_proof prf1 |> mk_min_proof prf2)
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      | 0 => if ora then MinProof ([], [], if_ora ora2 (if_ora ora1 [] prf1) prf2) else min_proof
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      | i => err_illegal_level i)
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  end;
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fun infer_derivs' f = infer_derivs (K f) (false, min_proof);
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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) = (case f x of NONE => raise SAME | some => some);
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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 map_proof_terms_option f g =
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  let
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    fun map_typs (T :: Ts) =
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          (case g T of
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            NONE => T :: map_typs Ts
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          | SOME T' => T' :: (map_typs Ts handle SAME => Ts))
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      | map_typs [] = raise SAME;
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    fun mapp (Abst (s, T, prf)) = (Abst (s, apsome 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 f t, mapph prf)
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          handle SAME => AbsP (s, t, mapp prf))
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      | mapp (prf % t) = (mapp prf % (apsome f t handle SAME => t)
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          handle SAME => prf % apsome 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 (map_typs Ts))
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      | mapp (PAxm (a, prop, SOME Ts)) =
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          PAxm (a, prop, SOME (map_typs 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 same f x =
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   291
  let val x' = f x
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   292
  in if x = x' then raise SAME else x' end;
berghofe@11715
   293
berghofe@11715
   294
fun map_proof_terms f g =
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   295
  map_proof_terms_option
wenzelm@20000
   296
   (fn t => SOME (same f t) handle SAME => NONE)
wenzelm@20000
   297
   (fn T => SOME (same g T) handle SAME => NONE);
berghofe@11519
   298
wenzelm@20147
   299
fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
wenzelm@20147
   300
  | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
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   301
  | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
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   302
  | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
wenzelm@20147
   303
  | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
wenzelm@20147
   304
  | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
wenzelm@20147
   305
  | fold_proof_terms f g (prf1 %% prf2) =
wenzelm@20147
   306
      fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
wenzelm@20159
   307
  | fold_proof_terms _ g (PThm (_, _, _, SOME Ts)) = fold g Ts
wenzelm@20159
   308
  | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
wenzelm@20147
   309
  | fold_proof_terms _ _ _ = I;
berghofe@11519
   310
wenzelm@20300
   311
fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
berghofe@12868
   312
berghofe@13744
   313
fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
berghofe@13749
   314
  | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
berghofe@13744
   315
  | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
berghofe@13749
   316
  | size_of_proof (prf % _) = 1 + size_of_proof prf
berghofe@13744
   317
  | size_of_proof _ = 1;
berghofe@13744
   318
berghofe@12907
   319
fun change_type opTs (PThm (name, prf, prop, _)) = PThm (name, prf, prop, opTs)
berghofe@12907
   320
  | change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
berghofe@12907
   321
  | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
berghofe@12907
   322
  | change_type _ prf = prf;
berghofe@12907
   323
berghofe@11519
   324
berghofe@11519
   325
(***** utilities *****)
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   326
berghofe@11519
   327
fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
berghofe@11519
   328
  | strip_abs _ t = t;
berghofe@11519
   329
skalberg@15570
   330
fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
berghofe@11519
   331
berghofe@11519
   332
berghofe@11519
   333
(*Abstraction of a proof term over its occurrences of v, 
berghofe@11519
   334
    which must contain no loose bound variables.
berghofe@11519
   335
  The resulting proof term is ready to become the body of an Abst.*)
berghofe@11519
   336
berghofe@11519
   337
fun prf_abstract_over v =
berghofe@11519
   338
  let
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   339
    fun abst' lev u = if v aconv u then Bound lev else
berghofe@11715
   340
      (case u of
berghofe@11715
   341
         Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
berghofe@11715
   342
       | f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t)
berghofe@11715
   343
       | _ => raise SAME)
berghofe@11715
   344
    and absth' lev t = (abst' lev t handle SAME => t);
berghofe@11519
   345
berghofe@11715
   346
    fun abst lev (AbsP (a, t, prf)) =
berghofe@11715
   347
          (AbsP (a, apsome' (abst' lev) t, absth lev prf)
berghofe@11715
   348
           handle SAME => AbsP (a, t, abst lev prf))
berghofe@11715
   349
      | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
berghofe@11715
   350
      | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
berghofe@11715
   351
          handle SAME => prf1 %% abst lev prf2)
skalberg@15570
   352
      | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
berghofe@11715
   353
          handle SAME => prf % apsome' (abst' lev) t)
berghofe@11715
   354
      | abst _ _ = raise SAME
berghofe@11715
   355
    and absth lev prf = (abst lev prf handle SAME => prf)
berghofe@11519
   356
berghofe@11715
   357
  in absth 0 end;
berghofe@11519
   358
berghofe@11519
   359
berghofe@11519
   360
(*increments a proof term's non-local bound variables
berghofe@11519
   361
  required when moving a proof term within abstractions
berghofe@11519
   362
     inc is  increment for bound variables
berghofe@11519
   363
     lev is  level at which a bound variable is considered 'loose'*)
berghofe@11519
   364
berghofe@11519
   365
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
berghofe@11519
   366
berghofe@11715
   367
fun prf_incr_bv' incP inct Plev tlev (PBound i) =
berghofe@11715
   368
      if i >= Plev then PBound (i+incP) else raise SAME 
berghofe@11715
   369
  | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
berghofe@11715
   370
      (AbsP (a, apsome' (same (incr_bv' inct tlev)) t,
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   371
         prf_incr_bv incP inct (Plev+1) tlev body) handle SAME =>
berghofe@11715
   372
           AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
berghofe@11715
   373
  | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
berghofe@11715
   374
      Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
berghofe@11715
   375
  | prf_incr_bv' incP inct Plev tlev (prf %% prf') = 
berghofe@11715
   376
      (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
berghofe@11715
   377
       handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
berghofe@11715
   378
  | prf_incr_bv' incP inct Plev tlev (prf % t) = 
skalberg@15570
   379
      (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
berghofe@11715
   380
       handle SAME => prf % apsome' (same (incr_bv' inct tlev)) t)
berghofe@11715
   381
  | prf_incr_bv' _ _ _ _ _ = raise SAME
berghofe@11715
   382
and prf_incr_bv incP inct Plev tlev prf =
berghofe@11715
   383
      (prf_incr_bv' incP inct Plev tlev prf handle SAME => prf);
berghofe@11519
   384
berghofe@11519
   385
fun incr_pboundvars  0 0 prf = prf
berghofe@11519
   386
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   387
berghofe@11519
   388
berghofe@11615
   389
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
skalberg@15531
   390
  | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
skalberg@15531
   391
  | prf_loose_bvar1 (_ % NONE) _ = true
skalberg@15531
   392
  | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
skalberg@15531
   393
  | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
berghofe@11519
   394
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
berghofe@11519
   395
  | prf_loose_bvar1 _ _ = false;
berghofe@11519
   396
berghofe@11519
   397
fun prf_loose_Pbvar1 (PBound i) k = i = k
berghofe@11615
   398
  | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
berghofe@11615
   399
  | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   400
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
berghofe@11519
   401
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
berghofe@11519
   402
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   403
berghofe@12279
   404
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
wenzelm@17492
   405
      if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
berghofe@12279
   406
  | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
berghofe@12279
   407
      prf_add_loose_bnos plev tlev prf2
berghofe@12279
   408
        (prf_add_loose_bnos plev tlev prf1 p)
berghofe@12279
   409
  | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
berghofe@12279
   410
      prf_add_loose_bnos plev tlev prf (case opt of
wenzelm@17492
   411
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   412
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   413
  | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
berghofe@12279
   414
      prf_add_loose_bnos (plev+1) tlev prf (case opt of
wenzelm@17492
   415
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   416
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   417
  | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
berghofe@12279
   418
      prf_add_loose_bnos plev (tlev+1) prf p
berghofe@12279
   419
  | prf_add_loose_bnos _ _ _ _ = ([], []);
berghofe@12279
   420
berghofe@11519
   421
berghofe@11519
   422
(**** substitutions ****)
berghofe@11519
   423
wenzelm@20509
   424
fun del_conflicting_tvars envT T = TermSubst.instantiateT
wenzelm@19482
   425
  (map_filter (fn ixnS as (_, S) =>
berghofe@18316
   426
     (Type.lookup (envT, ixnS); NONE) handle TYPE _ =>
berghofe@18316
   427
        SOME (ixnS, TFree ("'dummy", S))) (typ_tvars T)) T;
berghofe@18316
   428
wenzelm@20509
   429
fun del_conflicting_vars env t = TermSubst.instantiate
wenzelm@19482
   430
  (map_filter (fn ixnS as (_, S) =>
berghofe@18316
   431
     (Type.lookup (type_env env, ixnS); NONE) handle TYPE _ =>
berghofe@18316
   432
        SOME (ixnS, TFree ("'dummy", S))) (term_tvars t),
wenzelm@19482
   433
   map_filter (fn Var (ixnT as (_, T)) =>
berghofe@18316
   434
     (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
berghofe@18316
   435
        SOME (ixnT, Free ("dummy", T))) (term_vars t)) t;
berghofe@18316
   436
berghofe@11519
   437
fun norm_proof env =
berghofe@11519
   438
  let
wenzelm@12497
   439
    val envT = type_env env;
berghofe@18316
   440
    fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
berghofe@18316
   441
    fun htype f t = f env t handle TYPE (s, _, _) =>
berghofe@18316
   442
      (msg s; f env (del_conflicting_vars env t));
berghofe@18316
   443
    fun htypeT f T = f envT T handle TYPE (s, _, _) =>
berghofe@18316
   444
      (msg s; f envT (del_conflicting_tvars envT T));
berghofe@18316
   445
    fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
berghofe@18316
   446
      (msg s; f envT (map (del_conflicting_tvars envT) Ts));
berghofe@18316
   447
    fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (htypeT norm_type_same) T, normh prf)
berghofe@11519
   448
          handle SAME => Abst (s, T, norm prf))
berghofe@18316
   449
      | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (htype norm_term_same) t, normh prf)
berghofe@11519
   450
          handle SAME => AbsP (s, t, norm prf))
berghofe@18316
   451
      | norm (prf % t) = (norm prf % Option.map (htype norm_term) t
berghofe@18316
   452
          handle SAME => prf % apsome' (htype norm_term_same) t)
berghofe@11615
   453
      | norm (prf1 %% prf2) = (norm prf1 %% normh prf2
berghofe@11615
   454
          handle SAME => prf1 %% norm prf2)
berghofe@18316
   455
      | norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (htypeTs norm_types_same) Ts)
berghofe@18316
   456
      | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (htypeTs norm_types_same) Ts)
berghofe@11519
   457
      | norm _ = raise SAME
berghofe@11519
   458
    and normh prf = (norm prf handle SAME => prf);
berghofe@11519
   459
  in normh end;
berghofe@11519
   460
berghofe@11519
   461
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   462
berghofe@11519
   463
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   464
  | remove_types (t $ u) = remove_types t $ remove_types u
berghofe@11519
   465
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   466
  | remove_types t = t;
berghofe@11519
   467
berghofe@11519
   468
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
berghofe@15797
   469
  Envir.Envir {iTs = iTs, asol = Vartab.map (apsnd remove_types) asol,
berghofe@15797
   470
    maxidx = maxidx};
berghofe@11519
   471
berghofe@11519
   472
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   473
berghofe@11519
   474
(**** substitution of bound variables ****)
berghofe@11519
   475
berghofe@11519
   476
fun prf_subst_bounds args prf =
berghofe@11519
   477
  let
berghofe@11519
   478
    val n = length args;
berghofe@11519
   479
    fun subst' lev (Bound i) =
berghofe@11519
   480
         (if i<lev then raise SAME    (*var is locally bound*)
berghofe@11519
   481
          else  incr_boundvars lev (List.nth (args, i-lev))
berghofe@11519
   482
                  handle Subscript => Bound (i-n)  (*loose: change it*))
berghofe@11519
   483
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   484
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
berghofe@11519
   485
          handle SAME => f $ subst' lev t)
berghofe@11519
   486
      | subst' _ _ = raise SAME
berghofe@11519
   487
    and substh' lev t = (subst' lev t handle SAME => t);
berghofe@11519
   488
berghofe@11519
   489
    fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
berghofe@11519
   490
          handle SAME => AbsP (a, t, subst lev body))
berghofe@11519
   491
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11615
   492
      | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
berghofe@11615
   493
          handle SAME => prf %% subst lev prf')
skalberg@15570
   494
      | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
berghofe@11615
   495
          handle SAME => prf % apsome' (subst' lev) t)
berghofe@11519
   496
      | subst _ _ = raise SAME
berghofe@11519
   497
    and substh lev prf = (subst lev prf handle SAME => prf)
berghofe@11519
   498
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   499
berghofe@11519
   500
fun prf_subst_pbounds args prf =
berghofe@11519
   501
  let
berghofe@11519
   502
    val n = length args;
berghofe@11519
   503
    fun subst (PBound i) Plev tlev =
wenzelm@20147
   504
         (if i < Plev then raise SAME    (*var is locally bound*)
berghofe@11519
   505
          else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
berghofe@11519
   506
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   507
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   508
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11615
   509
      | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
berghofe@11615
   510
          handle SAME => prf %% subst prf' Plev tlev)
berghofe@11615
   511
      | subst (prf % t) Plev tlev = subst prf Plev tlev % t
berghofe@11519
   512
      | subst  prf _ _ = raise SAME
berghofe@11519
   513
    and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
berghofe@11519
   514
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   515
berghofe@11519
   516
berghofe@11519
   517
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   518
berghofe@11519
   519
fun frzT names =
haftmann@17325
   520
  map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
berghofe@11519
   521
berghofe@11519
   522
fun thawT names =
haftmann@17325
   523
  map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
skalberg@15531
   524
      NONE => TFree (s, xs)
skalberg@15531
   525
    | SOME ixn => TVar (ixn, xs));
berghofe@11519
   526
berghofe@11519
   527
fun freeze names names' (t $ u) =
berghofe@11519
   528
      freeze names names' t $ freeze names names' u
berghofe@11519
   529
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   530
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   531
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   532
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   533
  | freeze names names' (Var (ixn, T)) =
haftmann@17325
   534
      Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
berghofe@11519
   535
  | freeze names names' t = t;
berghofe@11519
   536
berghofe@11519
   537
fun thaw names names' (t $ u) =
berghofe@11519
   538
      thaw names names' t $ thaw names names' u
berghofe@11519
   539
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   540
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   541
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
berghofe@11519
   542
  | thaw names names' (Free (s, T)) = 
berghofe@11519
   543
      let val T' = thawT names' T
haftmann@17325
   544
      in case AList.lookup (op =) names s of
skalberg@15531
   545
          NONE => Free (s, T')
skalberg@15531
   546
        | SOME ixn => Var (ixn, T')
berghofe@11519
   547
      end
berghofe@11519
   548
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   549
  | thaw names names' t = t;
berghofe@11519
   550
berghofe@11519
   551
fun freeze_thaw_prf prf =
berghofe@11519
   552
  let
berghofe@11519
   553
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
wenzelm@20147
   554
      (fn t => fn (fs, Tfs, vs, Tvs) =>
berghofe@11519
   555
         (add_term_frees (t, fs), add_term_tfree_names (t, Tfs),
berghofe@11519
   556
          add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))
wenzelm@20147
   557
      (fn T => fn (fs, Tfs, vs, Tvs) =>
berghofe@11519
   558
         (fs, add_typ_tfree_names (T, Tfs),
berghofe@11519
   559
          vs, add_typ_ixns (Tvs, T)))
wenzelm@20147
   560
      prf ([], [], [], []);
berghofe@11519
   561
    val fs' = map (fst o dest_Free) fs;
berghofe@11519
   562
    val vs' = map (fst o dest_Var) vs;
wenzelm@20071
   563
    val names = vs' ~~ Name.variant_list fs' (map fst vs');
wenzelm@20071
   564
    val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
berghofe@11519
   565
    val rnames = map swap names;
berghofe@11519
   566
    val rnames' = map swap names';
berghofe@11519
   567
  in
berghofe@11519
   568
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   569
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   570
  end;
berghofe@11519
   571
berghofe@11519
   572
berghofe@11519
   573
(***** implication introduction *****)
berghofe@11519
   574
berghofe@11519
   575
fun implies_intr_proof h prf =
berghofe@11519
   576
  let
berghofe@11715
   577
    fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME
berghofe@11519
   578
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
berghofe@11519
   579
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
berghofe@11615
   580
      | abshyp i (prf % t) = abshyp i prf % t
berghofe@11715
   581
      | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2
berghofe@11715
   582
          handle SAME => prf1 %% abshyp i prf2)
berghofe@11715
   583
      | abshyp _ _ = raise SAME
berghofe@11715
   584
    and abshyph i prf = (abshyp i prf handle SAME => prf)
berghofe@11519
   585
  in
skalberg@15531
   586
    AbsP ("H", NONE (*h*), abshyph 0 prf)
berghofe@11519
   587
  end;
berghofe@11519
   588
berghofe@11519
   589
berghofe@11519
   590
(***** forall introduction *****)
berghofe@11519
   591
skalberg@15531
   592
fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
berghofe@11519
   593
berghofe@11519
   594
berghofe@11519
   595
(***** varify *****)
berghofe@11519
   596
berghofe@11519
   597
fun varify_proof t fixed prf =
berghofe@11519
   598
  let
wenzelm@19304
   599
    val fs = Term.fold_types (Term.fold_atyps
wenzelm@19304
   600
      (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
berghofe@11519
   601
    val ixns = add_term_tvar_ixns (t, []);
wenzelm@20071
   602
    val fmap = fs ~~ Name.variant_list (map #1 ixns) (map fst fs)
berghofe@11519
   603
    fun thaw (f as (a, S)) =
haftmann@17314
   604
      (case AList.lookup (op =) fmap f of
skalberg@15531
   605
        NONE => TFree f
skalberg@15531
   606
      | SOME b => TVar ((b, 0), S));
wenzelm@20548
   607
  in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf
berghofe@11519
   608
  end;
berghofe@11519
   609
berghofe@11519
   610
berghofe@11519
   611
local
berghofe@11519
   612
berghofe@11519
   613
fun new_name (ix, (pairs,used)) =
wenzelm@20071
   614
  let val v = Name.variant used (string_of_indexname ix)
berghofe@11519
   615
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   616
haftmann@17325
   617
fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
skalberg@15531
   618
    NONE => TVar (ix, sort)
skalberg@15531
   619
  | SOME name => TFree (name, sort));
berghofe@11519
   620
berghofe@11519
   621
in
berghofe@11519
   622
berghofe@11519
   623
fun freezeT t prf =
berghofe@11519
   624
  let
berghofe@11519
   625
    val used = it_term_types add_typ_tfree_names (t, [])
berghofe@11519
   626
    and tvars = map #1 (it_term_types add_typ_tvars (t, []));
skalberg@15574
   627
    val (alist, _) = foldr new_name ([], used) tvars;
berghofe@11519
   628
  in
berghofe@11519
   629
    (case alist of
berghofe@11519
   630
      [] => prf (*nothing to do!*)
berghofe@11519
   631
    | _ =>
berghofe@11519
   632
      let val frzT = map_type_tvar (freeze_one alist)
wenzelm@20548
   633
      in map_proof_terms (map_types frzT) frzT prf end)
berghofe@11519
   634
  end;
berghofe@11519
   635
berghofe@11519
   636
end;
berghofe@11519
   637
berghofe@11519
   638
berghofe@11519
   639
(***** rotate assumptions *****)
berghofe@11519
   640
berghofe@11519
   641
fun rotate_proof Bs Bi m prf =
berghofe@11519
   642
  let
berghofe@11519
   643
    val params = Term.strip_all_vars Bi;
berghofe@11519
   644
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   645
    val i = length asms;
berghofe@11519
   646
    val j = length Bs;
berghofe@11519
   647
  in
berghofe@11519
   648
    mk_AbsP (j+1, proof_combP (prf, map PBound
skalberg@15574
   649
      (j downto 1) @ [mk_Abst (mk_AbsP (i,
berghofe@11519
   650
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
skalberg@15574
   651
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m)))))) params]))
berghofe@11519
   652
  end;
berghofe@11519
   653
berghofe@11519
   654
berghofe@11519
   655
(***** permute premises *****)
berghofe@11519
   656
berghofe@11519
   657
fun permute_prems_prf prems j k prf =
berghofe@11519
   658
  let val n = length prems
berghofe@11519
   659
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   660
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   661
  end;
berghofe@11519
   662
berghofe@11519
   663
wenzelm@19908
   664
(***** generalization *****)
wenzelm@19908
   665
wenzelm@20000
   666
fun generalize (tfrees, frees) idx =
wenzelm@20000
   667
  map_proof_terms_option
wenzelm@20509
   668
    (TermSubst.generalize_option (tfrees, frees) idx)
wenzelm@20509
   669
    (TermSubst.generalizeT_option tfrees idx);
wenzelm@19908
   670
wenzelm@19908
   671
berghofe@11519
   672
(***** instantiation *****)
berghofe@11519
   673
wenzelm@20000
   674
fun instantiate (instT, inst) =
wenzelm@20000
   675
  map_proof_terms_option
wenzelm@20509
   676
    (TermSubst.instantiate_option (instT, map (apsnd remove_types) inst))
wenzelm@20509
   677
    (TermSubst.instantiateT_option instT);
berghofe@11519
   678
berghofe@11519
   679
berghofe@11519
   680
(***** lifting *****)
berghofe@11519
   681
berghofe@11519
   682
fun lift_proof Bi inc prop prf =
berghofe@11519
   683
  let
berghofe@11519
   684
    fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   685
berghofe@11715
   686
    fun lift' Us Ts (Abst (s, T, prf)) =
wenzelm@16880
   687
          (Abst (s, apsome' (same (Logic.incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf)
berghofe@11715
   688
           handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
berghofe@11715
   689
      | lift' Us Ts (AbsP (s, t, prf)) =
berghofe@11715
   690
          (AbsP (s, apsome' (same (lift'' Us Ts)) t, lifth' Us Ts prf)
berghofe@11715
   691
           handle SAME => AbsP (s, t, lift' Us Ts prf))
skalberg@15570
   692
      | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
berghofe@11715
   693
          handle SAME => prf % apsome' (same (lift'' Us Ts)) t)
berghofe@11715
   694
      | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
berghofe@11715
   695
          handle SAME => prf1 %% lift' Us Ts prf2)
berghofe@11715
   696
      | lift' _ _ (PThm (s, prf, prop, Ts)) =
wenzelm@16880
   697
          PThm (s, prf, prop, apsome' (same (map (Logic.incr_tvar inc))) Ts)
berghofe@11715
   698
      | lift' _ _ (PAxm (s, prop, Ts)) =
wenzelm@16880
   699
          PAxm (s, prop, apsome' (same (map (Logic.incr_tvar inc))) Ts)
berghofe@11715
   700
      | lift' _ _ _ = raise SAME
berghofe@11715
   701
    and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf);
berghofe@11519
   702
wenzelm@18030
   703
    val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
berghofe@11519
   704
    val k = length ps;
berghofe@11519
   705
berghofe@11519
   706
    fun mk_app (b, (i, j, prf)) = 
berghofe@11615
   707
          if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
berghofe@11519
   708
berghofe@11519
   709
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
wenzelm@20147
   710
            AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
berghofe@11519
   711
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 
wenzelm@20147
   712
            Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11715
   713
      | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
skalberg@15574
   714
            map (fn k => (#3 (foldr mk_app (i-1, j-1, PBound k) bs)))
berghofe@11519
   715
              (i + k - 1 downto i));
berghofe@11519
   716
  in
berghofe@11519
   717
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   718
  end;
berghofe@11519
   719
berghofe@11519
   720
berghofe@11519
   721
(***** proof by assumption *****)
berghofe@11519
   722
skalberg@15531
   723
fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", NONE (*A*), mk_asm_prf B (i+1))
skalberg@15531
   724
  | mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, NONE (*T*), mk_asm_prf t i)
berghofe@11519
   725
  | mk_asm_prf _ i = PBound i;
berghofe@11519
   726
berghofe@11519
   727
fun assumption_proof Bs Bi n prf =
berghofe@11519
   728
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@11519
   729
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi (~n)]));
berghofe@11519
   730
berghofe@11519
   731
berghofe@11519
   732
(***** Composition of object rule with proof state *****)
berghofe@11519
   733
berghofe@11519
   734
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
skalberg@15531
   735
      AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
berghofe@11519
   736
  | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
skalberg@15531
   737
      Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
berghofe@11519
   738
  | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
wenzelm@19304
   739
      map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
berghofe@11519
   740
wenzelm@18485
   741
fun bicompose_proof flatten Bs oldAs newAs A n rprf sprf =
berghofe@11519
   742
  let
berghofe@11519
   743
    val la = length newAs;
berghofe@11519
   744
    val lb = length Bs;
berghofe@11519
   745
  in
berghofe@11519
   746
    mk_AbsP (lb+la, proof_combP (sprf,
berghofe@11615
   747
      map PBound (lb + la - 1 downto la)) %%
wenzelm@18485
   748
        proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @
wenzelm@18485
   749
          map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
wenzelm@18485
   750
            (oldAs ~~ (la - 1 downto 0))))
berghofe@11519
   751
  end;
berghofe@11519
   752
berghofe@11519
   753
berghofe@11519
   754
(***** axioms for equality *****)
berghofe@11519
   755
wenzelm@14854
   756
val aT = TFree ("'a", []);
wenzelm@14854
   757
val bT = TFree ("'b", []);
berghofe@11519
   758
val x = Free ("x", aT);
berghofe@11519
   759
val y = Free ("y", aT);
berghofe@11519
   760
val z = Free ("z", aT);
berghofe@11519
   761
val A = Free ("A", propT);
berghofe@11519
   762
val B = Free ("B", propT);
berghofe@11519
   763
val f = Free ("f", aT --> bT);
berghofe@11519
   764
val g = Free ("g", aT --> bT);
berghofe@11519
   765
berghofe@11519
   766
local open Logic in
berghofe@11519
   767
berghofe@11519
   768
val equality_axms =
berghofe@11519
   769
  [("reflexive", mk_equals (x, x)),
berghofe@11519
   770
   ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
berghofe@11519
   771
   ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
berghofe@11519
   772
   ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
berghofe@11519
   773
   ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
berghofe@11519
   774
   ("abstract_rule", Logic.mk_implies
berghofe@11519
   775
      (all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),
berghofe@11519
   776
       equals (aT --> bT) $
berghofe@11519
   777
         Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),
berghofe@11519
   778
   ("combination", Logic.list_implies
berghofe@11519
   779
      ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],
berghofe@11519
   780
       Logic.mk_equals (f $ x, g $ y)))];
berghofe@11519
   781
berghofe@11519
   782
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   783
  equal_elim_axm, abstract_rule_axm, combination_axm] =
skalberg@15531
   784
    map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, NONE)) equality_axms;
berghofe@11519
   785
berghofe@11519
   786
end;
berghofe@11519
   787
skalberg@15531
   788
val reflexive = reflexive_axm % NONE;
berghofe@11519
   789
berghofe@11615
   790
fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) % _) = prf
skalberg@15531
   791
  | symmetric prf = symmetric_axm % NONE % NONE %% prf;
berghofe@11519
   792
berghofe@11615
   793
fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) % _) prf2 = prf2
berghofe@11615
   794
  | transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) % _) = prf1
berghofe@11519
   795
  | transitive u (Type ("prop", [])) prf1 prf2 =
skalberg@15531
   796
      transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
berghofe@11519
   797
  | transitive u T prf1 prf2 =
skalberg@15531
   798
      transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
berghofe@11519
   799
berghofe@11519
   800
fun abstract_rule x a prf =
skalberg@15531
   801
  abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
berghofe@11519
   802
berghofe@11615
   803
fun check_comb (PAxm ("ProtoPure.combination", _, _) % f % g % _ % _ %% prf %% _) =
wenzelm@19502
   804
      is_some f orelse check_comb prf
berghofe@11615
   805
  | check_comb (PAxm ("ProtoPure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
berghofe@11519
   806
      check_comb prf1 andalso check_comb prf2
berghofe@11615
   807
  | check_comb (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
berghofe@11519
   808
  | check_comb _ = false;
berghofe@11519
   809
berghofe@11519
   810
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   811
  let
berghofe@11519
   812
    val f = Envir.beta_norm f;
berghofe@11519
   813
    val g = Envir.beta_norm g;
berghofe@11519
   814
    val prf =  if check_comb prf1 then
skalberg@15531
   815
        combination_axm % NONE % NONE
berghofe@11519
   816
      else (case prf1 of
berghofe@11615
   817
          PAxm ("ProtoPure.reflexive", _, _) % _ =>
skalberg@15531
   818
            combination_axm %> remove_types f % NONE
berghofe@11615
   819
        | _ => combination_axm %> remove_types f %> remove_types g)
berghofe@11519
   820
  in
berghofe@11519
   821
    (case T of
berghofe@11615
   822
       Type ("fun", _) => prf %
berghofe@11519
   823
         (case head_of f of
skalberg@15531
   824
            Abs _ => SOME (remove_types t)
skalberg@15531
   825
          | Var _ => SOME (remove_types t)
skalberg@15531
   826
          | _ => NONE) %
berghofe@11519
   827
         (case head_of g of
skalberg@15531
   828
            Abs _ => SOME (remove_types u)
skalberg@15531
   829
          | Var _ => SOME (remove_types u)
skalberg@15531
   830
          | _ => NONE) %% prf1 %% prf2
skalberg@15531
   831
     | _ => prf % NONE % NONE %% prf1 %% prf2)
berghofe@11519
   832
  end;
berghofe@11519
   833
berghofe@11519
   834
fun equal_intr A B prf1 prf2 =
berghofe@11615
   835
  equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   836
berghofe@11519
   837
fun equal_elim A B prf1 prf2 =
berghofe@11615
   838
  equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   839
berghofe@11519
   840
berghofe@11519
   841
(***** axioms and theorems *****)
berghofe@11519
   842
wenzelm@17492
   843
fun vars_of t = rev (fold_aterms (fn v as Var _ => insert (op =) v | _ => I) t []);
berghofe@11519
   844
berghofe@11519
   845
fun test_args _ [] = true
berghofe@11519
   846
  | test_args is (Bound i :: ts) =
wenzelm@17492
   847
      not (member (op =) is i) andalso test_args (i :: is) ts
berghofe@11519
   848
  | test_args _ _ = false;
berghofe@11519
   849
berghofe@11519
   850
fun is_fun (Type ("fun", _)) = true
berghofe@11519
   851
  | is_fun (TVar _) = true
berghofe@11519
   852
  | is_fun _ = false;
berghofe@11519
   853
berghofe@11519
   854
fun add_funvars Ts (vs, t) =
berghofe@11519
   855
  if is_fun (fastype_of1 (Ts, t)) then
wenzelm@19482
   856
    vs union map_filter (fn Var (ixn, T) =>
skalberg@15531
   857
      if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t)
berghofe@11519
   858
  else vs;
berghofe@11519
   859
berghofe@11519
   860
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
berghofe@11519
   861
      add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
berghofe@11519
   862
  | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
berghofe@11519
   863
      add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
berghofe@12041
   864
  | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
berghofe@12041
   865
  | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
berghofe@12041
   866
and add_npvars' Ts (vs, t) = (case strip_comb t of
berghofe@11519
   867
    (Var (ixn, _), ts) => if test_args [] ts then vs
haftmann@17314
   868
      else Library.foldl (add_npvars' Ts)
haftmann@17314
   869
        (AList.update (op =) (ixn,
haftmann@17314
   870
          Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
skalberg@15570
   871
  | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
skalberg@15570
   872
  | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
berghofe@11519
   873
berghofe@11519
   874
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
berghofe@11519
   875
  | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
berghofe@11519
   876
  | prop_vars t = (case strip_comb t of
berghofe@11519
   877
      (Var (ixn, _), _) => [ixn] | _ => []);
berghofe@11519
   878
berghofe@11519
   879
fun is_proj t =
berghofe@11519
   880
  let
berghofe@11519
   881
    fun is_p i t = (case strip_comb t of
berghofe@11519
   882
        (Bound j, []) => false
berghofe@11519
   883
      | (Bound j, ts) => j >= i orelse exists (is_p i) ts
berghofe@11519
   884
      | (Abs (_, _, u), _) => is_p (i+1) u
berghofe@11519
   885
      | (_, ts) => exists (is_p i) ts)
berghofe@11519
   886
  in (case strip_abs_body t of
berghofe@11519
   887
        Bound _ => true
berghofe@11519
   888
      | t' => is_p 0 t')
berghofe@11519
   889
  end;
berghofe@11519
   890
berghofe@11519
   891
fun needed_vars prop = 
haftmann@20853
   892
  Library.foldl (op union)
haftmann@20853
   893
    ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))) union
berghofe@11519
   894
  prop_vars prop;
berghofe@11519
   895
berghofe@11519
   896
fun gen_axm_proof c name prop =
berghofe@11519
   897
  let
berghofe@11519
   898
    val nvs = needed_vars prop;
berghofe@11519
   899
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
   900
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
wenzelm@16983
   901
      map SOME (sort Term.term_ord (term_frees prop));
berghofe@11519
   902
  in
skalberg@15531
   903
    proof_combt' (c (name, prop, NONE), args)
berghofe@11519
   904
  end;
berghofe@11519
   905
berghofe@11519
   906
val axm_proof = gen_axm_proof PAxm;
berghofe@17017
   907
berghofe@17017
   908
val dummy = Const (Term.dummy_patternN, dummyT);
berghofe@17017
   909
berghofe@17017
   910
fun oracle_proof name prop =
berghofe@17017
   911
  if !proofs = 0 then Oracle (name, dummy, NONE)
berghofe@17017
   912
  else gen_axm_proof Oracle name prop;
berghofe@11519
   913
wenzelm@17492
   914
fun shrink_proof thy =
wenzelm@17492
   915
  let
wenzelm@17492
   916
    val compress_typ = Compress.typ thy;
wenzelm@17492
   917
    val compress_term = Compress.term thy;
wenzelm@17492
   918
  
wenzelm@17492
   919
    fun shrink ls lev (prf as Abst (a, T, body)) =
wenzelm@17492
   920
          let val (b, is, ch, body') = shrink ls (lev+1) body
wenzelm@17492
   921
          in (b, is, ch, if ch then Abst (a, Option.map compress_typ T, body') else prf) end
wenzelm@17492
   922
      | shrink ls lev (prf as AbsP (a, t, body)) =
wenzelm@17492
   923
          let val (b, is, ch, body') = shrink (lev::ls) lev body
wenzelm@19482
   924
          in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
wenzelm@17492
   925
            ch, if ch then AbsP (a, Option.map compress_term t, body') else prf)
wenzelm@17492
   926
          end
wenzelm@17492
   927
      | shrink ls lev prf =
wenzelm@17492
   928
          let val (is, ch, _, prf') = shrink' ls lev [] [] prf
wenzelm@17492
   929
          in (false, is, ch, prf') end
wenzelm@17492
   930
    and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
wenzelm@17492
   931
          let
wenzelm@17492
   932
            val p as (_, is', ch', prf') = shrink ls lev prf2;
wenzelm@17492
   933
            val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
wenzelm@17492
   934
          in (is union is', ch orelse ch', ts',
wenzelm@17492
   935
              if ch orelse ch' then prf'' %% prf' else prf)
wenzelm@17492
   936
          end
wenzelm@17492
   937
      | shrink' ls lev ts prfs (prf as prf1 % t) =
wenzelm@17492
   938
          let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
wenzelm@17492
   939
          in (is, ch orelse ch', ts',
wenzelm@17492
   940
              if ch orelse ch' then prf' % Option.map compress_term t' else prf) end
wenzelm@17492
   941
      | shrink' ls lev ts prfs (prf as PBound i) =
wenzelm@17492
   942
          (if exists (fn SOME (Bound j) => lev-j <= List.nth (ls, i) | _ => true) ts
haftmann@18928
   943
             orelse has_duplicates (op =)
haftmann@18928
   944
               (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
wenzelm@17492
   945
             orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
wenzelm@17492
   946
      | shrink' ls lev ts prfs (Hyp t) = ([], false, map (pair false) ts, Hyp (compress_term t))
wenzelm@17492
   947
      | shrink' ls lev ts prfs (prf as MinProof _) =
wenzelm@17492
   948
          ([], false, map (pair false) ts, prf)
wenzelm@17492
   949
      | shrink' ls lev ts prfs prf =
wenzelm@17492
   950
          let
wenzelm@17492
   951
            val prop = (case prf of PThm (_, _, prop, _) => prop | PAxm (_, prop, _) => prop
wenzelm@17492
   952
              | Oracle (_, prop, _) => prop | _ => error "shrink: proof not in normal form");
wenzelm@17492
   953
            val vs = vars_of prop;
wenzelm@19012
   954
            val (ts', ts'') = chop (length vs) ts;
wenzelm@17492
   955
            val insts = Library.take (length ts', map (fst o dest_Var) vs) ~~ ts';
wenzelm@17492
   956
            val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
wenzelm@17492
   957
              insert (op =) ixn (case AList.lookup (op =) insts ixn of
wenzelm@17492
   958
                  SOME (SOME t) => if is_proj t then ixns union ixns' else ixns'
wenzelm@17492
   959
                | _ => ixns union ixns'))
wenzelm@17492
   960
                  (needed prop ts'' prfs, add_npvars false true [] ([], prop));
wenzelm@17492
   961
            val insts' = map
wenzelm@17492
   962
              (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
wenzelm@17492
   963
                | (_, x) => (false, x)) insts
wenzelm@17492
   964
          in ([], false, insts' @ map (pair false) ts'', prf) end
wenzelm@17492
   965
    and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
wenzelm@17492
   966
          (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
wenzelm@17492
   967
      | needed (Var (ixn, _)) (_::_) _ = [ixn]
wenzelm@17492
   968
      | needed _ _ _ = [];
wenzelm@17492
   969
  in shrink end;
berghofe@11519
   970
berghofe@11519
   971
berghofe@11519
   972
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
   973
berghofe@11519
   974
exception PMatch;
berghofe@11519
   975
berghofe@11519
   976
(** see pattern.ML **)
berghofe@11519
   977
skalberg@15570
   978
fun flt (i: int) = List.filter (fn n => n < i);
berghofe@12279
   979
berghofe@12279
   980
fun fomatch Ts tymatch j =
berghofe@11519
   981
  let
berghofe@11519
   982
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
   983
        (Var (ixn, T), t)  =>
berghofe@12279
   984
          if j>0 andalso not (null (flt j (loose_bnos t)))
berghofe@12279
   985
          then raise PMatch
berghofe@12279
   986
          else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
berghofe@12279
   987
            (ixn, t) :: insts)
berghofe@11519
   988
      | (Free (a, T), Free (b, U)) =>
wenzelm@20147
   989
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   990
      | (Const (a, T), Const (b, U))  =>
wenzelm@20147
   991
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   992
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@12279
   993
      | (Bound i, Bound j) => if i=j then instsp else raise PMatch
berghofe@11519
   994
      | _ => raise PMatch
berghofe@11519
   995
  in mtch end;
berghofe@11519
   996
berghofe@12279
   997
fun match_proof Ts tymatch =
berghofe@11519
   998
  let
skalberg@15531
   999
    fun optmatch _ inst (NONE, _) = inst
skalberg@15531
  1000
      | optmatch _ _ (SOME _, NONE) = raise PMatch
skalberg@15531
  1001
      | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
berghofe@12279
  1002
berghofe@12279
  1003
    fun matcht Ts j (pinst, tinst) (t, u) =
berghofe@12279
  1004
      (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
berghofe@12279
  1005
    fun matchT (pinst, (tyinsts, insts)) p =
berghofe@12279
  1006
      (pinst, (tymatch (tyinsts, K p), insts));
skalberg@15570
  1007
    fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
berghofe@12279
  1008
berghofe@12279
  1009
    fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
berghofe@12279
  1010
          if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
berghofe@12279
  1011
          else (case apfst (flt i) (apsnd (flt j)
berghofe@12279
  1012
                  (prf_add_loose_bnos 0 0 prf ([], []))) of
berghofe@12279
  1013
              ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1014
            | ([], _) => if j = 0 then
berghofe@12279
  1015
                   ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1016
                 else raise PMatch
berghofe@12279
  1017
            | _ => raise PMatch)
berghofe@12279
  1018
      | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
berghofe@12279
  1019
          optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
berghofe@12279
  1020
      | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
berghofe@12279
  1021
          mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
berghofe@12279
  1022
      | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
wenzelm@18485
  1023
          mtch (the_default dummyT opU :: Ts) i (j+1)
berghofe@12279
  1024
            (optmatch matchT inst (opT, opU)) (prf1, prf2)
berghofe@12279
  1025
      | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
wenzelm@18485
  1026
          mtch (the_default dummyT opU :: Ts) i (j+1) inst
berghofe@12279
  1027
            (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
berghofe@12279
  1028
      | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
berghofe@12279
  1029
          mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
berghofe@12279
  1030
      | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
berghofe@12279
  1031
          mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
berghofe@12279
  1032
      | mtch Ts i j inst (PThm ((name1, _), _, prop1, opTs),
berghofe@12279
  1033
            PThm ((name2, _), _, prop2, opUs)) =
berghofe@11519
  1034
          if name1=name2 andalso prop1=prop2 then
berghofe@12279
  1035
            optmatch matchTs inst (opTs, opUs)
berghofe@11519
  1036
          else raise PMatch
berghofe@12279
  1037
      | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
berghofe@12279
  1038
          if s1=s2 then optmatch matchTs inst (opTs, opUs)
berghofe@11519
  1039
          else raise PMatch
berghofe@12279
  1040
      | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
berghofe@12279
  1041
      | mtch _ _ _ _ _ = raise PMatch
berghofe@12279
  1042
  in mtch Ts 0 0 end;
berghofe@11519
  1043
berghofe@11519
  1044
fun prf_subst (pinst, (tyinsts, insts)) =
berghofe@11519
  1045
  let
berghofe@15797
  1046
    val substT = Envir.typ_subst_TVars tyinsts;
berghofe@11519
  1047
haftmann@17325
  1048
    fun subst' lev (t as Var (ixn, _)) = (case AList.lookup (op =) insts ixn of
skalberg@15531
  1049
          NONE => t
skalberg@15531
  1050
        | SOME u => incr_boundvars lev u)
berghofe@11519
  1051
      | subst' lev (Const (s, T)) = Const (s, substT T)
berghofe@11519
  1052
      | subst' lev (Free (s, T)) = Free (s, substT T)
berghofe@11519
  1053
      | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
berghofe@11519
  1054
      | subst' lev (f $ t) = subst' lev f $ subst' lev t
berghofe@11519
  1055
      | subst' _ t = t;
berghofe@11519
  1056
berghofe@11519
  1057
    fun subst plev tlev (AbsP (a, t, body)) =
skalberg@15570
  1058
          AbsP (a, Option.map (subst' tlev) t, subst (plev+1) tlev body)
berghofe@11519
  1059
      | subst plev tlev (Abst (a, T, body)) =
skalberg@15570
  1060
          Abst (a, Option.map substT T, subst plev (tlev+1) body)
berghofe@11615
  1061
      | subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf'
skalberg@15570
  1062
      | subst plev tlev (prf % t) = subst plev tlev prf % Option.map (subst' tlev) t
haftmann@17325
  1063
      | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case AList.lookup (op =) pinst ixn of
skalberg@15531
  1064
          NONE => prf
skalberg@15531
  1065
        | SOME prf' => incr_pboundvars plev tlev prf')
berghofe@11519
  1066
      | subst _ _ (PThm (id, prf, prop, Ts)) =
skalberg@15570
  1067
          PThm (id, prf, prop, Option.map (map substT) Ts)
berghofe@11519
  1068
      | subst _ _ (PAxm (id, prop, Ts)) =
skalberg@15570
  1069
          PAxm (id, prop, Option.map (map substT) Ts)
berghofe@11519
  1070
      | subst _ _ t = t
berghofe@11519
  1071
  in subst 0 0 end;
berghofe@11519
  1072
berghofe@12871
  1073
(*A fast unification filter: true unless the two terms cannot be unified. 
berghofe@12871
  1074
  Terms must be NORMAL.  Treats all Vars as distinct. *)
berghofe@12871
  1075
fun could_unify prf1 prf2 =
berghofe@12871
  1076
  let
berghofe@12871
  1077
    fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
berghofe@12871
  1078
          could_unify prf2 prf2' andalso matchrands prf1 prf1'
skalberg@15531
  1079
      | matchrands (prf % SOME t) (prf' % SOME t') =
berghofe@12871
  1080
          Term.could_unify (t, t') andalso matchrands prf prf'
berghofe@12871
  1081
      | matchrands (prf % _) (prf' % _) = matchrands prf prf'
berghofe@12871
  1082
      | matchrands _ _ = true
berghofe@12871
  1083
berghofe@12871
  1084
    fun head_of (prf %% _) = head_of prf
berghofe@12871
  1085
      | head_of (prf % _) = head_of prf
berghofe@12871
  1086
      | head_of prf = prf
berghofe@12871
  1087
berghofe@12871
  1088
  in case (head_of prf1, head_of prf2) of
berghofe@12871
  1089
        (_, Hyp (Var _)) => true
berghofe@12871
  1090
      | (Hyp (Var _), _) => true
berghofe@12871
  1091
      | (PThm ((a, _), _, propa, _), PThm ((b, _), _, propb, _)) =>
berghofe@12871
  1092
          a = b andalso propa = propb andalso matchrands prf1 prf2
berghofe@12871
  1093
      | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
berghofe@12871
  1094
      | (PBound i, PBound j) =>  i = j andalso matchrands prf1 prf2
berghofe@12871
  1095
      | (AbsP _, _) =>  true   (*because of possible eta equality*)
berghofe@12871
  1096
      | (Abst _, _) =>  true
berghofe@12871
  1097
      | (_, AbsP _) =>  true
berghofe@12871
  1098
      | (_, Abst _) =>  true
berghofe@12871
  1099
      | _ => false
berghofe@12871
  1100
  end;
berghofe@12871
  1101
berghofe@11519
  1102
(**** rewriting on proof terms ****)
berghofe@11519
  1103
berghofe@13102
  1104
val skel0 = PBound 0;
berghofe@13102
  1105
berghofe@12279
  1106
fun rewrite_prf tymatch (rules, procs) prf =
berghofe@11519
  1107
  let
skalberg@15531
  1108
    fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, skel0)
skalberg@15531
  1109
      | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, skel0)
berghofe@11519
  1110
      | rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of
skalberg@15531
  1111
          SOME prf' => SOME (prf', skel0)
skalberg@15531
  1112
        | NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
berghofe@13102
  1113
            (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
skalberg@15570
  1114
               handle PMatch => NONE) (List.filter (could_unify prf o fst) rules));
berghofe@11519
  1115
berghofe@11615
  1116
    fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
berghofe@11519
  1117
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
  1118
          else
berghofe@11519
  1119
            let val prf'' = incr_pboundvars (~1) 0 prf'
wenzelm@19502
  1120
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
skalberg@15531
  1121
      | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
berghofe@11519
  1122
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
  1123
          else
berghofe@11519
  1124
            let val prf'' = incr_pboundvars 0 (~1) prf'
wenzelm@19502
  1125
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
berghofe@11519
  1126
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
  1127
skalberg@15531
  1128
    fun rew1 _ (Hyp (Var _)) _ = NONE
berghofe@13102
  1129
      | rew1 Ts skel prf = (case rew2 Ts skel prf of
skalberg@15531
  1130
          SOME prf1 => (case rew0 Ts prf1 of
wenzelm@19502
  1131
              SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts skel' prf2))
skalberg@15531
  1132
            | NONE => SOME prf1)
skalberg@15531
  1133
        | NONE => (case rew0 Ts prf of
wenzelm@19502
  1134
              SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts skel' prf1))
skalberg@15531
  1135
            | NONE => NONE))
berghofe@11519
  1136
skalberg@15531
  1137
    and rew2 Ts skel (prf % SOME t) = (case prf of
berghofe@11519
  1138
            Abst (_, _, body) =>
berghofe@11519
  1139
              let val prf' = prf_subst_bounds [t] body
wenzelm@19502
  1140
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1141
          | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf of
skalberg@15531
  1142
              SOME prf' => SOME (prf' % SOME t)
skalberg@15531
  1143
            | NONE => NONE))
skalberg@15570
  1144
      | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
berghofe@13102
  1145
          (rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf)
berghofe@13102
  1146
      | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
berghofe@11519
  1147
            AbsP (_, _, body) =>
berghofe@11519
  1148
              let val prf' = prf_subst_pbounds [prf2] body
wenzelm@19502
  1149
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1150
          | _ =>
berghofe@13102
  1151
            let val (skel1, skel2) = (case skel of
berghofe@13102
  1152
                skel1 %% skel2 => (skel1, skel2)
berghofe@13102
  1153
              | _ => (skel0, skel0))
berghofe@13102
  1154
            in case rew1 Ts skel1 prf1 of
skalberg@15531
  1155
                SOME prf1' => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1156
                    SOME prf2' => SOME (prf1' %% prf2')
skalberg@15531
  1157
                  | NONE => SOME (prf1' %% prf2))
skalberg@15531
  1158
              | NONE => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1159
                    SOME prf2' => SOME (prf1 %% prf2')
skalberg@15531
  1160
                  | NONE => NONE)
berghofe@13102
  1161
            end)
wenzelm@19502
  1162
      | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts)
berghofe@13102
  1163
              (case skel of Abst (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1164
            SOME prf' => SOME (Abst (s, T, prf'))
skalberg@15531
  1165
          | NONE => NONE)
berghofe@13102
  1166
      | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
berghofe@13102
  1167
              (case skel of AbsP (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1168
            SOME prf' => SOME (AbsP (s, t, prf'))
skalberg@15531
  1169
          | NONE => NONE)
skalberg@15531
  1170
      | rew2 _ _ _ = NONE
berghofe@11519
  1171
wenzelm@19502
  1172
  in the_default prf (rew1 [] skel0 prf) end;
berghofe@11519
  1173
wenzelm@17203
  1174
fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
wenzelm@17203
  1175
  Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
  1176
berghofe@11715
  1177
fun rewrite_proof_notypes rews = rewrite_prf fst rews;
berghofe@11615
  1178
wenzelm@16940
  1179
berghofe@11519
  1180
(**** theory data ****)
berghofe@11519
  1181
wenzelm@16458
  1182
structure ProofData = TheoryDataFun
wenzelm@16458
  1183
(struct
berghofe@11519
  1184
  val name = "Pure/proof";
berghofe@11519
  1185
  type T = ((proof * proof) list *
berghofe@12233
  1186
    (string * (typ list -> proof -> proof option)) list);
berghofe@11519
  1187
berghofe@12233
  1188
  val empty = ([], []);
berghofe@12233
  1189
  val copy = I;
wenzelm@16458
  1190
  val extend = I;
wenzelm@16458
  1191
  fun merge _ ((rules1, procs1), (rules2, procs2)) =
wenzelm@12293
  1192
    (merge_lists rules1 rules2, merge_alists procs1 procs2);
berghofe@11519
  1193
  fun print _ _ = ();
wenzelm@16458
  1194
end);
berghofe@11519
  1195
wenzelm@16536
  1196
val init_data = ProofData.init;
berghofe@11519
  1197
berghofe@12233
  1198
fun add_prf_rrules rs thy =
berghofe@11519
  1199
  let val r = ProofData.get thy
berghofe@12233
  1200
  in ProofData.put (rs @ fst r, snd r) thy end;
berghofe@11519
  1201
berghofe@12233
  1202
fun add_prf_rprocs ps thy =
berghofe@11519
  1203
  let val r = ProofData.get thy
berghofe@12233
  1204
  in ProofData.put (fst r, ps @ snd r) thy end;
berghofe@11519
  1205
wenzelm@16458
  1206
fun thm_proof thy (name, tags) hyps prop prf =
berghofe@11519
  1207
  let
wenzelm@12923
  1208
    val prop = Logic.list_implies (hyps, prop);
berghofe@11519
  1209
    val nvs = needed_vars prop;
berghofe@11519
  1210
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
  1211
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
wenzelm@16983
  1212
      map SOME (sort Term.term_ord (term_frees prop));
wenzelm@11543
  1213
    val opt_prf = if ! proofs = 2 then
wenzelm@17492
  1214
        #4 (shrink_proof thy [] 0 (rewrite_prf fst (ProofData.get thy)
skalberg@15574
  1215
          (foldr (uncurry implies_intr_proof) prf hyps)))
berghofe@17017
  1216
      else MinProof (mk_min_proof prf ([], [], []));
berghofe@12233
  1217
    val head = (case strip_combt (fst (strip_combP prf)) of
skalberg@15531
  1218
        (PThm ((old_name, _), prf', prop', NONE), args') =>
berghofe@11519
  1219
          if (old_name="" orelse old_name=name) andalso
berghofe@11519
  1220
             prop = prop' andalso args = args' then
skalberg@15531
  1221
            PThm ((name, tags), prf', prop, NONE)
berghofe@11519
  1222
          else
skalberg@15531
  1223
            PThm ((name, tags), opt_prf, prop, NONE)
skalberg@15531
  1224
      | _ => PThm ((name, tags), opt_prf, prop, NONE))
berghofe@11519
  1225
  in
wenzelm@12923
  1226
    proof_combP (proof_combt' (head, args), map Hyp hyps)
berghofe@11519
  1227
  end;
berghofe@11519
  1228
wenzelm@12923
  1229
fun get_name_tags hyps prop prf =
wenzelm@12923
  1230
  let val prop = Logic.list_implies (hyps, prop) in
wenzelm@12923
  1231
    (case strip_combt (fst (strip_combP prf)) of
berghofe@11519
  1232
      (PThm ((name, tags), _, prop', _), _) =>
berghofe@11519
  1233
        if prop=prop' then (name, tags) else ("", [])
berghofe@11519
  1234
    | (PAxm (name, prop', _), _) =>
berghofe@11519
  1235
        if prop=prop' then (name, []) else ("", [])
wenzelm@12923
  1236
    | _ => ("", []))
wenzelm@12923
  1237
  end;
berghofe@11519
  1238
berghofe@11519
  1239
end;
berghofe@11519
  1240
berghofe@11519
  1241
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
berghofe@11519
  1242
open BasicProofterm;