src/Pure/proofterm.ML
author wenzelm
Tue Dec 30 21:49:09 2008 +0100 (2008-12-30)
changeset 29261 7ee78cc8ef2c
parent 28971 300ec36a19af
child 29265 5b4247055bd7
permissions -rw-r--r--
freeze_thaw: canonical Term.add_XXX operations;
varify: regular name context;
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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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     MinProof
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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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   | PAxm of string * term * typ list option
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   | Oracle of string * term * typ list option
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   | Promise of serial * term * typ list
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   | PThm of serial * ((string * term * typ list option) * proof_body lazy)
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  and proof_body = PBody of
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    {oracles: (string * term) OrdList.T,
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     thms: (serial * (string * term * proof_body lazy)) OrdList.T,
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     proof: proof}
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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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  type oracle = string * term
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  type pthm = serial * (string * term * proof_body lazy)
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  val force_body: proof_body lazy ->
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    {oracles: oracle OrdList.T, thms: pthm OrdList.T, proof: proof}
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  val force_proof: proof_body lazy -> proof
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  val proof_of: proof_body -> proof
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  val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
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  val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
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  val oracle_ord: oracle * oracle -> order
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  val thm_ord: pthm * pthm -> order
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  val make_proof_body: proof -> proof_body
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  val merge_oracles: oracle OrdList.T -> oracle OrdList.T -> oracle OrdList.T
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  val make_oracles: proof -> oracle OrdList.T
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  val merge_thms: pthm OrdList.T -> pthm OrdList.T -> pthm OrdList.T
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  val make_thms: proof -> pthm OrdList.T
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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_body -> proof_body
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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 -> 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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  (** 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 -> 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 promise_proof: theory -> serial -> term -> proof
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  val fulfill_proof: theory -> (serial * proof) list -> proof_body -> proof_body
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  val thm_proof: theory -> string -> term list -> term ->
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    (serial * proof) list lazy -> proof_body -> pthm * proof
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  val get_name: term list -> term -> proof -> string
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  (** rewriting on proof terms **)
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  val add_prf_rrule: proof * proof -> theory -> theory
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  val add_prf_rproc: (typ list -> proof -> proof option) -> theory -> theory
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  val rewrite_proof: theory -> (proof * proof) list *
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    (typ list -> proof -> proof option) list -> proof -> proof
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  val rewrite_proof_notypes: (proof * proof) list *
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    (typ list -> proof -> proof option) list -> proof -> proof
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  val rew_proof: theory -> proof -> proof
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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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datatype proof =
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   MinProof
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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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 | PAxm of string * term * typ list option
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 | Oracle of string * term * typ list option
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 | Promise of serial * term * typ list
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 | PThm of serial * ((string * term * typ list option) * proof_body lazy)
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and proof_body = PBody of
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  {oracles: (string * term) OrdList.T,
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   thms: (serial * (string * term * proof_body lazy)) OrdList.T,
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   proof: proof};
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type oracle = string * term;
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type pthm = serial * (string * term * proof_body lazy);
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val force_body = Lazy.force #> (fn PBody args => args);
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val force_proof = #proof o force_body;
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fun proof_of (PBody {proof, ...}) = proof;
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(***** proof atoms *****)
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fun fold_body_thms f =
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  let
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    fun app (PBody {thms, ...}) = thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
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      if Inttab.defined seen i then (x, seen)
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      else
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        let
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          val body' = Lazy.force body;
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          val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
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        in (f (name, prop, body') x', seen') end);
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  in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
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fun fold_proof_atoms all f =
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  let
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    fun app (Abst (_, _, prf)) = app prf
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      | app (AbsP (_, _, prf)) = app prf
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      | app (prf % _) = app prf
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      | app (prf1 %% prf2) = app prf1 #> app prf2
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      | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
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          if Inttab.defined seen i then (x, seen)
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          else
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            let val (x', seen') =
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              (if all then app (force_proof body) else I) (x, Inttab.update (i, ()) seen)
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            in (f prf x', seen') end)
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      | app prf = (fn (x, seen) => (f prf x, seen));
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  in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
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(* proof body *)
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val oracle_ord = prod_ord fast_string_ord Term.fast_term_ord;
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fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
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fun make_body prf =
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  let
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    val (oracles, thms) = fold_proof_atoms false
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      (fn Oracle (s, prop, _) => apfst (cons (s, prop))
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        | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
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        | _ => I) [prf] ([], []);
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  in (OrdList.make oracle_ord oracles, OrdList.make thm_ord thms) end;
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fun make_proof_body prf =
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  let val (oracles, thms) = make_body prf
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  in PBody {oracles = oracles, thms = thms, proof = prf} end;
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val make_oracles = #1 o make_body;
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val make_thms = #2 o make_body;
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val merge_oracles = OrdList.union oracle_ord;
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val merge_thms = OrdList.union thm_ord;
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fun merge_body (oracles1, thms1) (oracles2, thms2) =
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  (merge_oracles oracles1 oracles2, merge_thms thms1 thms2);
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(***** proof objects with different levels of detail *****)
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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 (body as PBody {proof, ...}) =
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  (case strip_combt (fst (strip_combP proof)) of
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    (PThm (_, (_, body')), _) => Lazy.force body'
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  | _ => body);
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val mk_Abst = fold_rev (fn (s, T:typ) => fn 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 (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (map_typs Ts))
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      | mapp (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (map_typs Ts))
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      | mapp (Promise (i, prop, Ts)) = Promise (i, prop, map_typs Ts)
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      | mapp (PThm (i, ((a, prop, SOME Ts), body))) =
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          PThm (i, ((a, prop, SOME (map_typs Ts)), body))
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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 eq f x =
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  let val x' = f x
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  in if eq (x, x') then raise SAME else x' end;
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fun map_proof_terms f g =
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  map_proof_terms_option
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   (fn t => SOME (same (op =) f t) handle SAME => NONE)
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   (fn T => SOME (same (op =) g T) handle SAME => NONE);
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fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
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  | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
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  | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
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  | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
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  | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
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  | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
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  | fold_proof_terms f g (prf1 %% prf2) =
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      fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
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  | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
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  | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
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  | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
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  | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
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  | fold_proof_terms _ _ _ = I;
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fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ 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 (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 _ = 1;
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fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
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  | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
wenzelm@28828
   308
  | change_type opTs (Promise _) = error "change_type: unexpected promise"
wenzelm@28803
   309
  | change_type opTs (PThm (i, ((name, prop, _), body))) = PThm (i, ((name, prop, opTs), body))
berghofe@12907
   310
  | change_type _ prf = prf;
berghofe@12907
   311
berghofe@11519
   312
berghofe@11519
   313
(***** utilities *****)
berghofe@11519
   314
berghofe@11519
   315
fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
berghofe@11519
   316
  | strip_abs _ t = t;
berghofe@11519
   317
skalberg@15570
   318
fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
berghofe@11519
   319
berghofe@11519
   320
wenzelm@21646
   321
(*Abstraction of a proof term over its occurrences of v,
berghofe@11519
   322
    which must contain no loose bound variables.
berghofe@11519
   323
  The resulting proof term is ready to become the body of an Abst.*)
berghofe@11519
   324
berghofe@11519
   325
fun prf_abstract_over v =
berghofe@11519
   326
  let
berghofe@11715
   327
    fun abst' lev u = if v aconv u then Bound lev else
berghofe@11715
   328
      (case u of
berghofe@11715
   329
         Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
berghofe@11715
   330
       | f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t)
berghofe@11715
   331
       | _ => raise SAME)
berghofe@11715
   332
    and absth' lev t = (abst' lev t handle SAME => t);
berghofe@11519
   333
berghofe@11715
   334
    fun abst lev (AbsP (a, t, prf)) =
berghofe@11715
   335
          (AbsP (a, apsome' (abst' lev) t, absth lev prf)
berghofe@11715
   336
           handle SAME => AbsP (a, t, abst lev prf))
berghofe@11715
   337
      | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
berghofe@11715
   338
      | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
berghofe@11715
   339
          handle SAME => prf1 %% abst lev prf2)
skalberg@15570
   340
      | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
berghofe@11715
   341
          handle SAME => prf % apsome' (abst' lev) t)
berghofe@11715
   342
      | abst _ _ = raise SAME
berghofe@11715
   343
    and absth lev prf = (abst lev prf handle SAME => prf)
berghofe@11519
   344
berghofe@11715
   345
  in absth 0 end;
berghofe@11519
   346
berghofe@11519
   347
berghofe@11519
   348
(*increments a proof term's non-local bound variables
berghofe@11519
   349
  required when moving a proof term within abstractions
berghofe@11519
   350
     inc is  increment for bound variables
berghofe@11519
   351
     lev is  level at which a bound variable is considered 'loose'*)
berghofe@11519
   352
berghofe@11519
   353
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
berghofe@11519
   354
berghofe@11715
   355
fun prf_incr_bv' incP inct Plev tlev (PBound i) =
wenzelm@21646
   356
      if i >= Plev then PBound (i+incP) else raise SAME
berghofe@11715
   357
  | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
haftmann@22662
   358
      (AbsP (a, apsome' (same (op =) (incr_bv' inct tlev)) t,
berghofe@11715
   359
         prf_incr_bv incP inct (Plev+1) tlev body) handle SAME =>
berghofe@11715
   360
           AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
berghofe@11715
   361
  | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
berghofe@11715
   362
      Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
wenzelm@21646
   363
  | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
berghofe@11715
   364
      (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
berghofe@11715
   365
       handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
wenzelm@21646
   366
  | prf_incr_bv' incP inct Plev tlev (prf % t) =
skalberg@15570
   367
      (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
haftmann@22662
   368
       handle SAME => prf % apsome' (same (op =) (incr_bv' inct tlev)) t)
berghofe@11715
   369
  | prf_incr_bv' _ _ _ _ _ = raise SAME
berghofe@11715
   370
and prf_incr_bv incP inct Plev tlev prf =
berghofe@11715
   371
      (prf_incr_bv' incP inct Plev tlev prf handle SAME => prf);
berghofe@11519
   372
berghofe@11519
   373
fun incr_pboundvars  0 0 prf = prf
berghofe@11519
   374
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   375
berghofe@11519
   376
berghofe@11615
   377
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
skalberg@15531
   378
  | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
skalberg@15531
   379
  | prf_loose_bvar1 (_ % NONE) _ = true
skalberg@15531
   380
  | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
skalberg@15531
   381
  | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
berghofe@11519
   382
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
berghofe@11519
   383
  | prf_loose_bvar1 _ _ = false;
berghofe@11519
   384
berghofe@11519
   385
fun prf_loose_Pbvar1 (PBound i) k = i = k
berghofe@11615
   386
  | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
berghofe@11615
   387
  | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   388
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
berghofe@11519
   389
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
berghofe@11519
   390
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   391
berghofe@12279
   392
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
wenzelm@17492
   393
      if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
berghofe@12279
   394
  | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
berghofe@12279
   395
      prf_add_loose_bnos plev tlev prf2
berghofe@12279
   396
        (prf_add_loose_bnos plev tlev prf1 p)
berghofe@12279
   397
  | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
berghofe@12279
   398
      prf_add_loose_bnos plev tlev prf (case opt of
wenzelm@17492
   399
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   400
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   401
  | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
berghofe@12279
   402
      prf_add_loose_bnos (plev+1) tlev prf (case opt of
wenzelm@17492
   403
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   404
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   405
  | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
berghofe@12279
   406
      prf_add_loose_bnos plev (tlev+1) prf p
berghofe@12279
   407
  | prf_add_loose_bnos _ _ _ _ = ([], []);
berghofe@12279
   408
berghofe@11519
   409
berghofe@11519
   410
(**** substitutions ****)
berghofe@11519
   411
wenzelm@20509
   412
fun del_conflicting_tvars envT T = TermSubst.instantiateT
wenzelm@19482
   413
  (map_filter (fn ixnS as (_, S) =>
haftmann@26328
   414
     (Type.lookup envT ixnS; NONE) handle TYPE _ =>
berghofe@18316
   415
        SOME (ixnS, TFree ("'dummy", S))) (typ_tvars T)) T;
berghofe@18316
   416
wenzelm@20509
   417
fun del_conflicting_vars env t = TermSubst.instantiate
wenzelm@19482
   418
  (map_filter (fn ixnS as (_, S) =>
haftmann@26328
   419
     (Type.lookup (type_env env) ixnS; NONE) handle TYPE _ =>
berghofe@18316
   420
        SOME (ixnS, TFree ("'dummy", S))) (term_tvars t),
wenzelm@19482
   421
   map_filter (fn Var (ixnT as (_, T)) =>
berghofe@18316
   422
     (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
berghofe@18316
   423
        SOME (ixnT, Free ("dummy", T))) (term_vars t)) t;
berghofe@18316
   424
berghofe@11519
   425
fun norm_proof env =
berghofe@11519
   426
  let
wenzelm@12497
   427
    val envT = type_env env;
berghofe@18316
   428
    fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
berghofe@18316
   429
    fun htype f t = f env t handle TYPE (s, _, _) =>
berghofe@18316
   430
      (msg s; f env (del_conflicting_vars env t));
berghofe@18316
   431
    fun htypeT f T = f envT T handle TYPE (s, _, _) =>
berghofe@18316
   432
      (msg s; f envT (del_conflicting_tvars envT T));
berghofe@18316
   433
    fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
berghofe@18316
   434
      (msg s; f envT (map (del_conflicting_tvars envT) Ts));
berghofe@18316
   435
    fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (htypeT norm_type_same) T, normh prf)
berghofe@11519
   436
          handle SAME => Abst (s, T, norm prf))
berghofe@18316
   437
      | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (htype norm_term_same) t, normh prf)
berghofe@11519
   438
          handle SAME => AbsP (s, t, norm prf))
berghofe@18316
   439
      | norm (prf % t) = (norm prf % Option.map (htype norm_term) t
berghofe@18316
   440
          handle SAME => prf % apsome' (htype norm_term_same) t)
berghofe@11615
   441
      | norm (prf1 %% prf2) = (norm prf1 %% normh prf2
berghofe@11615
   442
          handle SAME => prf1 %% norm prf2)
berghofe@18316
   443
      | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (htypeTs norm_types_same) Ts)
wenzelm@28828
   444
      | norm (Oracle (s, prop, Ts)) = Oracle (s, prop, apsome' (htypeTs norm_types_same) Ts)
wenzelm@28828
   445
      | norm (Promise (i, prop, Ts)) = Promise (i, prop, htypeTs norm_types_same Ts)
wenzelm@28803
   446
      | norm (PThm (i, ((s, t, Ts), body))) =
wenzelm@28803
   447
          PThm (i, ((s, t, apsome' (htypeTs norm_types_same) Ts), body))
berghofe@11519
   448
      | norm _ = raise SAME
berghofe@11519
   449
    and normh prf = (norm prf handle SAME => prf);
berghofe@11519
   450
  in normh end;
berghofe@11519
   451
wenzelm@28803
   452
berghofe@11519
   453
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   454
berghofe@11519
   455
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   456
  | remove_types (t $ u) = remove_types t $ remove_types u
berghofe@11519
   457
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   458
  | remove_types t = t;
berghofe@11519
   459
berghofe@11519
   460
fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
berghofe@15797
   461
  Envir.Envir {iTs = iTs, asol = Vartab.map (apsnd remove_types) asol,
berghofe@15797
   462
    maxidx = maxidx};
berghofe@11519
   463
berghofe@11519
   464
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   465
wenzelm@28803
   466
berghofe@11519
   467
(**** substitution of bound variables ****)
berghofe@11519
   468
berghofe@11519
   469
fun prf_subst_bounds args prf =
berghofe@11519
   470
  let
berghofe@11519
   471
    val n = length args;
berghofe@11519
   472
    fun subst' lev (Bound i) =
berghofe@11519
   473
         (if i<lev then raise SAME    (*var is locally bound*)
berghofe@11519
   474
          else  incr_boundvars lev (List.nth (args, i-lev))
berghofe@11519
   475
                  handle Subscript => Bound (i-n)  (*loose: change it*))
berghofe@11519
   476
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   477
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
berghofe@11519
   478
          handle SAME => f $ subst' lev t)
berghofe@11519
   479
      | subst' _ _ = raise SAME
berghofe@11519
   480
    and substh' lev t = (subst' lev t handle SAME => t);
berghofe@11519
   481
berghofe@11519
   482
    fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
berghofe@11519
   483
          handle SAME => AbsP (a, t, subst lev body))
berghofe@11519
   484
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11615
   485
      | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
berghofe@11615
   486
          handle SAME => prf %% subst lev prf')
skalberg@15570
   487
      | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
berghofe@11615
   488
          handle SAME => prf % apsome' (subst' lev) t)
berghofe@11519
   489
      | subst _ _ = raise SAME
berghofe@11519
   490
    and substh lev prf = (subst lev prf handle SAME => prf)
berghofe@11519
   491
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   492
berghofe@11519
   493
fun prf_subst_pbounds args prf =
berghofe@11519
   494
  let
berghofe@11519
   495
    val n = length args;
berghofe@11519
   496
    fun subst (PBound i) Plev tlev =
wenzelm@20147
   497
         (if i < Plev then raise SAME    (*var is locally bound*)
berghofe@11519
   498
          else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
berghofe@11519
   499
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   500
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   501
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11615
   502
      | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
berghofe@11615
   503
          handle SAME => prf %% subst prf' Plev tlev)
berghofe@11615
   504
      | subst (prf % t) Plev tlev = subst prf Plev tlev % t
berghofe@11519
   505
      | subst  prf _ _ = raise SAME
berghofe@11519
   506
    and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
berghofe@11519
   507
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   508
berghofe@11519
   509
berghofe@11519
   510
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   511
berghofe@11519
   512
fun frzT names =
haftmann@17325
   513
  map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
berghofe@11519
   514
berghofe@11519
   515
fun thawT names =
haftmann@17325
   516
  map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
skalberg@15531
   517
      NONE => TFree (s, xs)
skalberg@15531
   518
    | SOME ixn => TVar (ixn, xs));
berghofe@11519
   519
berghofe@11519
   520
fun freeze names names' (t $ u) =
berghofe@11519
   521
      freeze names names' t $ freeze names names' u
berghofe@11519
   522
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   523
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   524
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   525
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   526
  | freeze names names' (Var (ixn, T)) =
haftmann@17325
   527
      Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
berghofe@11519
   528
  | freeze names names' t = t;
berghofe@11519
   529
berghofe@11519
   530
fun thaw names names' (t $ u) =
berghofe@11519
   531
      thaw names names' t $ thaw names names' u
berghofe@11519
   532
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   533
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   534
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
wenzelm@21646
   535
  | thaw names names' (Free (s, T)) =
berghofe@11519
   536
      let val T' = thawT names' T
haftmann@17325
   537
      in case AList.lookup (op =) names s of
skalberg@15531
   538
          NONE => Free (s, T')
skalberg@15531
   539
        | SOME ixn => Var (ixn, T')
berghofe@11519
   540
      end
berghofe@11519
   541
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   542
  | thaw names names' t = t;
berghofe@11519
   543
berghofe@11519
   544
fun freeze_thaw_prf prf =
berghofe@11519
   545
  let
berghofe@11519
   546
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
wenzelm@20147
   547
      (fn t => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   548
         (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
wenzelm@29261
   549
          Term.add_var_names t vs, Term.add_tvar_names t Tvs))
wenzelm@20147
   550
      (fn T => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   551
         (fs, Term.add_tfree_namesT T Tfs,
wenzelm@29261
   552
          vs, Term.add_tvar_namesT T Tvs))
wenzelm@20147
   553
      prf ([], [], [], []);
wenzelm@29261
   554
    val names = vs ~~ Name.variant_list fs (map fst vs);
wenzelm@20071
   555
    val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
berghofe@11519
   556
    val rnames = map swap names;
berghofe@11519
   557
    val rnames' = map swap names';
berghofe@11519
   558
  in
berghofe@11519
   559
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   560
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   561
  end;
berghofe@11519
   562
berghofe@11519
   563
berghofe@11519
   564
(***** implication introduction *****)
berghofe@11519
   565
berghofe@11519
   566
fun implies_intr_proof h prf =
berghofe@11519
   567
  let
berghofe@11715
   568
    fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME
berghofe@11519
   569
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
berghofe@11519
   570
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
berghofe@11615
   571
      | abshyp i (prf % t) = abshyp i prf % t
berghofe@11715
   572
      | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2
berghofe@11715
   573
          handle SAME => prf1 %% abshyp i prf2)
berghofe@11715
   574
      | abshyp _ _ = raise SAME
berghofe@11715
   575
    and abshyph i prf = (abshyp i prf handle SAME => prf)
berghofe@11519
   576
  in
skalberg@15531
   577
    AbsP ("H", NONE (*h*), abshyph 0 prf)
berghofe@11519
   578
  end;
berghofe@11519
   579
berghofe@11519
   580
berghofe@11519
   581
(***** forall introduction *****)
berghofe@11519
   582
skalberg@15531
   583
fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
berghofe@11519
   584
berghofe@11519
   585
berghofe@11519
   586
(***** varify *****)
berghofe@11519
   587
berghofe@11519
   588
fun varify_proof t fixed prf =
berghofe@11519
   589
  let
wenzelm@19304
   590
    val fs = Term.fold_types (Term.fold_atyps
wenzelm@19304
   591
      (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
wenzelm@29261
   592
    val used = Name.context
wenzelm@29261
   593
      |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
wenzelm@29261
   594
    val fmap = fs ~~ (#1 (Name.variants (map fst fs) used));
berghofe@11519
   595
    fun thaw (f as (a, S)) =
haftmann@17314
   596
      (case AList.lookup (op =) fmap f of
skalberg@15531
   597
        NONE => TFree f
skalberg@15531
   598
      | SOME b => TVar ((b, 0), S));
wenzelm@28803
   599
  in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
berghofe@11519
   600
berghofe@11519
   601
berghofe@11519
   602
local
berghofe@11519
   603
berghofe@11519
   604
fun new_name (ix, (pairs,used)) =
wenzelm@20071
   605
  let val v = Name.variant used (string_of_indexname ix)
berghofe@11519
   606
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   607
haftmann@17325
   608
fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
skalberg@15531
   609
    NONE => TVar (ix, sort)
skalberg@15531
   610
  | SOME name => TFree (name, sort));
berghofe@11519
   611
berghofe@11519
   612
in
berghofe@11519
   613
berghofe@11519
   614
fun freezeT t prf =
berghofe@11519
   615
  let
berghofe@11519
   616
    val used = it_term_types add_typ_tfree_names (t, [])
berghofe@11519
   617
    and tvars = map #1 (it_term_types add_typ_tvars (t, []));
wenzelm@23178
   618
    val (alist, _) = List.foldr new_name ([], used) tvars;
berghofe@11519
   619
  in
berghofe@11519
   620
    (case alist of
berghofe@11519
   621
      [] => prf (*nothing to do!*)
berghofe@11519
   622
    | _ =>
berghofe@11519
   623
      let val frzT = map_type_tvar (freeze_one alist)
wenzelm@20548
   624
      in map_proof_terms (map_types frzT) frzT prf end)
berghofe@11519
   625
  end;
berghofe@11519
   626
berghofe@11519
   627
end;
berghofe@11519
   628
berghofe@11519
   629
berghofe@11519
   630
(***** rotate assumptions *****)
berghofe@11519
   631
berghofe@11519
   632
fun rotate_proof Bs Bi m prf =
berghofe@11519
   633
  let
berghofe@11519
   634
    val params = Term.strip_all_vars Bi;
berghofe@11519
   635
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   636
    val i = length asms;
berghofe@11519
   637
    val j = length Bs;
berghofe@11519
   638
  in
berghofe@11519
   639
    mk_AbsP (j+1, proof_combP (prf, map PBound
wenzelm@23178
   640
      (j downto 1) @ [mk_Abst params (mk_AbsP (i,
berghofe@11519
   641
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
wenzelm@23178
   642
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
berghofe@11519
   643
  end;
berghofe@11519
   644
berghofe@11519
   645
berghofe@11519
   646
(***** permute premises *****)
berghofe@11519
   647
berghofe@11519
   648
fun permute_prems_prf prems j k prf =
berghofe@11519
   649
  let val n = length prems
berghofe@11519
   650
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   651
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   652
  end;
berghofe@11519
   653
berghofe@11519
   654
wenzelm@19908
   655
(***** generalization *****)
wenzelm@19908
   656
wenzelm@20000
   657
fun generalize (tfrees, frees) idx =
wenzelm@20000
   658
  map_proof_terms_option
wenzelm@20509
   659
    (TermSubst.generalize_option (tfrees, frees) idx)
wenzelm@20509
   660
    (TermSubst.generalizeT_option tfrees idx);
wenzelm@19908
   661
wenzelm@19908
   662
berghofe@11519
   663
(***** instantiation *****)
berghofe@11519
   664
wenzelm@20000
   665
fun instantiate (instT, inst) =
wenzelm@20000
   666
  map_proof_terms_option
wenzelm@20509
   667
    (TermSubst.instantiate_option (instT, map (apsnd remove_types) inst))
wenzelm@20509
   668
    (TermSubst.instantiateT_option instT);
berghofe@11519
   669
berghofe@11519
   670
berghofe@11519
   671
(***** lifting *****)
berghofe@11519
   672
berghofe@11519
   673
fun lift_proof Bi inc prop prf =
berghofe@11519
   674
  let
berghofe@11519
   675
    fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   676
berghofe@11715
   677
    fun lift' Us Ts (Abst (s, T, prf)) =
haftmann@22662
   678
          (Abst (s, apsome' (same (op =) (Logic.incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf)
berghofe@11715
   679
           handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
berghofe@11715
   680
      | lift' Us Ts (AbsP (s, t, prf)) =
haftmann@22662
   681
          (AbsP (s, apsome' (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
berghofe@11715
   682
           handle SAME => AbsP (s, t, lift' Us Ts prf))
skalberg@15570
   683
      | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
haftmann@22662
   684
          handle SAME => prf % apsome' (same (op =) (lift'' Us Ts)) t)
berghofe@11715
   685
      | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
berghofe@11715
   686
          handle SAME => prf1 %% lift' Us Ts prf2)
berghofe@11715
   687
      | lift' _ _ (PAxm (s, prop, Ts)) =
haftmann@22662
   688
          PAxm (s, prop, apsome' (same (op =) (map (Logic.incr_tvar inc))) Ts)
wenzelm@28828
   689
      | lift' _ _ (Oracle (s, prop, Ts)) =
wenzelm@28828
   690
          Oracle (s, prop, apsome' (same (op =) (map (Logic.incr_tvar inc))) Ts)
wenzelm@28828
   691
      | lift' _ _ (Promise (i, prop, Ts)) =
wenzelm@28828
   692
          Promise (i, prop, same (op =) (map (Logic.incr_tvar inc)) Ts)
wenzelm@28803
   693
      | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
wenzelm@28803
   694
          PThm (i, ((s, prop, apsome' (same (op =) (map (Logic.incr_tvar inc))) Ts), body))
berghofe@11715
   695
      | lift' _ _ _ = raise SAME
berghofe@11715
   696
    and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf);
berghofe@11519
   697
wenzelm@18030
   698
    val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
berghofe@11519
   699
    val k = length ps;
berghofe@11519
   700
wenzelm@23178
   701
    fun mk_app b (i, j, prf) =
berghofe@11615
   702
          if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
berghofe@11519
   703
berghofe@11519
   704
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
wenzelm@20147
   705
            AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
wenzelm@21646
   706
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
wenzelm@20147
   707
            Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11715
   708
      | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
wenzelm@23178
   709
            map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
berghofe@11519
   710
              (i + k - 1 downto i));
berghofe@11519
   711
  in
berghofe@11519
   712
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   713
  end;
berghofe@11519
   714
berghofe@11519
   715
berghofe@11519
   716
(***** proof by assumption *****)
berghofe@11519
   717
berghofe@23296
   718
fun mk_asm_prf t i m =
berghofe@23296
   719
  let
berghofe@23296
   720
    fun imp_prf _ i 0 = PBound i
berghofe@23296
   721
      | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
berghofe@23296
   722
      | imp_prf _ i _ = PBound i;
berghofe@23296
   723
    fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
berghofe@23296
   724
      | all_prf t = imp_prf t (~i) m
berghofe@23296
   725
  in all_prf t end;
berghofe@11519
   726
berghofe@11519
   727
fun assumption_proof Bs Bi n prf =
berghofe@11519
   728
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@23296
   729
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
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
berghofe@23296
   741
fun bicompose_proof flatten Bs oldAs newAs A n m 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)) %%
berghofe@23296
   748
        proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] 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)),
wenzelm@27330
   774
   ("abstract_rule", mk_implies
wenzelm@27330
   775
      (all x (mk_equals (f $ x, g $ x)), mk_equals (lambda x (f $ x), lambda x (g $ x)))),
wenzelm@27330
   776
   ("combination", list_implies
wenzelm@27330
   777
      ([mk_equals (f, g), mk_equals (x, y)], mk_equals (f $ x, g $ y)))];
berghofe@11519
   778
berghofe@11519
   779
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   780
  equal_elim_axm, abstract_rule_axm, combination_axm] =
wenzelm@26424
   781
    map (fn (s, t) => PAxm ("Pure." ^ s, varify t, NONE)) equality_axms;
berghofe@11519
   782
berghofe@11519
   783
end;
berghofe@11519
   784
skalberg@15531
   785
val reflexive = reflexive_axm % NONE;
berghofe@11519
   786
wenzelm@26424
   787
fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
skalberg@15531
   788
  | symmetric prf = symmetric_axm % NONE % NONE %% prf;
berghofe@11519
   789
wenzelm@26424
   790
fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
wenzelm@26424
   791
  | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
berghofe@11519
   792
  | transitive u (Type ("prop", [])) prf1 prf2 =
skalberg@15531
   793
      transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
berghofe@11519
   794
  | transitive u T prf1 prf2 =
skalberg@15531
   795
      transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
berghofe@11519
   796
berghofe@11519
   797
fun abstract_rule x a prf =
skalberg@15531
   798
  abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
berghofe@11519
   799
wenzelm@26424
   800
fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
wenzelm@19502
   801
      is_some f orelse check_comb prf
wenzelm@26424
   802
  | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
berghofe@11519
   803
      check_comb prf1 andalso check_comb prf2
wenzelm@26424
   804
  | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
berghofe@11519
   805
  | check_comb _ = false;
berghofe@11519
   806
berghofe@11519
   807
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   808
  let
berghofe@11519
   809
    val f = Envir.beta_norm f;
berghofe@11519
   810
    val g = Envir.beta_norm g;
berghofe@11519
   811
    val prf =  if check_comb prf1 then
skalberg@15531
   812
        combination_axm % NONE % NONE
berghofe@11519
   813
      else (case prf1 of
wenzelm@26424
   814
          PAxm ("Pure.reflexive", _, _) % _ =>
skalberg@15531
   815
            combination_axm %> remove_types f % NONE
berghofe@11615
   816
        | _ => combination_axm %> remove_types f %> remove_types g)
berghofe@11519
   817
  in
berghofe@11519
   818
    (case T of
berghofe@11615
   819
       Type ("fun", _) => prf %
berghofe@11519
   820
         (case head_of f of
skalberg@15531
   821
            Abs _ => SOME (remove_types t)
skalberg@15531
   822
          | Var _ => SOME (remove_types t)
skalberg@15531
   823
          | _ => NONE) %
berghofe@11519
   824
         (case head_of g of
skalberg@15531
   825
            Abs _ => SOME (remove_types u)
skalberg@15531
   826
          | Var _ => SOME (remove_types u)
skalberg@15531
   827
          | _ => NONE) %% prf1 %% prf2
skalberg@15531
   828
     | _ => prf % NONE % NONE %% prf1 %% prf2)
berghofe@11519
   829
  end;
berghofe@11519
   830
berghofe@11519
   831
fun equal_intr A B prf1 prf2 =
berghofe@11615
   832
  equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   833
berghofe@11519
   834
fun equal_elim A B prf1 prf2 =
berghofe@11615
   835
  equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   836
berghofe@11519
   837
berghofe@11519
   838
(***** axioms and theorems *****)
berghofe@11519
   839
wenzelm@28803
   840
val proofs = ref 2;
wenzelm@28803
   841
berghofe@28812
   842
fun vars_of t = map Var (rev (Term.add_vars t []));
berghofe@28812
   843
fun frees_of t = map Free (rev (Term.add_frees 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
wenzelm@21646
   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) @
berghofe@28812
   901
      map SOME (frees_of 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
    fun shrink ls lev (prf as Abst (a, T, body)) =
wenzelm@17492
   917
          let val (b, is, ch, body') = shrink ls (lev+1) body
wenzelm@26631
   918
          in (b, is, ch, if ch then Abst (a, T, body') else prf) end
wenzelm@17492
   919
      | shrink ls lev (prf as AbsP (a, t, body)) =
wenzelm@17492
   920
          let val (b, is, ch, body') = shrink (lev::ls) lev body
wenzelm@19482
   921
          in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
wenzelm@26631
   922
            ch, if ch then AbsP (a, t, body') else prf)
wenzelm@17492
   923
          end
wenzelm@17492
   924
      | shrink ls lev prf =
wenzelm@17492
   925
          let val (is, ch, _, prf') = shrink' ls lev [] [] prf
wenzelm@17492
   926
          in (false, is, ch, prf') end
wenzelm@17492
   927
    and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
wenzelm@17492
   928
          let
wenzelm@17492
   929
            val p as (_, is', ch', prf') = shrink ls lev prf2;
wenzelm@17492
   930
            val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
wenzelm@17492
   931
          in (is union is', ch orelse ch', ts',
wenzelm@17492
   932
              if ch orelse ch' then prf'' %% prf' else prf)
wenzelm@17492
   933
          end
wenzelm@17492
   934
      | shrink' ls lev ts prfs (prf as prf1 % t) =
wenzelm@17492
   935
          let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
wenzelm@17492
   936
          in (is, ch orelse ch', ts',
wenzelm@26631
   937
              if ch orelse ch' then prf' % t' else prf) end
wenzelm@17492
   938
      | shrink' ls lev ts prfs (prf as PBound i) =
wenzelm@17492
   939
          (if exists (fn SOME (Bound j) => lev-j <= List.nth (ls, i) | _ => true) ts
haftmann@18928
   940
             orelse has_duplicates (op =)
haftmann@18928
   941
               (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
wenzelm@17492
   942
             orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
wenzelm@26631
   943
      | shrink' ls lev ts prfs (Hyp t) = ([], false, map (pair false) ts, Hyp t)
wenzelm@28803
   944
      | shrink' ls lev ts prfs MinProof = ([], false, map (pair false) ts, MinProof)
wenzelm@17492
   945
      | shrink' ls lev ts prfs prf =
wenzelm@17492
   946
          let
wenzelm@28803
   947
            val prop =
wenzelm@28803
   948
              (case prf of
wenzelm@28803
   949
                PAxm (_, prop, _) => prop
wenzelm@28803
   950
              | Oracle (_, prop, _) => prop
wenzelm@28803
   951
              | Promise (_, prop, _) => prop
wenzelm@28803
   952
              | PThm (_, ((_, prop, _), _)) => prop
wenzelm@28319
   953
              | _ => error "shrink: proof not in normal form");
wenzelm@17492
   954
            val vs = vars_of prop;
wenzelm@19012
   955
            val (ts', ts'') = chop (length vs) ts;
wenzelm@17492
   956
            val insts = Library.take (length ts', map (fst o dest_Var) vs) ~~ ts';
wenzelm@17492
   957
            val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
wenzelm@17492
   958
              insert (op =) ixn (case AList.lookup (op =) insts ixn of
wenzelm@17492
   959
                  SOME (SOME t) => if is_proj t then ixns union ixns' else ixns'
wenzelm@17492
   960
                | _ => ixns union ixns'))
wenzelm@17492
   961
                  (needed prop ts'' prfs, add_npvars false true [] ([], prop));
wenzelm@17492
   962
            val insts' = map
wenzelm@17492
   963
              (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
wenzelm@17492
   964
                | (_, x) => (false, x)) insts
wenzelm@17492
   965
          in ([], false, insts' @ map (pair false) ts'', prf) end
wenzelm@17492
   966
    and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
wenzelm@17492
   967
          (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
wenzelm@17492
   968
      | needed (Var (ixn, _)) (_::_) _ = [ixn]
wenzelm@17492
   969
      | needed _ _ _ = [];
wenzelm@17492
   970
  in shrink end;
berghofe@11519
   971
berghofe@11519
   972
berghofe@11519
   973
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
   974
berghofe@11519
   975
exception PMatch;
berghofe@11519
   976
berghofe@11519
   977
(** see pattern.ML **)
berghofe@11519
   978
skalberg@15570
   979
fun flt (i: int) = List.filter (fn n => n < i);
berghofe@12279
   980
berghofe@12279
   981
fun fomatch Ts tymatch j =
berghofe@11519
   982
  let
berghofe@11519
   983
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
   984
        (Var (ixn, T), t)  =>
berghofe@12279
   985
          if j>0 andalso not (null (flt j (loose_bnos t)))
berghofe@12279
   986
          then raise PMatch
berghofe@12279
   987
          else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
berghofe@12279
   988
            (ixn, t) :: insts)
berghofe@11519
   989
      | (Free (a, T), Free (b, U)) =>
wenzelm@20147
   990
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   991
      | (Const (a, T), Const (b, U))  =>
wenzelm@20147
   992
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
   993
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@12279
   994
      | (Bound i, Bound j) => if i=j then instsp else raise PMatch
berghofe@11519
   995
      | _ => raise PMatch
berghofe@11519
   996
  in mtch end;
berghofe@11519
   997
berghofe@12279
   998
fun match_proof Ts tymatch =
berghofe@11519
   999
  let
skalberg@15531
  1000
    fun optmatch _ inst (NONE, _) = inst
skalberg@15531
  1001
      | optmatch _ _ (SOME _, NONE) = raise PMatch
skalberg@15531
  1002
      | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
berghofe@12279
  1003
berghofe@12279
  1004
    fun matcht Ts j (pinst, tinst) (t, u) =
berghofe@12279
  1005
      (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
berghofe@12279
  1006
    fun matchT (pinst, (tyinsts, insts)) p =
berghofe@12279
  1007
      (pinst, (tymatch (tyinsts, K p), insts));
skalberg@15570
  1008
    fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
berghofe@12279
  1009
berghofe@12279
  1010
    fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
berghofe@12279
  1011
          if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
berghofe@12279
  1012
          else (case apfst (flt i) (apsnd (flt j)
berghofe@12279
  1013
                  (prf_add_loose_bnos 0 0 prf ([], []))) of
berghofe@12279
  1014
              ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1015
            | ([], _) => if j = 0 then
berghofe@12279
  1016
                   ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1017
                 else raise PMatch
berghofe@12279
  1018
            | _ => raise PMatch)
berghofe@12279
  1019
      | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
berghofe@12279
  1020
          optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
berghofe@12279
  1021
      | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
berghofe@12279
  1022
          mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
berghofe@12279
  1023
      | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
wenzelm@18485
  1024
          mtch (the_default dummyT opU :: Ts) i (j+1)
berghofe@12279
  1025
            (optmatch matchT inst (opT, opU)) (prf1, prf2)
berghofe@12279
  1026
      | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
wenzelm@18485
  1027
          mtch (the_default dummyT opU :: Ts) i (j+1) inst
berghofe@12279
  1028
            (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
berghofe@12279
  1029
      | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
berghofe@12279
  1030
          mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
berghofe@12279
  1031
      | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
berghofe@12279
  1032
          mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
wenzelm@28803
  1033
      | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
wenzelm@28803
  1034
          if s1 = s2 then optmatch matchTs inst (opTs, opUs)
wenzelm@28803
  1035
          else raise PMatch
wenzelm@28803
  1036
      | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
wenzelm@28803
  1037
          if name1 = name2 andalso prop1 = prop2 then
berghofe@12279
  1038
            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')
wenzelm@28828
  1066
      | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Option.map (map substT) Ts)
wenzelm@28828
  1067
      | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Option.map (map substT) Ts)
wenzelm@28828
  1068
      | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, (map substT) Ts)
wenzelm@28803
  1069
      | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
wenzelm@28803
  1070
          PThm (i, ((id, prop, Option.map (map substT) Ts), body))
wenzelm@28803
  1071
      | subst _ _ t = t;
berghofe@11519
  1072
  in subst 0 0 end;
berghofe@11519
  1073
wenzelm@21646
  1074
(*A fast unification filter: true unless the two terms cannot be unified.
berghofe@12871
  1075
  Terms must be NORMAL.  Treats all Vars as distinct. *)
berghofe@12871
  1076
fun could_unify prf1 prf2 =
berghofe@12871
  1077
  let
berghofe@12871
  1078
    fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
berghofe@12871
  1079
          could_unify prf2 prf2' andalso matchrands prf1 prf1'
skalberg@15531
  1080
      | matchrands (prf % SOME t) (prf' % SOME t') =
berghofe@12871
  1081
          Term.could_unify (t, t') andalso matchrands prf prf'
berghofe@12871
  1082
      | matchrands (prf % _) (prf' % _) = matchrands prf prf'
berghofe@12871
  1083
      | matchrands _ _ = true
berghofe@12871
  1084
berghofe@12871
  1085
    fun head_of (prf %% _) = head_of prf
berghofe@12871
  1086
      | head_of (prf % _) = head_of prf
berghofe@12871
  1087
      | head_of prf = prf
berghofe@12871
  1088
berghofe@12871
  1089
  in case (head_of prf1, head_of prf2) of
berghofe@12871
  1090
        (_, Hyp (Var _)) => true
berghofe@12871
  1091
      | (Hyp (Var _), _) => true
wenzelm@28803
  1092
      | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
wenzelm@28803
  1093
      | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
berghofe@12871
  1094
          a = b andalso propa = propb andalso matchrands prf1 prf2
wenzelm@28803
  1095
      | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
berghofe@12871
  1096
      | (AbsP _, _) =>  true   (*because of possible eta equality*)
berghofe@12871
  1097
      | (Abst _, _) =>  true
berghofe@12871
  1098
      | (_, AbsP _) =>  true
berghofe@12871
  1099
      | (_, Abst _) =>  true
berghofe@12871
  1100
      | _ => false
berghofe@12871
  1101
  end;
berghofe@12871
  1102
wenzelm@28329
  1103
berghofe@11519
  1104
(**** rewriting on proof terms ****)
berghofe@11519
  1105
berghofe@13102
  1106
val skel0 = PBound 0;
berghofe@13102
  1107
berghofe@12279
  1108
fun rewrite_prf tymatch (rules, procs) prf =
berghofe@11519
  1109
  let
skalberg@15531
  1110
    fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, skel0)
skalberg@15531
  1111
      | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, skel0)
wenzelm@28803
  1112
      | rew Ts prf = (case get_first (fn r => r Ts prf) procs of
skalberg@15531
  1113
          SOME prf' => SOME (prf', skel0)
skalberg@15531
  1114
        | NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
berghofe@13102
  1115
            (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
wenzelm@28803
  1116
               handle PMatch => NONE) (filter (could_unify prf o fst) rules));
berghofe@11519
  1117
berghofe@11615
  1118
    fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
berghofe@11519
  1119
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
  1120
          else
berghofe@11519
  1121
            let val prf'' = incr_pboundvars (~1) 0 prf'
wenzelm@19502
  1122
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
skalberg@15531
  1123
      | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
berghofe@11519
  1124
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
  1125
          else
berghofe@11519
  1126
            let val prf'' = incr_pboundvars 0 (~1) prf'
wenzelm@19502
  1127
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
berghofe@11519
  1128
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
  1129
skalberg@15531
  1130
    fun rew1 _ (Hyp (Var _)) _ = NONE
berghofe@13102
  1131
      | rew1 Ts skel prf = (case rew2 Ts skel prf of
skalberg@15531
  1132
          SOME prf1 => (case rew0 Ts prf1 of
wenzelm@19502
  1133
              SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts skel' prf2))
skalberg@15531
  1134
            | NONE => SOME prf1)
skalberg@15531
  1135
        | NONE => (case rew0 Ts prf of
wenzelm@19502
  1136
              SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts skel' prf1))
skalberg@15531
  1137
            | NONE => NONE))
berghofe@11519
  1138
skalberg@15531
  1139
    and rew2 Ts skel (prf % SOME t) = (case prf of
berghofe@11519
  1140
            Abst (_, _, body) =>
berghofe@11519
  1141
              let val prf' = prf_subst_bounds [t] body
wenzelm@19502
  1142
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1143
          | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf of
skalberg@15531
  1144
              SOME prf' => SOME (prf' % SOME t)
skalberg@15531
  1145
            | NONE => NONE))
skalberg@15570
  1146
      | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
berghofe@13102
  1147
          (rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf)
berghofe@13102
  1148
      | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
berghofe@11519
  1149
            AbsP (_, _, body) =>
berghofe@11519
  1150
              let val prf' = prf_subst_pbounds [prf2] body
wenzelm@19502
  1151
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1152
          | _ =>
berghofe@13102
  1153
            let val (skel1, skel2) = (case skel of
berghofe@13102
  1154
                skel1 %% skel2 => (skel1, skel2)
berghofe@13102
  1155
              | _ => (skel0, skel0))
berghofe@13102
  1156
            in case rew1 Ts skel1 prf1 of
skalberg@15531
  1157
                SOME prf1' => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1158
                    SOME prf2' => SOME (prf1' %% prf2')
skalberg@15531
  1159
                  | NONE => SOME (prf1' %% prf2))
skalberg@15531
  1160
              | NONE => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1161
                    SOME prf2' => SOME (prf1 %% prf2')
skalberg@15531
  1162
                  | NONE => NONE)
berghofe@13102
  1163
            end)
wenzelm@19502
  1164
      | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts)
berghofe@13102
  1165
              (case skel of Abst (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1166
            SOME prf' => SOME (Abst (s, T, prf'))
skalberg@15531
  1167
          | NONE => NONE)
berghofe@13102
  1168
      | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
berghofe@13102
  1169
              (case skel of AbsP (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1170
            SOME prf' => SOME (AbsP (s, t, prf'))
skalberg@15531
  1171
          | NONE => NONE)
skalberg@15531
  1172
      | rew2 _ _ _ = NONE
berghofe@11519
  1173
wenzelm@19502
  1174
  in the_default prf (rew1 [] skel0 prf) end;
berghofe@11519
  1175
wenzelm@17203
  1176
fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
wenzelm@17203
  1177
  Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
  1178
berghofe@11715
  1179
fun rewrite_proof_notypes rews = rewrite_prf fst rews;
berghofe@11615
  1180
wenzelm@16940
  1181
berghofe@11519
  1182
(**** theory data ****)
berghofe@11519
  1183
wenzelm@16458
  1184
structure ProofData = TheoryDataFun
wenzelm@22846
  1185
(
wenzelm@28803
  1186
  type T = (stamp * (proof * proof)) list * (stamp * (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@28803
  1191
  fun merge _ ((rules1, procs1), (rules2, procs2)) : T =
wenzelm@28803
  1192
    (AList.merge (op =) (K true) (rules1, rules2),
haftmann@22662
  1193
      AList.merge (op =) (K true) (procs1, procs2));
wenzelm@22846
  1194
);
berghofe@11519
  1195
wenzelm@28803
  1196
fun get_data thy = let val (rules, procs) = ProofData.get thy in (map #2 rules, map #2 procs) end;
wenzelm@28803
  1197
fun rew_proof thy = rewrite_prf fst (get_data thy);
berghofe@23780
  1198
wenzelm@28803
  1199
fun add_prf_rrule r = (ProofData.map o apfst) (cons (stamp (), r));
wenzelm@28803
  1200
fun add_prf_rproc p = (ProofData.map o apsnd) (cons (stamp (), p));
wenzelm@28803
  1201
wenzelm@28803
  1202
wenzelm@28828
  1203
(***** promises *****)
berghofe@11519
  1204
wenzelm@28828
  1205
fun promise_proof thy i prop =
wenzelm@28828
  1206
  let
wenzelm@28828
  1207
    val _ = prop |> Term.exists_subterm (fn t =>
wenzelm@28828
  1208
      (Term.is_Free t orelse Term.is_Var t) andalso
wenzelm@28828
  1209
        error ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
wenzelm@28828
  1210
    val _ = prop |> Term.exists_type (Term.exists_subtype
wenzelm@28828
  1211
      (fn TFree (a, _) => error ("promise_proof: illegal type variable " ^ quote a)
wenzelm@28828
  1212
        | _ => false));
wenzelm@28828
  1213
  in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
wenzelm@28828
  1214
wenzelm@28828
  1215
fun fulfill_proof _ [] body0 = body0
wenzelm@28828
  1216
  | fulfill_proof thy promises body0 =
wenzelm@28828
  1217
      let
wenzelm@28828
  1218
        val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
wenzelm@28846
  1219
        val (oracles, thms) = fold (merge_body o make_body o #2) promises (oracles0, thms0);
wenzelm@28875
  1220
wenzelm@28875
  1221
        val tab = Inttab.make promises;
wenzelm@28875
  1222
        fun fill (Promise (i, prop, Ts)) =
wenzelm@28875
  1223
            (case Inttab.lookup tab i of
wenzelm@28875
  1224
              NONE => NONE
wenzelm@28875
  1225
            | SOME p => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) p))
wenzelm@28875
  1226
          | fill _ = NONE;
wenzelm@28875
  1227
        val (rules, procs) = get_data thy;
wenzelm@28875
  1228
        val proof = rewrite_prf fst (rules, K fill :: procs) proof0;
wenzelm@28828
  1229
      in PBody {oracles = oracles, thms = thms, proof = proof} end;
wenzelm@28828
  1230
wenzelm@28828
  1231
wenzelm@28828
  1232
(***** theorems *****)
berghofe@11519
  1233
wenzelm@28803
  1234
fun thm_proof thy name hyps prop promises body =
berghofe@11519
  1235
  let
wenzelm@28803
  1236
    val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
wenzelm@12923
  1237
    val prop = Logic.list_implies (hyps, prop);
berghofe@11519
  1238
    val nvs = needed_vars prop;
berghofe@11519
  1239
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
  1240
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
berghofe@28812
  1241
      map SOME (frees_of prop);
wenzelm@28803
  1242
wenzelm@28803
  1243
    val proof0 =
wenzelm@28876
  1244
      if ! proofs = 2 then
wenzelm@28876
  1245
        #4 (shrink_proof thy [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)))
wenzelm@28876
  1246
      else MinProof;
wenzelm@28803
  1247
wenzelm@28846
  1248
    fun new_prf () = (serial (), name, prop,
wenzelm@28846
  1249
      Lazy.lazy (fn () => fulfill_proof thy (Lazy.force promises)
wenzelm@28846
  1250
        (PBody {oracles = oracles0, thms = thms0, proof = proof0})));
wenzelm@28803
  1251
wenzelm@28815
  1252
    val (i, name, prop, body') =
wenzelm@28803
  1253
      (case strip_combt (fst (strip_combP prf)) of
wenzelm@28803
  1254
        (PThm (i, ((old_name, prop', NONE), body')), args') =>
wenzelm@28815
  1255
          if (old_name = "" orelse old_name = name) andalso prop = prop' andalso args = args'
wenzelm@28815
  1256
          then (i, name, prop, body')
wenzelm@28803
  1257
          else new_prf ()
wenzelm@28815
  1258
      | _ => new_prf ());
wenzelm@28815
  1259
    val head = PThm (i, ((name, prop, NONE), body'));
berghofe@11519
  1260
  in
wenzelm@28815
  1261
    ((i, (name, prop, body')), proof_combP (proof_combt' (head, args), map Hyp hyps))
berghofe@11519
  1262
  end;
berghofe@11519
  1263
wenzelm@21646
  1264
fun get_name hyps prop prf =
wenzelm@12923
  1265
  let val prop = Logic.list_implies (hyps, prop) in
wenzelm@12923
  1266
    (case strip_combt (fst (strip_combP prf)) of
wenzelm@28803
  1267
      (PAxm (name, prop', _), _) => if prop = prop' then name else ""   (* FIXME !? *)
wenzelm@28803
  1268
    | (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
wenzelm@21646
  1269
    | _ => "")
wenzelm@12923
  1270
  end;
berghofe@11519
  1271
berghofe@11519
  1272
end;
berghofe@11519
  1273
berghofe@11519
  1274
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
berghofe@11519
  1275
open BasicProofterm;