src/Pure/proofterm.ML
author wenzelm
Fri Jul 17 23:11:40 2009 +0200 (2009-07-17)
changeset 32035 8e77b6a250d5
parent 32032 a6a6e8031c14
child 32049 d6065a237059
permissions -rw-r--r--
tuned/modernized Envir.subst_XXX;
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(*  Title:      Pure/proofterm.ML
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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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   | OfClass of typ * class
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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 future)
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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 future)) 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 future)
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  val join_body: proof_body future ->
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    {oracles: oracle OrdList.T, thms: pthm OrdList.T, proof: proof}
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  val join_proof: proof_body future -> proof
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  val proof_of: proof_body -> proof
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  val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
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  val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
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  val status_of: proof_body list -> {failed: bool, oracle: bool, unfinished: bool}
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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 merge_oracles: oracle OrdList.T -> oracle OrdList.T -> oracle OrdList.T
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  val merge_thms: pthm OrdList.T -> pthm OrdList.T -> pthm OrdList.T
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  val all_oracles_of: proof_body -> oracle OrdList.T
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  val approximate_proof_body: proof -> proof_body
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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 incr_indexes: int -> 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 -> oracle * proof
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  val promise_proof: theory -> serial -> term -> proof
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  val fulfill_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
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  val thm_proof: theory -> string -> term list -> term ->
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    (serial * proof_body future) list -> 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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(***** 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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 | OfClass of typ * class
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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 future)
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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 future)) 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 future);
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val join_body = Future.join #> (fn PBody args => args);
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val join_proof = #proof o join_body;
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fun proof_of (PBody {proof, ...}) = proof;
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(***** proof atoms *****)
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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 (join_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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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' = Future.join 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 status_of bodies =
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  let
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    fun status (PBody {oracles, thms, ...}) x =
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      let
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        val ((oracle, unfinished, failed), seen) =
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          (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
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            if Inttab.defined seen i then (st, seen)
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            else
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              let val seen' = Inttab.update (i, ()) seen in
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                (case Future.peek body of
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                  SOME (Exn.Result body') => status body' (st, seen')
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                | SOME (Exn.Exn _) =>
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                    let val (oracle, unfinished, _) = st
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                    in ((oracle, unfinished, true), seen') end
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                | NONE =>
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                    let val (oracle, _, failed) = st
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                    in ((oracle, true, failed), seen') end)
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              end);
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      in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
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    val (oracle, unfinished, failed) = #1 (fold status bodies ((false, false, false), Inttab.empty));
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  in {oracle = oracle, unfinished = unfinished, failed = failed} end;
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(* proof body *)
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val oracle_ord = prod_ord fast_string_ord TermOrd.fast_term_ord;
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fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
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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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val all_oracles_of =
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  let
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    fun collect (PBody {oracles, thms, ...}) = thms |> fold (fn (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
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          val body' = Future.join body;
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          val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
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        in (merge_oracles oracles x', seen') end);
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  in fn body => #1 (collect body ([], Inttab.empty)) end;
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fun approximate_proof_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
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    PBody
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     {oracles = OrdList.make oracle_ord oracles,
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      thms = OrdList.make thm_ord thms,
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      proof = prf}
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  end;
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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')), _) => Future.join 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 map_proof_terms_option f g =
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  let
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    val term = Same.function f;
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    val typ = Same.function g;
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    val typs = Same.map typ;
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    fun proof (Abst (s, T, prf)) =
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          (Abst (s, Same.map_option typ T, Same.commit proof prf)
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            handle Same.SAME => Abst (s, T, proof prf))
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      | proof (AbsP (s, t, prf)) =
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          (AbsP (s, Same.map_option term t, Same.commit proof prf)
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            handle Same.SAME => AbsP (s, t, proof prf))
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      | proof (prf % t) =
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          (proof prf % Same.commit (Same.map_option term) t
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            handle Same.SAME => prf % Same.map_option term t)
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      | proof (prf1 %% prf2) =
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          (proof prf1 %% Same.commit proof prf2
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            handle Same.SAME => prf1 %% proof prf2)
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      | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
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      | proof (OfClass (T, c)) = OfClass (typ T, c)
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      | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
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      | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
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      | proof (PThm (i, ((a, prop, SOME Ts), body))) = PThm (i, ((a, prop, SOME (typs Ts)), body))
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      | proof _ = raise Same.SAME;
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  in Same.commit proof 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.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.SAME => NONE)
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   (fn T => SOME (same (op =) g T) handle Same.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) =
wenzelm@20147
   312
      fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
wenzelm@20159
   313
  | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
wenzelm@31943
   314
  | fold_proof_terms _ g (OfClass (T, _)) = g T
wenzelm@28828
   315
  | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
wenzelm@28828
   316
  | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
wenzelm@28803
   317
  | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
wenzelm@20147
   318
  | fold_proof_terms _ _ _ = I;
berghofe@11519
   319
wenzelm@20300
   320
fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
berghofe@12868
   321
berghofe@13744
   322
fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
berghofe@13749
   323
  | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
wenzelm@28803
   324
  | size_of_proof (prf % _) = 1 + size_of_proof prf
berghofe@13744
   325
  | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
berghofe@13744
   326
  | size_of_proof _ = 1;
berghofe@13744
   327
wenzelm@28803
   328
fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
wenzelm@31943
   329
  | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
berghofe@12907
   330
  | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
wenzelm@28828
   331
  | change_type opTs (Promise _) = error "change_type: unexpected promise"
wenzelm@28803
   332
  | change_type opTs (PThm (i, ((name, prop, _), body))) = PThm (i, ((name, prop, opTs), body))
berghofe@12907
   333
  | change_type _ prf = prf;
berghofe@12907
   334
berghofe@11519
   335
berghofe@11519
   336
(***** utilities *****)
berghofe@11519
   337
berghofe@11519
   338
fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
berghofe@11519
   339
  | strip_abs _ t = t;
berghofe@11519
   340
skalberg@15570
   341
fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
berghofe@11519
   342
berghofe@11519
   343
wenzelm@21646
   344
(*Abstraction of a proof term over its occurrences of v,
berghofe@11519
   345
    which must contain no loose bound variables.
berghofe@11519
   346
  The resulting proof term is ready to become the body of an Abst.*)
berghofe@11519
   347
berghofe@11519
   348
fun prf_abstract_over v =
berghofe@11519
   349
  let
berghofe@11715
   350
    fun abst' lev u = if v aconv u then Bound lev else
berghofe@11715
   351
      (case u of
berghofe@11715
   352
         Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
wenzelm@32019
   353
       | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
wenzelm@32019
   354
       | _ => raise Same.SAME)
wenzelm@32019
   355
    and absth' lev t = (abst' lev t handle Same.SAME => t);
berghofe@11519
   356
berghofe@11715
   357
    fun abst lev (AbsP (a, t, prf)) =
wenzelm@32024
   358
          (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
wenzelm@32019
   359
           handle Same.SAME => AbsP (a, t, abst lev prf))
berghofe@11715
   360
      | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
berghofe@11715
   361
      | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
wenzelm@32019
   362
          handle Same.SAME => prf1 %% abst lev prf2)
skalberg@15570
   363
      | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
wenzelm@32024
   364
          handle Same.SAME => prf % Same.map_option (abst' lev) t)
wenzelm@32019
   365
      | abst _ _ = raise Same.SAME
wenzelm@32024
   366
    and absth lev prf = (abst lev prf handle Same.SAME => prf);
berghofe@11519
   367
berghofe@11715
   368
  in absth 0 end;
berghofe@11519
   369
berghofe@11519
   370
berghofe@11519
   371
(*increments a proof term's non-local bound variables
berghofe@11519
   372
  required when moving a proof term within abstractions
berghofe@11519
   373
     inc is  increment for bound variables
berghofe@11519
   374
     lev is  level at which a bound variable is considered 'loose'*)
berghofe@11519
   375
berghofe@11519
   376
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
berghofe@11519
   377
berghofe@11715
   378
fun prf_incr_bv' incP inct Plev tlev (PBound i) =
wenzelm@32019
   379
      if i >= Plev then PBound (i+incP) else raise Same.SAME
berghofe@11715
   380
  | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
wenzelm@32024
   381
      (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
wenzelm@32019
   382
         prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
berghofe@11715
   383
           AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
berghofe@11715
   384
  | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
berghofe@11715
   385
      Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
wenzelm@21646
   386
  | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
berghofe@11715
   387
      (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
wenzelm@32019
   388
       handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
wenzelm@21646
   389
  | prf_incr_bv' incP inct Plev tlev (prf % t) =
skalberg@15570
   390
      (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
wenzelm@32024
   391
       handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
wenzelm@32019
   392
  | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
berghofe@11715
   393
and prf_incr_bv incP inct Plev tlev prf =
wenzelm@32019
   394
      (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
berghofe@11519
   395
berghofe@11519
   396
fun incr_pboundvars  0 0 prf = prf
berghofe@11519
   397
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   398
berghofe@11519
   399
berghofe@11615
   400
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
skalberg@15531
   401
  | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
skalberg@15531
   402
  | prf_loose_bvar1 (_ % NONE) _ = true
skalberg@15531
   403
  | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
skalberg@15531
   404
  | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
berghofe@11519
   405
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
berghofe@11519
   406
  | prf_loose_bvar1 _ _ = false;
berghofe@11519
   407
berghofe@11519
   408
fun prf_loose_Pbvar1 (PBound i) k = i = k
berghofe@11615
   409
  | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
berghofe@11615
   410
  | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   411
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
berghofe@11519
   412
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
berghofe@11519
   413
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   414
berghofe@12279
   415
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
wenzelm@17492
   416
      if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
berghofe@12279
   417
  | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
berghofe@12279
   418
      prf_add_loose_bnos plev tlev prf2
berghofe@12279
   419
        (prf_add_loose_bnos plev tlev prf1 p)
berghofe@12279
   420
  | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
berghofe@12279
   421
      prf_add_loose_bnos plev tlev prf (case opt of
wenzelm@17492
   422
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   423
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   424
  | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
berghofe@12279
   425
      prf_add_loose_bnos (plev+1) tlev prf (case opt of
wenzelm@17492
   426
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   427
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   428
  | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
berghofe@12279
   429
      prf_add_loose_bnos plev (tlev+1) prf p
berghofe@12279
   430
  | prf_add_loose_bnos _ _ _ _ = ([], []);
berghofe@12279
   431
berghofe@11519
   432
berghofe@11519
   433
(**** substitutions ****)
berghofe@11519
   434
wenzelm@31977
   435
fun del_conflicting_tvars envT T = Term_Subst.instantiateT
wenzelm@19482
   436
  (map_filter (fn ixnS as (_, S) =>
haftmann@26328
   437
     (Type.lookup envT ixnS; NONE) handle TYPE _ =>
wenzelm@29270
   438
        SOME (ixnS, TFree ("'dummy", S))) (OldTerm.typ_tvars T)) T;
berghofe@18316
   439
wenzelm@31977
   440
fun del_conflicting_vars env t = Term_Subst.instantiate
wenzelm@19482
   441
  (map_filter (fn ixnS as (_, S) =>
wenzelm@32019
   442
     (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
wenzelm@29270
   443
        SOME (ixnS, TFree ("'dummy", S))) (OldTerm.term_tvars t),
wenzelm@19482
   444
   map_filter (fn Var (ixnT as (_, T)) =>
berghofe@18316
   445
     (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
wenzelm@29265
   446
        SOME (ixnT, Free ("dummy", T))) (OldTerm.term_vars t)) t;
berghofe@18316
   447
berghofe@11519
   448
fun norm_proof env =
berghofe@11519
   449
  let
wenzelm@32019
   450
    val envT = Envir.type_env env;
berghofe@18316
   451
    fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
berghofe@18316
   452
    fun htype f t = f env t handle TYPE (s, _, _) =>
berghofe@18316
   453
      (msg s; f env (del_conflicting_vars env t));
berghofe@18316
   454
    fun htypeT f T = f envT T handle TYPE (s, _, _) =>
berghofe@18316
   455
      (msg s; f envT (del_conflicting_tvars envT T));
berghofe@18316
   456
    fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
berghofe@18316
   457
      (msg s; f envT (map (del_conflicting_tvars envT) Ts));
wenzelm@32024
   458
wenzelm@32019
   459
    fun norm (Abst (s, T, prf)) =
wenzelm@32024
   460
          (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
wenzelm@32019
   461
            handle Same.SAME => Abst (s, T, norm prf))
wenzelm@32019
   462
      | norm (AbsP (s, t, prf)) =
wenzelm@32024
   463
          (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
wenzelm@32019
   464
            handle Same.SAME => AbsP (s, t, norm prf))
wenzelm@32019
   465
      | norm (prf % t) =
wenzelm@32019
   466
          (norm prf % Option.map (htype Envir.norm_term) t
wenzelm@32024
   467
            handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
wenzelm@32019
   468
      | norm (prf1 %% prf2) =
wenzelm@32019
   469
          (norm prf1 %% Same.commit norm prf2
wenzelm@32019
   470
            handle Same.SAME => prf1 %% norm prf2)
wenzelm@32019
   471
      | norm (PAxm (s, prop, Ts)) =
wenzelm@32024
   472
          PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
wenzelm@32019
   473
      | norm (OfClass (T, c)) =
wenzelm@32019
   474
          OfClass (htypeT Envir.norm_type_same T, c)
wenzelm@32019
   475
      | norm (Oracle (s, prop, Ts)) =
wenzelm@32024
   476
          Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
wenzelm@32019
   477
      | norm (Promise (i, prop, Ts)) =
wenzelm@32019
   478
          Promise (i, prop, htypeTs Envir.norm_types_same Ts)
wenzelm@28803
   479
      | norm (PThm (i, ((s, t, Ts), body))) =
wenzelm@32024
   480
          PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
wenzelm@32019
   481
      | norm _ = raise Same.SAME;
wenzelm@32019
   482
  in Same.commit norm end;
berghofe@11519
   483
wenzelm@28803
   484
berghofe@11519
   485
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   486
berghofe@11519
   487
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   488
  | remove_types (t $ u) = remove_types t $ remove_types u
berghofe@11519
   489
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   490
  | remove_types t = t;
berghofe@11519
   491
wenzelm@32032
   492
fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
wenzelm@32032
   493
  Envir.Envir {maxidx = maxidx, tenv = Vartab.map (apsnd remove_types) tenv, tyenv = tyenv};
berghofe@11519
   494
berghofe@11519
   495
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   496
wenzelm@28803
   497
berghofe@11519
   498
(**** substitution of bound variables ****)
berghofe@11519
   499
berghofe@11519
   500
fun prf_subst_bounds args prf =
berghofe@11519
   501
  let
berghofe@11519
   502
    val n = length args;
berghofe@11519
   503
    fun subst' lev (Bound i) =
wenzelm@32019
   504
         (if i<lev then raise Same.SAME    (*var is locally bound*)
wenzelm@30146
   505
          else  incr_boundvars lev (nth args (i-lev))
wenzelm@30146
   506
                  handle Subscript => Bound (i-n))  (*loose: change it*)
berghofe@11519
   507
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   508
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
wenzelm@32019
   509
          handle Same.SAME => f $ subst' lev t)
wenzelm@32019
   510
      | subst' _ _ = raise Same.SAME
wenzelm@32019
   511
    and substh' lev t = (subst' lev t handle Same.SAME => t);
berghofe@11519
   512
wenzelm@32024
   513
    fun subst lev (AbsP (a, t, body)) = (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
wenzelm@32019
   514
          handle Same.SAME => AbsP (a, t, subst lev body))
berghofe@11519
   515
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11615
   516
      | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
wenzelm@32019
   517
          handle Same.SAME => prf %% subst lev prf')
skalberg@15570
   518
      | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
wenzelm@32024
   519
          handle Same.SAME => prf % Same.map_option (subst' lev) t)
wenzelm@32019
   520
      | subst _ _ = raise Same.SAME
wenzelm@32024
   521
    and substh lev prf = (subst lev prf handle Same.SAME => prf);
berghofe@11519
   522
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   523
berghofe@11519
   524
fun prf_subst_pbounds args prf =
berghofe@11519
   525
  let
berghofe@11519
   526
    val n = length args;
berghofe@11519
   527
    fun subst (PBound i) Plev tlev =
wenzelm@32019
   528
         (if i < Plev then raise Same.SAME    (*var is locally bound*)
wenzelm@30146
   529
          else incr_pboundvars Plev tlev (nth args (i-Plev))
berghofe@11519
   530
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   531
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   532
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11615
   533
      | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
wenzelm@32019
   534
          handle Same.SAME => prf %% subst prf' Plev tlev)
berghofe@11615
   535
      | subst (prf % t) Plev tlev = subst prf Plev tlev % t
wenzelm@32019
   536
      | subst  prf _ _ = raise Same.SAME
wenzelm@32019
   537
    and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
berghofe@11519
   538
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   539
berghofe@11519
   540
berghofe@11519
   541
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   542
berghofe@11519
   543
fun frzT names =
haftmann@17325
   544
  map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
berghofe@11519
   545
berghofe@11519
   546
fun thawT names =
haftmann@17325
   547
  map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
skalberg@15531
   548
      NONE => TFree (s, xs)
skalberg@15531
   549
    | SOME ixn => TVar (ixn, xs));
berghofe@11519
   550
berghofe@11519
   551
fun freeze names names' (t $ u) =
berghofe@11519
   552
      freeze names names' t $ freeze names names' u
berghofe@11519
   553
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   554
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   555
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   556
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   557
  | freeze names names' (Var (ixn, T)) =
haftmann@17325
   558
      Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
berghofe@11519
   559
  | freeze names names' t = t;
berghofe@11519
   560
berghofe@11519
   561
fun thaw names names' (t $ u) =
berghofe@11519
   562
      thaw names names' t $ thaw names names' u
berghofe@11519
   563
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   564
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   565
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
wenzelm@21646
   566
  | thaw names names' (Free (s, T)) =
berghofe@11519
   567
      let val T' = thawT names' T
haftmann@17325
   568
      in case AList.lookup (op =) names s of
skalberg@15531
   569
          NONE => Free (s, T')
skalberg@15531
   570
        | SOME ixn => Var (ixn, T')
berghofe@11519
   571
      end
berghofe@11519
   572
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   573
  | thaw names names' t = t;
berghofe@11519
   574
berghofe@11519
   575
fun freeze_thaw_prf prf =
berghofe@11519
   576
  let
berghofe@11519
   577
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
wenzelm@20147
   578
      (fn t => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   579
         (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
wenzelm@29261
   580
          Term.add_var_names t vs, Term.add_tvar_names t Tvs))
wenzelm@20147
   581
      (fn T => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   582
         (fs, Term.add_tfree_namesT T Tfs,
wenzelm@29261
   583
          vs, Term.add_tvar_namesT T Tvs))
wenzelm@20147
   584
      prf ([], [], [], []);
wenzelm@29261
   585
    val names = vs ~~ Name.variant_list fs (map fst vs);
wenzelm@20071
   586
    val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
berghofe@11519
   587
    val rnames = map swap names;
berghofe@11519
   588
    val rnames' = map swap names';
berghofe@11519
   589
  in
berghofe@11519
   590
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   591
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   592
  end;
berghofe@11519
   593
berghofe@11519
   594
berghofe@11519
   595
(***** implication introduction *****)
berghofe@11519
   596
berghofe@11519
   597
fun implies_intr_proof h prf =
berghofe@11519
   598
  let
wenzelm@32019
   599
    fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
berghofe@11519
   600
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
wenzelm@32024
   601
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
berghofe@11615
   602
      | abshyp i (prf % t) = abshyp i prf % t
wenzelm@32024
   603
      | abshyp i (prf1 %% prf2) =
wenzelm@32024
   604
          (abshyp i prf1 %% abshyph i prf2
wenzelm@32024
   605
            handle Same.SAME => prf1 %% abshyp i prf2)
wenzelm@32019
   606
      | abshyp _ _ = raise Same.SAME
wenzelm@32024
   607
    and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
berghofe@11519
   608
  in
skalberg@15531
   609
    AbsP ("H", NONE (*h*), abshyph 0 prf)
berghofe@11519
   610
  end;
berghofe@11519
   611
berghofe@11519
   612
berghofe@11519
   613
(***** forall introduction *****)
berghofe@11519
   614
skalberg@15531
   615
fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
berghofe@11519
   616
berghofe@11519
   617
berghofe@11519
   618
(***** varify *****)
berghofe@11519
   619
berghofe@11519
   620
fun varify_proof t fixed prf =
berghofe@11519
   621
  let
wenzelm@19304
   622
    val fs = Term.fold_types (Term.fold_atyps
wenzelm@19304
   623
      (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
wenzelm@29261
   624
    val used = Name.context
wenzelm@29261
   625
      |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
wenzelm@32024
   626
    val fmap = fs ~~ #1 (Name.variants (map fst fs) used);
berghofe@11519
   627
    fun thaw (f as (a, S)) =
haftmann@17314
   628
      (case AList.lookup (op =) fmap f of
skalberg@15531
   629
        NONE => TFree f
skalberg@15531
   630
      | SOME b => TVar ((b, 0), S));
wenzelm@28803
   631
  in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
berghofe@11519
   632
berghofe@11519
   633
berghofe@11519
   634
local
berghofe@11519
   635
berghofe@11519
   636
fun new_name (ix, (pairs,used)) =
wenzelm@20071
   637
  let val v = Name.variant used (string_of_indexname ix)
berghofe@11519
   638
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   639
haftmann@17325
   640
fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
skalberg@15531
   641
    NONE => TVar (ix, sort)
skalberg@15531
   642
  | SOME name => TFree (name, sort));
berghofe@11519
   643
berghofe@11519
   644
in
berghofe@11519
   645
berghofe@11519
   646
fun freezeT t prf =
berghofe@11519
   647
  let
wenzelm@29270
   648
    val used = OldTerm.it_term_types OldTerm.add_typ_tfree_names (t, [])
wenzelm@29270
   649
    and tvars = map #1 (OldTerm.it_term_types OldTerm.add_typ_tvars (t, []));
wenzelm@23178
   650
    val (alist, _) = List.foldr new_name ([], used) tvars;
berghofe@11519
   651
  in
berghofe@11519
   652
    (case alist of
berghofe@11519
   653
      [] => prf (*nothing to do!*)
berghofe@11519
   654
    | _ =>
berghofe@11519
   655
      let val frzT = map_type_tvar (freeze_one alist)
wenzelm@20548
   656
      in map_proof_terms (map_types frzT) frzT prf end)
berghofe@11519
   657
  end;
berghofe@11519
   658
berghofe@11519
   659
end;
berghofe@11519
   660
berghofe@11519
   661
berghofe@11519
   662
(***** rotate assumptions *****)
berghofe@11519
   663
berghofe@11519
   664
fun rotate_proof Bs Bi m prf =
berghofe@11519
   665
  let
berghofe@11519
   666
    val params = Term.strip_all_vars Bi;
berghofe@11519
   667
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   668
    val i = length asms;
berghofe@11519
   669
    val j = length Bs;
berghofe@11519
   670
  in
berghofe@11519
   671
    mk_AbsP (j+1, proof_combP (prf, map PBound
wenzelm@23178
   672
      (j downto 1) @ [mk_Abst params (mk_AbsP (i,
berghofe@11519
   673
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
wenzelm@23178
   674
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
berghofe@11519
   675
  end;
berghofe@11519
   676
berghofe@11519
   677
berghofe@11519
   678
(***** permute premises *****)
berghofe@11519
   679
berghofe@11519
   680
fun permute_prems_prf prems j k prf =
berghofe@11519
   681
  let val n = length prems
berghofe@11519
   682
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   683
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   684
  end;
berghofe@11519
   685
berghofe@11519
   686
wenzelm@19908
   687
(***** generalization *****)
wenzelm@19908
   688
wenzelm@20000
   689
fun generalize (tfrees, frees) idx =
wenzelm@20000
   690
  map_proof_terms_option
wenzelm@31977
   691
    (Term_Subst.generalize_option (tfrees, frees) idx)
wenzelm@31977
   692
    (Term_Subst.generalizeT_option tfrees idx);
wenzelm@19908
   693
wenzelm@19908
   694
berghofe@11519
   695
(***** instantiation *****)
berghofe@11519
   696
wenzelm@20000
   697
fun instantiate (instT, inst) =
wenzelm@20000
   698
  map_proof_terms_option
wenzelm@31977
   699
    (Term_Subst.instantiate_option (instT, map (apsnd remove_types) inst))
wenzelm@31977
   700
    (Term_Subst.instantiateT_option instT);
berghofe@11519
   701
berghofe@11519
   702
berghofe@11519
   703
(***** lifting *****)
berghofe@11519
   704
berghofe@11519
   705
fun lift_proof Bi inc prop prf =
berghofe@11519
   706
  let
wenzelm@32024
   707
    fun lift'' Us Ts t =
wenzelm@32024
   708
      strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   709
berghofe@11715
   710
    fun lift' Us Ts (Abst (s, T, prf)) =
wenzelm@32024
   711
          (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
wenzelm@32019
   712
           handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
berghofe@11715
   713
      | lift' Us Ts (AbsP (s, t, prf)) =
wenzelm@32024
   714
          (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
wenzelm@32019
   715
           handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
skalberg@15570
   716
      | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
wenzelm@32024
   717
          handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
berghofe@11715
   718
      | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
wenzelm@32019
   719
          handle Same.SAME => prf1 %% lift' Us Ts prf2)
berghofe@11715
   720
      | lift' _ _ (PAxm (s, prop, Ts)) =
wenzelm@32024
   721
          PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
wenzelm@31943
   722
      | lift' _ _ (OfClass (T, c)) =
wenzelm@32024
   723
          OfClass (Logic.incr_tvar_same inc T, c)
wenzelm@28828
   724
      | lift' _ _ (Oracle (s, prop, Ts)) =
wenzelm@32024
   725
          Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
wenzelm@28828
   726
      | lift' _ _ (Promise (i, prop, Ts)) =
wenzelm@32024
   727
          Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
wenzelm@28803
   728
      | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
wenzelm@32024
   729
          PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
wenzelm@32019
   730
      | lift' _ _ _ = raise Same.SAME
wenzelm@32019
   731
    and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
berghofe@11519
   732
wenzelm@18030
   733
    val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
berghofe@11519
   734
    val k = length ps;
berghofe@11519
   735
wenzelm@23178
   736
    fun mk_app b (i, j, prf) =
berghofe@11615
   737
          if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
berghofe@11519
   738
berghofe@11519
   739
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
wenzelm@20147
   740
            AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
wenzelm@21646
   741
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
wenzelm@20147
   742
            Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11715
   743
      | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
wenzelm@23178
   744
            map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
berghofe@11519
   745
              (i + k - 1 downto i));
berghofe@11519
   746
  in
berghofe@11519
   747
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   748
  end;
berghofe@11519
   749
wenzelm@32027
   750
fun incr_indexes i =
wenzelm@32027
   751
  map_proof_terms_option
wenzelm@32027
   752
    (Same.capture (Logic.incr_indexes_same ([], i)))
wenzelm@32027
   753
    (Same.capture (Logic.incr_tvar_same i));
wenzelm@32027
   754
berghofe@11519
   755
berghofe@11519
   756
(***** proof by assumption *****)
berghofe@11519
   757
berghofe@23296
   758
fun mk_asm_prf t i m =
berghofe@23296
   759
  let
berghofe@23296
   760
    fun imp_prf _ i 0 = PBound i
berghofe@23296
   761
      | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
berghofe@23296
   762
      | imp_prf _ i _ = PBound i;
berghofe@23296
   763
    fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
berghofe@23296
   764
      | all_prf t = imp_prf t (~i) m
berghofe@23296
   765
  in all_prf t end;
berghofe@11519
   766
berghofe@11519
   767
fun assumption_proof Bs Bi n prf =
berghofe@11519
   768
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@23296
   769
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
berghofe@11519
   770
berghofe@11519
   771
berghofe@11519
   772
(***** Composition of object rule with proof state *****)
berghofe@11519
   773
berghofe@11519
   774
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
skalberg@15531
   775
      AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
berghofe@11519
   776
  | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
skalberg@15531
   777
      Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
berghofe@11519
   778
  | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
wenzelm@19304
   779
      map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
berghofe@11519
   780
berghofe@23296
   781
fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
berghofe@11519
   782
  let
berghofe@11519
   783
    val la = length newAs;
berghofe@11519
   784
    val lb = length Bs;
berghofe@11519
   785
  in
berghofe@11519
   786
    mk_AbsP (lb+la, proof_combP (sprf,
berghofe@11615
   787
      map PBound (lb + la - 1 downto la)) %%
berghofe@23296
   788
        proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
wenzelm@18485
   789
          map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
wenzelm@18485
   790
            (oldAs ~~ (la - 1 downto 0))))
berghofe@11519
   791
  end;
berghofe@11519
   792
berghofe@11519
   793
berghofe@11519
   794
(***** axioms for equality *****)
berghofe@11519
   795
wenzelm@14854
   796
val aT = TFree ("'a", []);
wenzelm@14854
   797
val bT = TFree ("'b", []);
berghofe@11519
   798
val x = Free ("x", aT);
berghofe@11519
   799
val y = Free ("y", aT);
berghofe@11519
   800
val z = Free ("z", aT);
berghofe@11519
   801
val A = Free ("A", propT);
berghofe@11519
   802
val B = Free ("B", propT);
berghofe@11519
   803
val f = Free ("f", aT --> bT);
berghofe@11519
   804
val g = Free ("g", aT --> bT);
berghofe@11519
   805
berghofe@11519
   806
local open Logic in
berghofe@11519
   807
berghofe@11519
   808
val equality_axms =
berghofe@11519
   809
  [("reflexive", mk_equals (x, x)),
berghofe@11519
   810
   ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
berghofe@11519
   811
   ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
berghofe@11519
   812
   ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
berghofe@11519
   813
   ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
wenzelm@27330
   814
   ("abstract_rule", mk_implies
wenzelm@27330
   815
      (all x (mk_equals (f $ x, g $ x)), mk_equals (lambda x (f $ x), lambda x (g $ x)))),
wenzelm@27330
   816
   ("combination", list_implies
wenzelm@27330
   817
      ([mk_equals (f, g), mk_equals (x, y)], mk_equals (f $ x, g $ y)))];
berghofe@11519
   818
berghofe@11519
   819
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   820
  equal_elim_axm, abstract_rule_axm, combination_axm] =
wenzelm@26424
   821
    map (fn (s, t) => PAxm ("Pure." ^ s, varify t, NONE)) equality_axms;
berghofe@11519
   822
berghofe@11519
   823
end;
berghofe@11519
   824
skalberg@15531
   825
val reflexive = reflexive_axm % NONE;
berghofe@11519
   826
wenzelm@26424
   827
fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
skalberg@15531
   828
  | symmetric prf = symmetric_axm % NONE % NONE %% prf;
berghofe@11519
   829
wenzelm@26424
   830
fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
wenzelm@26424
   831
  | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
berghofe@11519
   832
  | transitive u (Type ("prop", [])) prf1 prf2 =
skalberg@15531
   833
      transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
berghofe@11519
   834
  | transitive u T prf1 prf2 =
skalberg@15531
   835
      transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
berghofe@11519
   836
berghofe@11519
   837
fun abstract_rule x a prf =
skalberg@15531
   838
  abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
berghofe@11519
   839
wenzelm@26424
   840
fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
wenzelm@19502
   841
      is_some f orelse check_comb prf
wenzelm@26424
   842
  | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
berghofe@11519
   843
      check_comb prf1 andalso check_comb prf2
wenzelm@26424
   844
  | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
berghofe@11519
   845
  | check_comb _ = false;
berghofe@11519
   846
berghofe@11519
   847
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   848
  let
berghofe@11519
   849
    val f = Envir.beta_norm f;
berghofe@11519
   850
    val g = Envir.beta_norm g;
berghofe@11519
   851
    val prf =  if check_comb prf1 then
skalberg@15531
   852
        combination_axm % NONE % NONE
berghofe@11519
   853
      else (case prf1 of
wenzelm@26424
   854
          PAxm ("Pure.reflexive", _, _) % _ =>
skalberg@15531
   855
            combination_axm %> remove_types f % NONE
berghofe@11615
   856
        | _ => combination_axm %> remove_types f %> remove_types g)
berghofe@11519
   857
  in
berghofe@11519
   858
    (case T of
berghofe@11615
   859
       Type ("fun", _) => prf %
berghofe@11519
   860
         (case head_of f of
skalberg@15531
   861
            Abs _ => SOME (remove_types t)
skalberg@15531
   862
          | Var _ => SOME (remove_types t)
skalberg@15531
   863
          | _ => NONE) %
berghofe@11519
   864
         (case head_of g of
skalberg@15531
   865
            Abs _ => SOME (remove_types u)
skalberg@15531
   866
          | Var _ => SOME (remove_types u)
skalberg@15531
   867
          | _ => NONE) %% prf1 %% prf2
skalberg@15531
   868
     | _ => prf % NONE % NONE %% prf1 %% prf2)
berghofe@11519
   869
  end;
berghofe@11519
   870
berghofe@11519
   871
fun equal_intr A B prf1 prf2 =
berghofe@11615
   872
  equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   873
berghofe@11519
   874
fun equal_elim A B prf1 prf2 =
berghofe@11615
   875
  equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   876
berghofe@11519
   877
berghofe@11519
   878
(***** axioms and theorems *****)
berghofe@11519
   879
wenzelm@28803
   880
val proofs = ref 2;
wenzelm@28803
   881
berghofe@28812
   882
fun vars_of t = map Var (rev (Term.add_vars t []));
berghofe@28812
   883
fun frees_of t = map Free (rev (Term.add_frees t []));
berghofe@11519
   884
berghofe@11519
   885
fun test_args _ [] = true
berghofe@11519
   886
  | test_args is (Bound i :: ts) =
wenzelm@17492
   887
      not (member (op =) is i) andalso test_args (i :: is) ts
berghofe@11519
   888
  | test_args _ _ = false;
berghofe@11519
   889
berghofe@11519
   890
fun is_fun (Type ("fun", _)) = true
berghofe@11519
   891
  | is_fun (TVar _) = true
berghofe@11519
   892
  | is_fun _ = false;
berghofe@11519
   893
berghofe@11519
   894
fun add_funvars Ts (vs, t) =
berghofe@11519
   895
  if is_fun (fastype_of1 (Ts, t)) then
wenzelm@19482
   896
    vs union map_filter (fn Var (ixn, T) =>
skalberg@15531
   897
      if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t)
berghofe@11519
   898
  else vs;
berghofe@11519
   899
berghofe@11519
   900
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
berghofe@11519
   901
      add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
berghofe@11519
   902
  | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
berghofe@11519
   903
      add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
berghofe@12041
   904
  | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
berghofe@12041
   905
  | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
berghofe@12041
   906
and add_npvars' Ts (vs, t) = (case strip_comb t of
berghofe@11519
   907
    (Var (ixn, _), ts) => if test_args [] ts then vs
haftmann@17314
   908
      else Library.foldl (add_npvars' Ts)
haftmann@17314
   909
        (AList.update (op =) (ixn,
haftmann@17314
   910
          Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
skalberg@15570
   911
  | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
skalberg@15570
   912
  | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
berghofe@11519
   913
berghofe@11519
   914
fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
berghofe@11519
   915
  | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
berghofe@11519
   916
  | prop_vars t = (case strip_comb t of
berghofe@11519
   917
      (Var (ixn, _), _) => [ixn] | _ => []);
berghofe@11519
   918
berghofe@11519
   919
fun is_proj t =
berghofe@11519
   920
  let
berghofe@11519
   921
    fun is_p i t = (case strip_comb t of
berghofe@11519
   922
        (Bound j, []) => false
berghofe@11519
   923
      | (Bound j, ts) => j >= i orelse exists (is_p i) ts
berghofe@11519
   924
      | (Abs (_, _, u), _) => is_p (i+1) u
berghofe@11519
   925
      | (_, ts) => exists (is_p i) ts)
berghofe@11519
   926
  in (case strip_abs_body t of
berghofe@11519
   927
        Bound _ => true
berghofe@11519
   928
      | t' => is_p 0 t')
berghofe@11519
   929
  end;
berghofe@11519
   930
wenzelm@21646
   931
fun needed_vars prop =
haftmann@20853
   932
  Library.foldl (op union)
haftmann@20853
   933
    ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))) union
berghofe@11519
   934
  prop_vars prop;
berghofe@11519
   935
berghofe@11519
   936
fun gen_axm_proof c name prop =
berghofe@11519
   937
  let
berghofe@11519
   938
    val nvs = needed_vars prop;
berghofe@11519
   939
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
   940
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
berghofe@28812
   941
      map SOME (frees_of prop);
berghofe@11519
   942
  in
skalberg@15531
   943
    proof_combt' (c (name, prop, NONE), args)
berghofe@11519
   944
  end;
berghofe@11519
   945
berghofe@11519
   946
val axm_proof = gen_axm_proof PAxm;
berghofe@17017
   947
berghofe@17017
   948
val dummy = Const (Term.dummy_patternN, dummyT);
berghofe@17017
   949
berghofe@17017
   950
fun oracle_proof name prop =
wenzelm@30716
   951
  if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
wenzelm@30716
   952
  else ((name, prop), gen_axm_proof Oracle name prop);
berghofe@11519
   953
wenzelm@17492
   954
fun shrink_proof thy =
wenzelm@17492
   955
  let
wenzelm@17492
   956
    fun shrink ls lev (prf as Abst (a, T, body)) =
wenzelm@17492
   957
          let val (b, is, ch, body') = shrink ls (lev+1) body
wenzelm@26631
   958
          in (b, is, ch, if ch then Abst (a, T, body') else prf) end
wenzelm@17492
   959
      | shrink ls lev (prf as AbsP (a, t, body)) =
wenzelm@17492
   960
          let val (b, is, ch, body') = shrink (lev::ls) lev body
wenzelm@19482
   961
          in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
wenzelm@26631
   962
            ch, if ch then AbsP (a, t, body') else prf)
wenzelm@17492
   963
          end
wenzelm@17492
   964
      | shrink ls lev prf =
wenzelm@17492
   965
          let val (is, ch, _, prf') = shrink' ls lev [] [] prf
wenzelm@17492
   966
          in (false, is, ch, prf') end
wenzelm@17492
   967
    and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
wenzelm@17492
   968
          let
wenzelm@17492
   969
            val p as (_, is', ch', prf') = shrink ls lev prf2;
wenzelm@17492
   970
            val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
wenzelm@17492
   971
          in (is union is', ch orelse ch', ts',
wenzelm@17492
   972
              if ch orelse ch' then prf'' %% prf' else prf)
wenzelm@17492
   973
          end
wenzelm@17492
   974
      | shrink' ls lev ts prfs (prf as prf1 % t) =
wenzelm@17492
   975
          let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
wenzelm@17492
   976
          in (is, ch orelse ch', ts',
wenzelm@26631
   977
              if ch orelse ch' then prf' % t' else prf) end
wenzelm@17492
   978
      | shrink' ls lev ts prfs (prf as PBound i) =
wenzelm@30146
   979
          (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
haftmann@18928
   980
             orelse has_duplicates (op =)
haftmann@18928
   981
               (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
wenzelm@17492
   982
             orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
wenzelm@31903
   983
      | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
wenzelm@31903
   984
      | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
wenzelm@31943
   985
      | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
wenzelm@17492
   986
      | shrink' ls lev ts prfs prf =
wenzelm@17492
   987
          let
wenzelm@28803
   988
            val prop =
wenzelm@28803
   989
              (case prf of
wenzelm@28803
   990
                PAxm (_, prop, _) => prop
wenzelm@28803
   991
              | Oracle (_, prop, _) => prop
wenzelm@28803
   992
              | Promise (_, prop, _) => prop
wenzelm@28803
   993
              | PThm (_, ((_, prop, _), _)) => prop
wenzelm@28319
   994
              | _ => error "shrink: proof not in normal form");
wenzelm@17492
   995
            val vs = vars_of prop;
wenzelm@19012
   996
            val (ts', ts'') = chop (length vs) ts;
wenzelm@17492
   997
            val insts = Library.take (length ts', map (fst o dest_Var) vs) ~~ ts';
wenzelm@17492
   998
            val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
wenzelm@17492
   999
              insert (op =) ixn (case AList.lookup (op =) insts ixn of
wenzelm@17492
  1000
                  SOME (SOME t) => if is_proj t then ixns union ixns' else ixns'
wenzelm@17492
  1001
                | _ => ixns union ixns'))
wenzelm@17492
  1002
                  (needed prop ts'' prfs, add_npvars false true [] ([], prop));
wenzelm@17492
  1003
            val insts' = map
wenzelm@17492
  1004
              (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
wenzelm@17492
  1005
                | (_, x) => (false, x)) insts
wenzelm@17492
  1006
          in ([], false, insts' @ map (pair false) ts'', prf) end
wenzelm@17492
  1007
    and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
wenzelm@17492
  1008
          (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
wenzelm@17492
  1009
      | needed (Var (ixn, _)) (_::_) _ = [ixn]
wenzelm@17492
  1010
      | needed _ _ _ = [];
wenzelm@17492
  1011
  in shrink end;
berghofe@11519
  1012
berghofe@11519
  1013
berghofe@11519
  1014
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
  1015
berghofe@11519
  1016
exception PMatch;
berghofe@11519
  1017
berghofe@11519
  1018
(** see pattern.ML **)
berghofe@11519
  1019
skalberg@15570
  1020
fun flt (i: int) = List.filter (fn n => n < i);
berghofe@12279
  1021
berghofe@12279
  1022
fun fomatch Ts tymatch j =
berghofe@11519
  1023
  let
berghofe@11519
  1024
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
  1025
        (Var (ixn, T), t)  =>
berghofe@12279
  1026
          if j>0 andalso not (null (flt j (loose_bnos t)))
berghofe@12279
  1027
          then raise PMatch
berghofe@12279
  1028
          else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
berghofe@12279
  1029
            (ixn, t) :: insts)
berghofe@11519
  1030
      | (Free (a, T), Free (b, U)) =>
wenzelm@20147
  1031
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
  1032
      | (Const (a, T), Const (b, U))  =>
wenzelm@20147
  1033
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
  1034
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@12279
  1035
      | (Bound i, Bound j) => if i=j then instsp else raise PMatch
berghofe@11519
  1036
      | _ => raise PMatch
berghofe@11519
  1037
  in mtch end;
berghofe@11519
  1038
berghofe@12279
  1039
fun match_proof Ts tymatch =
berghofe@11519
  1040
  let
skalberg@15531
  1041
    fun optmatch _ inst (NONE, _) = inst
skalberg@15531
  1042
      | optmatch _ _ (SOME _, NONE) = raise PMatch
skalberg@15531
  1043
      | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
berghofe@12279
  1044
berghofe@12279
  1045
    fun matcht Ts j (pinst, tinst) (t, u) =
berghofe@12279
  1046
      (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
berghofe@12279
  1047
    fun matchT (pinst, (tyinsts, insts)) p =
berghofe@12279
  1048
      (pinst, (tymatch (tyinsts, K p), insts));
skalberg@15570
  1049
    fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
berghofe@12279
  1050
berghofe@12279
  1051
    fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
berghofe@12279
  1052
          if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
berghofe@12279
  1053
          else (case apfst (flt i) (apsnd (flt j)
berghofe@12279
  1054
                  (prf_add_loose_bnos 0 0 prf ([], []))) of
berghofe@12279
  1055
              ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1056
            | ([], _) => if j = 0 then
berghofe@12279
  1057
                   ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1058
                 else raise PMatch
berghofe@12279
  1059
            | _ => raise PMatch)
berghofe@12279
  1060
      | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
berghofe@12279
  1061
          optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
berghofe@12279
  1062
      | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
berghofe@12279
  1063
          mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
berghofe@12279
  1064
      | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
wenzelm@18485
  1065
          mtch (the_default dummyT opU :: Ts) i (j+1)
berghofe@12279
  1066
            (optmatch matchT inst (opT, opU)) (prf1, prf2)
berghofe@12279
  1067
      | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
wenzelm@18485
  1068
          mtch (the_default dummyT opU :: Ts) i (j+1) inst
berghofe@12279
  1069
            (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
berghofe@12279
  1070
      | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
berghofe@12279
  1071
          mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
berghofe@12279
  1072
      | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
berghofe@12279
  1073
          mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
wenzelm@28803
  1074
      | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
wenzelm@28803
  1075
          if s1 = s2 then optmatch matchTs inst (opTs, opUs)
wenzelm@28803
  1076
          else raise PMatch
wenzelm@31943
  1077
      | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
wenzelm@31903
  1078
          if c1 = c2 then matchT inst (T1, T2)
wenzelm@31903
  1079
          else raise PMatch
wenzelm@28803
  1080
      | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
wenzelm@28803
  1081
          if name1 = name2 andalso prop1 = prop2 then
berghofe@12279
  1082
            optmatch matchTs inst (opTs, opUs)
berghofe@11519
  1083
          else raise PMatch
berghofe@12279
  1084
      | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
berghofe@12279
  1085
      | mtch _ _ _ _ _ = raise PMatch
berghofe@12279
  1086
  in mtch Ts 0 0 end;
berghofe@11519
  1087
berghofe@11519
  1088
fun prf_subst (pinst, (tyinsts, insts)) =
berghofe@11519
  1089
  let
wenzelm@32035
  1090
    val substT = Envir.subst_type tyinsts;
berghofe@11519
  1091
haftmann@17325
  1092
    fun subst' lev (t as Var (ixn, _)) = (case AList.lookup (op =) insts ixn of
skalberg@15531
  1093
          NONE => t
skalberg@15531
  1094
        | SOME u => incr_boundvars lev u)
berghofe@11519
  1095
      | subst' lev (Const (s, T)) = Const (s, substT T)
berghofe@11519
  1096
      | subst' lev (Free (s, T)) = Free (s, substT T)
berghofe@11519
  1097
      | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
berghofe@11519
  1098
      | subst' lev (f $ t) = subst' lev f $ subst' lev t
berghofe@11519
  1099
      | subst' _ t = t;
berghofe@11519
  1100
berghofe@11519
  1101
    fun subst plev tlev (AbsP (a, t, body)) =
skalberg@15570
  1102
          AbsP (a, Option.map (subst' tlev) t, subst (plev+1) tlev body)
berghofe@11519
  1103
      | subst plev tlev (Abst (a, T, body)) =
skalberg@15570
  1104
          Abst (a, Option.map substT T, subst plev (tlev+1) body)
berghofe@11615
  1105
      | subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf'
skalberg@15570
  1106
      | subst plev tlev (prf % t) = subst plev tlev prf % Option.map (subst' tlev) t
haftmann@17325
  1107
      | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case AList.lookup (op =) pinst ixn of
skalberg@15531
  1108
          NONE => prf
skalberg@15531
  1109
        | SOME prf' => incr_pboundvars plev tlev prf')
wenzelm@28828
  1110
      | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Option.map (map substT) Ts)
wenzelm@31943
  1111
      | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
wenzelm@28828
  1112
      | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Option.map (map substT) Ts)
wenzelm@28828
  1113
      | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, (map substT) Ts)
wenzelm@28803
  1114
      | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
wenzelm@28803
  1115
          PThm (i, ((id, prop, Option.map (map substT) Ts), body))
wenzelm@28803
  1116
      | subst _ _ t = t;
berghofe@11519
  1117
  in subst 0 0 end;
berghofe@11519
  1118
wenzelm@21646
  1119
(*A fast unification filter: true unless the two terms cannot be unified.
berghofe@12871
  1120
  Terms must be NORMAL.  Treats all Vars as distinct. *)
berghofe@12871
  1121
fun could_unify prf1 prf2 =
berghofe@12871
  1122
  let
berghofe@12871
  1123
    fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
berghofe@12871
  1124
          could_unify prf2 prf2' andalso matchrands prf1 prf1'
skalberg@15531
  1125
      | matchrands (prf % SOME t) (prf' % SOME t') =
berghofe@12871
  1126
          Term.could_unify (t, t') andalso matchrands prf prf'
berghofe@12871
  1127
      | matchrands (prf % _) (prf' % _) = matchrands prf prf'
berghofe@12871
  1128
      | matchrands _ _ = true
berghofe@12871
  1129
berghofe@12871
  1130
    fun head_of (prf %% _) = head_of prf
berghofe@12871
  1131
      | head_of (prf % _) = head_of prf
berghofe@12871
  1132
      | head_of prf = prf
berghofe@12871
  1133
berghofe@12871
  1134
  in case (head_of prf1, head_of prf2) of
berghofe@12871
  1135
        (_, Hyp (Var _)) => true
berghofe@12871
  1136
      | (Hyp (Var _), _) => true
wenzelm@28803
  1137
      | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
wenzelm@31943
  1138
      | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
wenzelm@28803
  1139
      | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
berghofe@12871
  1140
          a = b andalso propa = propb andalso matchrands prf1 prf2
wenzelm@28803
  1141
      | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
berghofe@12871
  1142
      | (AbsP _, _) =>  true   (*because of possible eta equality*)
berghofe@12871
  1143
      | (Abst _, _) =>  true
berghofe@12871
  1144
      | (_, AbsP _) =>  true
berghofe@12871
  1145
      | (_, Abst _) =>  true
berghofe@12871
  1146
      | _ => false
berghofe@12871
  1147
  end;
berghofe@12871
  1148
wenzelm@28329
  1149
berghofe@11519
  1150
(**** rewriting on proof terms ****)
berghofe@11519
  1151
berghofe@13102
  1152
val skel0 = PBound 0;
berghofe@13102
  1153
berghofe@12279
  1154
fun rewrite_prf tymatch (rules, procs) prf =
berghofe@11519
  1155
  let
skalberg@15531
  1156
    fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, skel0)
skalberg@15531
  1157
      | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, skel0)
wenzelm@28803
  1158
      | rew Ts prf = (case get_first (fn r => r Ts prf) procs of
skalberg@15531
  1159
          SOME prf' => SOME (prf', skel0)
skalberg@15531
  1160
        | NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
berghofe@13102
  1161
            (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
wenzelm@28803
  1162
               handle PMatch => NONE) (filter (could_unify prf o fst) rules));
berghofe@11519
  1163
berghofe@11615
  1164
    fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
berghofe@11519
  1165
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
  1166
          else
berghofe@11519
  1167
            let val prf'' = incr_pboundvars (~1) 0 prf'
wenzelm@19502
  1168
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
skalberg@15531
  1169
      | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
berghofe@11519
  1170
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
  1171
          else
berghofe@11519
  1172
            let val prf'' = incr_pboundvars 0 (~1) prf'
wenzelm@19502
  1173
            in SOME (the_default (prf'', skel0) (rew Ts prf'')) end
berghofe@11519
  1174
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
  1175
skalberg@15531
  1176
    fun rew1 _ (Hyp (Var _)) _ = NONE
berghofe@13102
  1177
      | rew1 Ts skel prf = (case rew2 Ts skel prf of
skalberg@15531
  1178
          SOME prf1 => (case rew0 Ts prf1 of
wenzelm@19502
  1179
              SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts skel' prf2))
skalberg@15531
  1180
            | NONE => SOME prf1)
skalberg@15531
  1181
        | NONE => (case rew0 Ts prf of
wenzelm@19502
  1182
              SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts skel' prf1))
skalberg@15531
  1183
            | NONE => NONE))
berghofe@11519
  1184
skalberg@15531
  1185
    and rew2 Ts skel (prf % SOME t) = (case prf of
berghofe@11519
  1186
            Abst (_, _, body) =>
berghofe@11519
  1187
              let val prf' = prf_subst_bounds [t] body
wenzelm@19502
  1188
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1189
          | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf of
skalberg@15531
  1190
              SOME prf' => SOME (prf' % SOME t)
skalberg@15531
  1191
            | NONE => NONE))
skalberg@15570
  1192
      | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
berghofe@13102
  1193
          (rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf)
berghofe@13102
  1194
      | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
berghofe@11519
  1195
            AbsP (_, _, body) =>
berghofe@11519
  1196
              let val prf' = prf_subst_pbounds [prf2] body
wenzelm@19502
  1197
              in SOME (the_default prf' (rew2 Ts skel0 prf')) end
berghofe@13102
  1198
          | _ =>
berghofe@13102
  1199
            let val (skel1, skel2) = (case skel of
berghofe@13102
  1200
                skel1 %% skel2 => (skel1, skel2)
berghofe@13102
  1201
              | _ => (skel0, skel0))
berghofe@13102
  1202
            in case rew1 Ts skel1 prf1 of
skalberg@15531
  1203
                SOME prf1' => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1204
                    SOME prf2' => SOME (prf1' %% prf2')
skalberg@15531
  1205
                  | NONE => SOME (prf1' %% prf2))
skalberg@15531
  1206
              | NONE => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1207
                    SOME prf2' => SOME (prf1 %% prf2')
skalberg@15531
  1208
                  | NONE => NONE)
berghofe@13102
  1209
            end)
wenzelm@19502
  1210
      | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts)
berghofe@13102
  1211
              (case skel of Abst (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1212
            SOME prf' => SOME (Abst (s, T, prf'))
skalberg@15531
  1213
          | NONE => NONE)
berghofe@13102
  1214
      | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
berghofe@13102
  1215
              (case skel of AbsP (_, _, skel') => skel' | _ => skel0) prf of
skalberg@15531
  1216
            SOME prf' => SOME (AbsP (s, t, prf'))
skalberg@15531
  1217
          | NONE => NONE)
skalberg@15531
  1218
      | rew2 _ _ _ = NONE
berghofe@11519
  1219
wenzelm@19502
  1220
  in the_default prf (rew1 [] skel0 prf) end;
berghofe@11519
  1221
wenzelm@17203
  1222
fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
wenzelm@17203
  1223
  Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
  1224
berghofe@11715
  1225
fun rewrite_proof_notypes rews = rewrite_prf fst rews;
berghofe@11615
  1226
wenzelm@16940
  1227
berghofe@11519
  1228
(**** theory data ****)
berghofe@11519
  1229
wenzelm@16458
  1230
structure ProofData = TheoryDataFun
wenzelm@22846
  1231
(
wenzelm@28803
  1232
  type T = (stamp * (proof * proof)) list * (stamp * (typ list -> proof -> proof option)) list;
berghofe@11519
  1233
berghofe@12233
  1234
  val empty = ([], []);
berghofe@12233
  1235
  val copy = I;
wenzelm@16458
  1236
  val extend = I;
wenzelm@28803
  1237
  fun merge _ ((rules1, procs1), (rules2, procs2)) : T =
wenzelm@28803
  1238
    (AList.merge (op =) (K true) (rules1, rules2),
haftmann@22662
  1239
      AList.merge (op =) (K true) (procs1, procs2));
wenzelm@22846
  1240
);
berghofe@11519
  1241
wenzelm@28803
  1242
fun get_data thy = let val (rules, procs) = ProofData.get thy in (map #2 rules, map #2 procs) end;
wenzelm@28803
  1243
fun rew_proof thy = rewrite_prf fst (get_data thy);
berghofe@23780
  1244
wenzelm@28803
  1245
fun add_prf_rrule r = (ProofData.map o apfst) (cons (stamp (), r));
wenzelm@28803
  1246
fun add_prf_rproc p = (ProofData.map o apsnd) (cons (stamp (), p));
wenzelm@28803
  1247
wenzelm@28803
  1248
wenzelm@28828
  1249
(***** promises *****)
berghofe@11519
  1250
wenzelm@28828
  1251
fun promise_proof thy i prop =
wenzelm@28828
  1252
  let
wenzelm@28828
  1253
    val _ = prop |> Term.exists_subterm (fn t =>
wenzelm@28828
  1254
      (Term.is_Free t orelse Term.is_Var t) andalso
wenzelm@28828
  1255
        error ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
wenzelm@28828
  1256
    val _ = prop |> Term.exists_type (Term.exists_subtype
wenzelm@28828
  1257
      (fn TFree (a, _) => error ("promise_proof: illegal type variable " ^ quote a)
wenzelm@28828
  1258
        | _ => false));
wenzelm@28828
  1259
  in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
wenzelm@28828
  1260
wenzelm@28828
  1261
fun fulfill_proof _ [] body0 = body0
wenzelm@30716
  1262
  | fulfill_proof thy ps body0 =
wenzelm@28828
  1263
      let
wenzelm@28828
  1264
        val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
wenzelm@30716
  1265
        val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
wenzelm@30716
  1266
        val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
wenzelm@30716
  1267
        val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
wenzelm@28875
  1268
wenzelm@28875
  1269
        fun fill (Promise (i, prop, Ts)) =
wenzelm@30716
  1270
            (case Inttab.lookup proofs i of
wenzelm@28875
  1271
              NONE => NONE
wenzelm@30716
  1272
            | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf))
wenzelm@28875
  1273
          | fill _ = NONE;
wenzelm@28875
  1274
        val (rules, procs) = get_data thy;
wenzelm@28875
  1275
        val proof = rewrite_prf fst (rules, K fill :: procs) proof0;
wenzelm@28828
  1276
      in PBody {oracles = oracles, thms = thms, proof = proof} end;
wenzelm@28828
  1277
wenzelm@29642
  1278
fun fulfill_proof_future _ [] body = Future.value body
wenzelm@29642
  1279
  | fulfill_proof_future thy promises body =
wenzelm@29642
  1280
      Future.fork_deps (map snd promises) (fn () =>
wenzelm@29642
  1281
        fulfill_proof thy (map (apsnd Future.join) promises) body);
wenzelm@29642
  1282
wenzelm@28828
  1283
wenzelm@28828
  1284
(***** theorems *****)
berghofe@11519
  1285
wenzelm@28803
  1286
fun thm_proof thy name hyps prop promises body =
berghofe@11519
  1287
  let
wenzelm@28803
  1288
    val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
wenzelm@12923
  1289
    val prop = Logic.list_implies (hyps, prop);
berghofe@11519
  1290
    val nvs = needed_vars prop;
berghofe@11519
  1291
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
  1292
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
berghofe@28812
  1293
      map SOME (frees_of prop);
wenzelm@28803
  1294
wenzelm@28803
  1295
    val proof0 =
wenzelm@28876
  1296
      if ! proofs = 2 then
wenzelm@28876
  1297
        #4 (shrink_proof thy [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)))
wenzelm@28876
  1298
      else MinProof;
wenzelm@29642
  1299
    val body0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
wenzelm@28803
  1300
wenzelm@29642
  1301
    fun new_prf () = (serial (), name, prop, fulfill_proof_future thy promises body0);
wenzelm@28815
  1302
    val (i, name, prop, body') =
wenzelm@28803
  1303
      (case strip_combt (fst (strip_combP prf)) of
wenzelm@28803
  1304
        (PThm (i, ((old_name, prop', NONE), body')), args') =>
wenzelm@28815
  1305
          if (old_name = "" orelse old_name = name) andalso prop = prop' andalso args = args'
wenzelm@28815
  1306
          then (i, name, prop, body')
wenzelm@28803
  1307
          else new_prf ()
wenzelm@28815
  1308
      | _ => new_prf ());
wenzelm@28815
  1309
    val head = PThm (i, ((name, prop, NONE), body'));
berghofe@11519
  1310
  in
wenzelm@28815
  1311
    ((i, (name, prop, body')), proof_combP (proof_combt' (head, args), map Hyp hyps))
berghofe@11519
  1312
  end;
berghofe@11519
  1313
wenzelm@21646
  1314
fun get_name hyps prop prf =
wenzelm@12923
  1315
  let val prop = Logic.list_implies (hyps, prop) in
wenzelm@12923
  1316
    (case strip_combt (fst (strip_combP prf)) of
wenzelm@28803
  1317
      (PAxm (name, prop', _), _) => if prop = prop' then name else ""   (* FIXME !? *)
wenzelm@28803
  1318
    | (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
wenzelm@21646
  1319
    | _ => "")
wenzelm@12923
  1320
  end;
berghofe@11519
  1321
berghofe@11519
  1322
end;
berghofe@11519
  1323
berghofe@11519
  1324
structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
berghofe@11519
  1325
open BasicProofterm;