src/Pure/Proof/extraction.ML
author wenzelm
Tue Aug 16 13:42:26 2005 +0200 (2005-08-16)
changeset 17057 0934ac31985f
parent 16983 c895701d55ea
child 17203 29b2563f5c11
permissions -rw-r--r--
OuterKeyword;
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(*  Title:      Pure/Proof/extraction.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen
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Extraction of programs from proofs.
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*)
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signature EXTRACTION =
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sig
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  val set_preprocessor : (theory -> Proofterm.proof -> Proofterm.proof) -> theory -> theory
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  val add_realizes_eqns_i : ((term * term) list * (term * term)) list -> theory -> theory
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  val add_realizes_eqns : string list -> theory -> theory
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  val add_typeof_eqns_i : ((term * term) list * (term * term)) list -> theory -> theory
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  val add_typeof_eqns : string list -> theory -> theory
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  val add_realizers_i : (string * (string list * term * Proofterm.proof)) list
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    -> theory -> theory
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  val add_realizers : (thm * (string list * string * string)) list
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    -> theory -> theory
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  val add_expand_thms : thm list -> theory -> theory
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  val add_types : (xstring * ((term -> term option) list *
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    (term -> typ -> term -> typ -> term) option)) list -> theory -> theory
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  val extract : (thm * string list) list -> theory -> theory
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  val nullT : typ
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  val nullt : term
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  val mk_typ : typ -> term
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  val etype_of : theory -> string list -> typ list -> term -> typ
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  val realizes_of: theory -> string list -> term -> term -> term
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end;
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structure Extraction : EXTRACTION =
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struct
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open Proofterm;
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(**** tools ****)
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fun add_syntax thy =
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  thy
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  |> Theory.copy
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  |> Theory.root_path
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  |> Theory.add_types [("Type", 0, NoSyn), ("Null", 0, NoSyn)]
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  |> Theory.add_consts
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      [("typeof", "'b::{} => Type", NoSyn),
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       ("Type", "'a::{} itself => Type", NoSyn),
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       ("Null", "Null", NoSyn),
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       ("realizes", "'a::{} => 'b::{} => 'b", NoSyn)];
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val nullT = Type ("Null", []);
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val nullt = Const ("Null", nullT);
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fun mk_typ T =
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  Const ("Type", itselfT T --> Type ("Type", [])) $ Logic.mk_type T;
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fun typeof_proc defaultS vs (Const ("typeof", _) $ u) =
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      SOME (mk_typ (case strip_comb u of
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          (Var ((a, i), _), _) =>
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            if a mem vs then TFree ("'" ^ a ^ ":" ^ string_of_int i, defaultS)
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            else nullT
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        | (Free (a, _), _) =>
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            if a mem vs then TFree ("'" ^ a, defaultS) else nullT
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        | _ => nullT))
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  | typeof_proc _ _ _ = NONE;
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fun rlz_proc (Const ("realizes", Type (_, [Type ("Null", []), _])) $ r $ t) = SOME t
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  | rlz_proc (Const ("realizes", Type (_, [T, _])) $ r $ t) =
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      (case strip_comb t of
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         (Var (ixn, U), ts) => SOME (list_comb (Var (ixn, T --> U), r :: ts))
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       | (Free (s, U), ts) => SOME (list_comb (Free (s, T --> U), r :: ts))
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       | _ => NONE)
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  | rlz_proc _ = NONE;
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val unpack_ixn = apfst implode o apsnd (fst o read_int o tl) o
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  take_prefix (not o equal ":") o explode;
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type rules =
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  {next: int, rs: ((term * term) list * (term * term)) list,
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   net: (int * ((term * term) list * (term * term))) Net.net};
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val empty_rules : rules = {next = 0, rs = [], net = Net.empty};
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fun add_rule (r as (_, (lhs, _)), {next, rs, net} : rules) =
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  {next = next - 1, rs = r :: rs, net = Net.insert_term (K false)
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     (Pattern.eta_contract lhs, (next, r)) net};
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fun merge_rules
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  ({next, rs = rs1, net} : rules) ({next = next2, rs = rs2, ...} : rules) =
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  foldr add_rule {next = next, rs = rs1, net = net} (rs2 \\ rs1);
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fun condrew thy rules procs =
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  let
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    val tsig = Sign.tsig_of thy;
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    fun rew tm =
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      Pattern.rewrite_term tsig [] (condrew' :: procs) tm
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    and condrew' tm =
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      let
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        val cache = ref ([] : (term * term) list);
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        fun lookup f x = (case gen_assoc (op =) (!cache, x) of
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            NONE =>
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              let val y = f x
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              in (cache := (x, y) :: !cache; y) end
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          | SOME y => y);
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      in
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        get_first (fn (_, (prems, (tm1, tm2))) =>
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        let
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          fun ren t = getOpt (Term.rename_abs tm1 tm t, t);
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          val inc = Logic.incr_indexes ([], maxidx_of_term tm + 1);
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          val env as (Tenv, tenv) = Pattern.match tsig (inc tm1, tm);
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          val prems' = map (pairself (Envir.subst_vars env o inc o ren)) prems;
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          val env' = Envir.Envir
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            {maxidx = Library.foldl Int.max
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              (~1, map (Int.max o pairself maxidx_of_term) prems'),
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             iTs = Tenv, asol = tenv};
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          val env'' = Library.foldl (fn (env, p) =>
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            Pattern.unify (thy, env, [pairself (lookup rew) p])) (env', prems')
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        in SOME (Envir.norm_term env'' (inc (ren tm2)))
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        end handle Pattern.MATCH => NONE | Pattern.Unif => NONE)
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          (sort (int_ord o pairself fst)
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            (Net.match_term rules (Pattern.eta_contract tm)))
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      end;
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  in rew end;
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val chtype = change_type o SOME;
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fun extr_name s vs = NameSpace.append "extr" (space_implode "_" (s :: vs));
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fun corr_name s vs = extr_name s vs ^ "_correctness";
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fun msg d s = priority (Symbol.spaces d ^ s);
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fun vars_of t = rev (fold_aterms (fn v as Var _ => insert (op =) v | _ => I) t []);
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fun vfs_of t = vars_of t @ sort Term.term_ord (term_frees t);
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fun forall_intr (t, prop) =
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  let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
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  in all T $ Abs (a, T, abstract_over (t, prop)) end;
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fun forall_intr_prf (t, prf) =
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  let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
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  in Abst (a, SOME T, prf_abstract_over t prf) end;
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val mkabs = foldr (fn (v, t) => Abs ("x", fastype_of v, abstract_over (v, t)));
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fun strip_abs 0 t = t
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  | strip_abs n (Abs (_, _, t)) = strip_abs (n-1) t
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  | strip_abs _ _ = error "strip_abs: not an abstraction";
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fun prf_subst_TVars tye =
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  map_proof_terms (subst_TVars tye) (typ_subst_TVars tye);
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fun relevant_vars types prop = foldr (fn
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      (Var ((a, i), T), vs) => (case strip_type T of
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        (_, Type (s, _)) => if s mem types then a :: vs else vs
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      | _ => vs)
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    | (_, vs) => vs) [] (vars_of prop);
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fun tname_of (Type (s, _)) = s
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  | tname_of _ = "";
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fun get_var_type t =
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  let
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    val vs = Term.add_vars t [];
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    val fs = Term.add_frees t [];
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  in fn 
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      Var (ixn, _) => (case assoc_string_int (vs, ixn) of
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          NONE => error "get_var_type: no such variable in term"
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        | SOME T => Var (ixn, T))
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    | Free (s, _) => (case assoc_string (fs, s) of
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          NONE => error "get_var_type: no such variable in term"
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        | SOME T => Free (s, T))
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    | _ => error "get_var_type: not a variable"
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  end;
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(**** theory data ****)
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(* data kind 'Pure/extraction' *)
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structure ExtractionData = TheoryDataFun
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(struct
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  val name = "Pure/extraction";
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  type T =
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    {realizes_eqns : rules,
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     typeof_eqns : rules,
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     types : (string * ((term -> term option) list *
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       (term -> typ -> term -> typ -> term) option)) list,
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     realizers : (string list * (term * proof)) list Symtab.table,
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     defs : thm list,
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     expand : (string * term) list,
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     prep : (theory -> proof -> proof) option}
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  val empty =
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    {realizes_eqns = empty_rules,
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     typeof_eqns = empty_rules,
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     types = [],
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     realizers = Symtab.empty,
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     defs = [],
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     expand = [],
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     prep = NONE};
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  val copy = I;
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  val extend = I;
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  fun merge _
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    (({realizes_eqns = realizes_eqns1, typeof_eqns = typeof_eqns1, types = types1,
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       realizers = realizers1, defs = defs1, expand = expand1, prep = prep1},
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      {realizes_eqns = realizes_eqns2, typeof_eqns = typeof_eqns2, types = types2,
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       realizers = realizers2, defs = defs2, expand = expand2, prep = prep2}) : T * T) =
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    {realizes_eqns = merge_rules realizes_eqns1 realizes_eqns2,
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     typeof_eqns = merge_rules typeof_eqns1 typeof_eqns2,
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     types = merge_alists types1 types2,
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     realizers = Symtab.merge_multi' (eq_set o pairself #1)
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       (realizers1, realizers2),
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     defs = gen_merge_lists eq_thm defs1 defs2,
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     expand = merge_lists expand1 expand2,
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     prep = (case prep1 of NONE => prep2 | _ => prep1)};
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  fun print _ _ = ();
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end);
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val _ = Context.add_setup [ExtractionData.init];
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fun read_condeq thy =
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  let val thy' = add_syntax thy
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  in fn s =>
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    let val t = Logic.varify (term_of (read_cterm thy' (s, propT)))
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    in (map Logic.dest_equals (Logic.strip_imp_prems t),
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      Logic.dest_equals (Logic.strip_imp_concl t))
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    end handle TERM _ => error ("Not a (conditional) meta equality:\n" ^ s)
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  end;
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(** preprocessor **)
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fun set_preprocessor prep thy =
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  let val {realizes_eqns, typeof_eqns, types, realizers,
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    defs, expand, ...} = ExtractionData.get thy
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  in
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    ExtractionData.put
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      {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns, types = types,
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       realizers = realizers, defs = defs, expand = expand, prep = SOME prep} thy
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  end;
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(** equations characterizing realizability **)
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fun gen_add_realizes_eqns prep_eq eqns thy =
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  let val {realizes_eqns, typeof_eqns, types, realizers,
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    defs, expand, prep} = ExtractionData.get thy;
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  in
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    ExtractionData.put
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      {realizes_eqns = foldr add_rule realizes_eqns (map (prep_eq thy) eqns),
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       typeof_eqns = typeof_eqns, types = types, realizers = realizers,
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       defs = defs, expand = expand, prep = prep} thy
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  end
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val add_realizes_eqns_i = gen_add_realizes_eqns (K I);
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val add_realizes_eqns = gen_add_realizes_eqns read_condeq;
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(** equations characterizing type of extracted program **)
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fun gen_add_typeof_eqns prep_eq eqns thy =
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  let
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    val {realizes_eqns, typeof_eqns, types, realizers,
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      defs, expand, prep} = ExtractionData.get thy;
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    val eqns' = map (prep_eq thy) eqns
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  in
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    ExtractionData.put
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      {realizes_eqns = realizes_eqns, realizers = realizers,
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       typeof_eqns = foldr add_rule typeof_eqns eqns',
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       types = types, defs = defs, expand = expand, prep = prep} thy
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  end
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val add_typeof_eqns_i = gen_add_typeof_eqns (K I);
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val add_typeof_eqns = gen_add_typeof_eqns read_condeq;
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fun thaw (T as TFree (a, S)) =
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      if exists_string (equal ":") a then TVar (unpack_ixn a, S) else T
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  | thaw (Type (a, Ts)) = Type (a, map thaw Ts)
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  | thaw T = T;
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fun freeze (TVar ((a, i), S)) = TFree (a ^ ":" ^ string_of_int i, S)
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  | freeze (Type (a, Ts)) = Type (a, map freeze Ts)
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  | freeze T = T;
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fun freeze_thaw f x =
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  map_term_types thaw (f (map_term_types freeze x));
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fun etype_of thy vs Ts t =
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  let
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    val {typeof_eqns, ...} = ExtractionData.get thy;
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    fun err () = error ("Unable to determine type of extracted program for\n" ^
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      Sign.string_of_term thy t)
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  in case strip_abs_body (freeze_thaw (condrew thy (#net typeof_eqns)
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    [typeof_proc (Sign.defaultS thy) vs]) (list_abs (map (pair "x") (rev Ts),
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      Const ("typeof", fastype_of1 (Ts, t) --> Type ("Type", [])) $ t))) of
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      Const ("Type", _) $ u => (Logic.dest_type u handle TERM _ => err ())
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    | _ => err ()
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  end;
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(** realizers for axioms / theorems, together with correctness proofs **)
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fun gen_add_realizers prep_rlz rs thy =
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  let val {realizes_eqns, typeof_eqns, types, realizers,
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    defs, expand, prep} = ExtractionData.get thy
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  in
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    ExtractionData.put
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      {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns, types = types,
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       realizers = foldr Symtab.update_multi
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         realizers (map (prep_rlz thy) (rev rs)),
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       defs = defs, expand = expand, prep = prep} thy
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  end
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fun prep_realizer thy =
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  let
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    val {realizes_eqns, typeof_eqns, defs, types, ...} =
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      ExtractionData.get thy;
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    val procs = List.concat (map (fst o snd) types);
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    val rtypes = map fst types;
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    val eqns = Net.merge (K false) (#net realizes_eqns, #net typeof_eqns);
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    val thy' = add_syntax thy;
berghofe@13402
   319
    val rd = ProofSyntax.read_proof thy' false
berghofe@13402
   320
  in fn (thm, (vs, s1, s2)) =>
berghofe@13402
   321
    let
berghofe@13402
   322
      val name = Thm.name_of_thm thm;
berghofe@13402
   323
      val _ = assert (name <> "") "add_realizers: unnamed theorem";
wenzelm@16458
   324
      val prop = Pattern.rewrite_term (Sign.tsig_of thy')
berghofe@13402
   325
        (map (Logic.dest_equals o prop_of) defs) [] (prop_of thm);
berghofe@13402
   326
      val vars = vars_of prop;
berghofe@13732
   327
      val vars' = filter_out (fn v =>
berghofe@13732
   328
        tname_of (body_type (fastype_of v)) mem rtypes) vars;
wenzelm@16458
   329
      val T = etype_of thy' vs [] prop;
berghofe@13402
   330
      val (T', thw) = Type.freeze_thaw_type
berghofe@13732
   331
        (if T = nullT then nullT else map fastype_of vars' ---> T);
wenzelm@16458
   332
      val t = map_term_types thw (term_of (read_cterm thy' (s1, T')));
wenzelm@16458
   333
      val r' = freeze_thaw (condrew thy' eqns
wenzelm@16458
   334
        (procs @ [typeof_proc (Sign.defaultS thy') vs, rlz_proc]))
berghofe@13402
   335
          (Const ("realizes", T --> propT --> propT) $
berghofe@13732
   336
            (if T = nullT then t else list_comb (t, vars')) $ prop);
skalberg@15574
   337
      val r = foldr forall_intr r' (map (get_var_type r') vars);
wenzelm@16458
   338
      val prf = Reconstruct.reconstruct_proof thy' r (rd s2);
berghofe@13402
   339
    in (name, (vs, (t, prf))) end
berghofe@13402
   340
  end;
berghofe@13402
   341
berghofe@13402
   342
val add_realizers_i = gen_add_realizers
berghofe@13402
   343
  (fn _ => fn (name, (vs, t, prf)) => (name, (vs, (t, prf))));
berghofe@13402
   344
val add_realizers = gen_add_realizers prep_realizer;
berghofe@13402
   345
berghofe@13714
   346
fun realizes_of thy vs t prop =
berghofe@13714
   347
  let
berghofe@13714
   348
    val thy' = add_syntax thy;
berghofe@13732
   349
    val {realizes_eqns, typeof_eqns, defs, types, ...} =
berghofe@13714
   350
      ExtractionData.get thy';
skalberg@15570
   351
    val procs = List.concat (map (fst o snd) types);
wenzelm@16800
   352
    val eqns = Net.merge (K false) (#net realizes_eqns, #net typeof_eqns);
wenzelm@16458
   353
    val prop' = Pattern.rewrite_term (Sign.tsig_of thy')
berghofe@13714
   354
      (map (Logic.dest_equals o prop_of) defs) [] prop;
wenzelm@16458
   355
  in freeze_thaw (condrew thy' eqns
wenzelm@16458
   356
    (procs @ [typeof_proc (Sign.defaultS thy') vs, rlz_proc]))
berghofe@13714
   357
      (Const ("realizes", fastype_of t --> propT --> propT) $ t $ prop')
berghofe@13714
   358
  end;
berghofe@13714
   359
berghofe@13402
   360
(** expanding theorems / definitions **)
berghofe@13402
   361
berghofe@13402
   362
fun add_expand_thm (thy, thm) =
berghofe@13402
   363
  let
berghofe@13402
   364
    val {realizes_eqns, typeof_eqns, types, realizers,
berghofe@13402
   365
      defs, expand, prep} = ExtractionData.get thy;
berghofe@13402
   366
berghofe@13402
   367
    val name = Thm.name_of_thm thm;
berghofe@13402
   368
    val _ = assert (name <> "") "add_expand_thms: unnamed theorem";
berghofe@13402
   369
berghofe@13402
   370
    val is_def =
berghofe@13402
   371
      (case strip_comb (fst (Logic.dest_equals (prop_of thm))) of
berghofe@13402
   372
         (Const _, ts) => forall is_Var ts andalso null (duplicates ts)
wenzelm@16349
   373
           andalso can (Thm.get_axiom_i thy) name
berghofe@13402
   374
       | _ => false) handle TERM _ => false;
berghofe@13402
   375
  in
berghofe@13402
   376
    (ExtractionData.put (if is_def then
berghofe@13402
   377
        {realizes_eqns = realizes_eqns,
berghofe@13402
   378
         typeof_eqns = add_rule (([],
berghofe@13402
   379
           Logic.dest_equals (prop_of (Drule.abs_def thm))), typeof_eqns),
berghofe@13402
   380
         types = types,
berghofe@13402
   381
         realizers = realizers, defs = gen_ins eq_thm (thm, defs),
berghofe@13402
   382
         expand = expand, prep = prep}
berghofe@13402
   383
      else
berghofe@13402
   384
        {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns, types = types,
berghofe@13402
   385
         realizers = realizers, defs = defs,
berghofe@13402
   386
         expand = (name, prop_of thm) ins expand, prep = prep}) thy, thm)
berghofe@13402
   387
  end;
berghofe@13402
   388
skalberg@15570
   389
fun add_expand_thms thms thy = Library.foldl (fst o add_expand_thm) (thy, thms);
berghofe@13402
   390
wenzelm@15801
   391
berghofe@13732
   392
(** types with computational content **)
berghofe@13732
   393
berghofe@13732
   394
fun add_types tys thy =
berghofe@13732
   395
  let val {realizes_eqns, typeof_eqns, types, realizers,
berghofe@13732
   396
    defs, expand, prep} = ExtractionData.get thy;
berghofe@13732
   397
  in
berghofe@13732
   398
    ExtractionData.put
berghofe@13732
   399
      {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns,
wenzelm@16458
   400
       types = map (apfst (Sign.intern_type thy)) tys @ types,
berghofe@13732
   401
       realizers = realizers, defs = defs, expand = expand, prep = prep} thy
berghofe@13732
   402
  end;
berghofe@13732
   403
berghofe@13402
   404
wenzelm@15801
   405
(** Pure setup **)
wenzelm@15801
   406
wenzelm@15801
   407
val _ = Context.add_setup
wenzelm@15801
   408
  [add_types [("prop", ([], NONE))],
wenzelm@15801
   409
wenzelm@15801
   410
   add_typeof_eqns
wenzelm@15801
   411
     ["(typeof (PROP P)) == (Type (TYPE(Null))) ==>  \
wenzelm@15801
   412
    \  (typeof (PROP Q)) == (Type (TYPE('Q))) ==>  \
wenzelm@15801
   413
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE('Q)))",
wenzelm@15801
   414
wenzelm@15801
   415
      "(typeof (PROP Q)) == (Type (TYPE(Null))) ==>  \
wenzelm@15801
   416
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE(Null)))",
wenzelm@15801
   417
wenzelm@15801
   418
      "(typeof (PROP P)) == (Type (TYPE('P))) ==>  \
wenzelm@15801
   419
    \  (typeof (PROP Q)) == (Type (TYPE('Q))) ==>  \
wenzelm@15801
   420
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE('P => 'Q)))",
wenzelm@15801
   421
wenzelm@15801
   422
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE(Null))) ==>  \
wenzelm@15801
   423
    \    (typeof (!!x. PROP P (x))) == (Type (TYPE(Null)))",
wenzelm@15801
   424
wenzelm@15801
   425
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE('P))) ==>  \
wenzelm@15801
   426
    \    (typeof (!!x::'a. PROP P (x))) == (Type (TYPE('a => 'P)))",
wenzelm@15801
   427
wenzelm@15801
   428
      "(%x. typeof (f (x))) == (%x. Type (TYPE('f))) ==>  \
wenzelm@15801
   429
    \    (typeof (f)) == (Type (TYPE('f)))"],
wenzelm@15801
   430
wenzelm@15801
   431
   add_realizes_eqns
wenzelm@15801
   432
     ["(typeof (PROP P)) == (Type (TYPE(Null))) ==>  \
wenzelm@15801
   433
    \    (realizes (r) (PROP P ==> PROP Q)) ==  \
wenzelm@15801
   434
    \    (PROP realizes (Null) (PROP P) ==> PROP realizes (r) (PROP Q))",
wenzelm@15801
   435
wenzelm@15801
   436
      "(typeof (PROP P)) == (Type (TYPE('P))) ==>  \
wenzelm@15801
   437
    \  (typeof (PROP Q)) == (Type (TYPE(Null))) ==>  \
wenzelm@15801
   438
    \    (realizes (r) (PROP P ==> PROP Q)) ==  \
wenzelm@15801
   439
    \    (!!x::'P. PROP realizes (x) (PROP P) ==> PROP realizes (Null) (PROP Q))",
wenzelm@15801
   440
wenzelm@15801
   441
      "(realizes (r) (PROP P ==> PROP Q)) ==  \
wenzelm@15801
   442
    \  (!!x. PROP realizes (x) (PROP P) ==> PROP realizes (r (x)) (PROP Q))",
wenzelm@15801
   443
wenzelm@15801
   444
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE(Null))) ==>  \
wenzelm@15801
   445
    \    (realizes (r) (!!x. PROP P (x))) ==  \
wenzelm@15801
   446
    \    (!!x. PROP realizes (Null) (PROP P (x)))",
wenzelm@15801
   447
wenzelm@15801
   448
      "(realizes (r) (!!x. PROP P (x))) ==  \
wenzelm@15801
   449
    \  (!!x. PROP realizes (r (x)) (PROP P (x)))"],
wenzelm@15801
   450
wenzelm@15801
   451
   Attrib.add_attributes
wenzelm@15801
   452
     [("extraction_expand",
wenzelm@15801
   453
       (Attrib.no_args add_expand_thm, K Attrib.undef_local_attribute),
wenzelm@15801
   454
       "specify theorems / definitions to be expanded during extraction")]];
wenzelm@15801
   455
wenzelm@15801
   456
berghofe@13402
   457
(**** extract program ****)
berghofe@13402
   458
berghofe@13402
   459
val dummyt = Const ("dummy", dummyT);
berghofe@13402
   460
berghofe@13402
   461
fun extract thms thy =
berghofe@13402
   462
  let
wenzelm@16458
   463
    val thy' = add_syntax thy;
berghofe@13402
   464
    val {realizes_eqns, typeof_eqns, types, realizers, defs, expand, prep} =
berghofe@13402
   465
      ExtractionData.get thy;
skalberg@15570
   466
    val procs = List.concat (map (fst o snd) types);
berghofe@13732
   467
    val rtypes = map fst types;
wenzelm@16458
   468
    val typroc = typeof_proc (Sign.defaultS thy');
wenzelm@16458
   469
    val prep = getOpt (prep, K I) thy' o ProofRewriteRules.elim_defs thy' false defs o
wenzelm@16458
   470
      Reconstruct.expand_proof thy' (("", NONE) :: map (apsnd SOME) expand);
wenzelm@16800
   471
    val rrews = Net.merge (K false) (#net realizes_eqns, #net typeof_eqns);
berghofe@13402
   472
berghofe@13402
   473
    fun find_inst prop Ts ts vs =
berghofe@13402
   474
      let
berghofe@13732
   475
        val rvs = relevant_vars rtypes prop;
berghofe@13402
   476
        val vars = vars_of prop;
berghofe@13402
   477
        val n = Int.min (length vars, length ts);
berghofe@13402
   478
berghofe@13402
   479
        fun add_args ((Var ((a, i), _), t), (vs', tye)) =
berghofe@13402
   480
          if a mem rvs then
wenzelm@16458
   481
            let val T = etype_of thy' vs Ts t
berghofe@13402
   482
            in if T = nullT then (vs', tye)
berghofe@13402
   483
               else (a :: vs', (("'" ^ a, i), T) :: tye)
berghofe@13402
   484
            end
berghofe@13402
   485
          else (vs', tye)
berghofe@13402
   486
skalberg@15574
   487
      in foldr add_args ([], []) (Library.take (n, vars) ~~ Library.take (n, ts)) end;
berghofe@13402
   488
skalberg@15570
   489
    fun find vs = Option.map snd o find_first (curry eq_set vs o fst);
skalberg@15570
   490
    fun find' s = map snd o List.filter (equal s o fst)
berghofe@13402
   491
berghofe@13732
   492
    fun app_rlz_rews Ts vs t = strip_abs (length Ts) (freeze_thaw
wenzelm@16458
   493
      (condrew thy' rrews (procs @ [typroc vs, rlz_proc])) (list_abs
berghofe@13732
   494
        (map (pair "x") (rev Ts), t)));
berghofe@13732
   495
berghofe@13732
   496
    fun realizes_null vs prop = app_rlz_rews [] vs
berghofe@13732
   497
      (Const ("realizes", nullT --> propT --> propT) $ nullt $ prop);
berghofe@13402
   498
berghofe@13402
   499
    fun corr d defs vs ts Ts hs (PBound i) _ _ = (defs, PBound i)
berghofe@13402
   500
skalberg@15531
   501
      | corr d defs vs ts Ts hs (Abst (s, SOME T, prf)) (Abst (_, _, prf')) t =
berghofe@13402
   502
          let val (defs', corr_prf) = corr d defs vs [] (T :: Ts)
berghofe@13402
   503
            (dummyt :: hs) prf (incr_pboundvars 1 0 prf')
skalberg@15531
   504
            (case t of SOME (Abs (_, _, u)) => SOME u | _ => NONE)
skalberg@15531
   505
          in (defs', Abst (s, SOME T, corr_prf)) end
berghofe@13402
   506
skalberg@15531
   507
      | corr d defs vs ts Ts hs (AbsP (s, SOME prop, prf)) (AbsP (_, _, prf')) t =
berghofe@13402
   508
          let
wenzelm@16458
   509
            val T = etype_of thy' vs Ts prop;
berghofe@13402
   510
            val u = if T = nullT then 
skalberg@15531
   511
                (case t of SOME u => SOME (incr_boundvars 1 u) | NONE => NONE)
skalberg@15531
   512
              else (case t of SOME (Abs (_, _, u)) => SOME u | _ => NONE);
berghofe@13402
   513
            val (defs', corr_prf) = corr d defs vs [] (T :: Ts) (prop :: hs)
berghofe@13402
   514
              (incr_pboundvars 0 1 prf) (incr_pboundvars 0 1 prf') u;
berghofe@13402
   515
            val rlz = Const ("realizes", T --> propT --> propT)
berghofe@13402
   516
          in (defs',
berghofe@13732
   517
            if T = nullT then AbsP ("R",
skalberg@15531
   518
              SOME (app_rlz_rews Ts vs (rlz $ nullt $ prop)),
berghofe@13732
   519
                prf_subst_bounds [nullt] corr_prf)
skalberg@15531
   520
            else Abst (s, SOME T, AbsP ("R",
skalberg@15531
   521
              SOME (app_rlz_rews (T :: Ts) vs
berghofe@13732
   522
                (rlz $ Bound 0 $ incr_boundvars 1 prop)), corr_prf)))
berghofe@13402
   523
          end
berghofe@13402
   524
skalberg@15531
   525
      | corr d defs vs ts Ts hs (prf % SOME t) (prf' % _) t' =
berghofe@13732
   526
          let
berghofe@13732
   527
            val (Us, T) = strip_type (fastype_of1 (Ts, t));
berghofe@13732
   528
            val (defs', corr_prf) = corr d defs vs (t :: ts) Ts hs prf prf'
berghofe@13732
   529
              (if tname_of T mem rtypes then t'
skalberg@15531
   530
               else (case t' of SOME (u $ _) => SOME u | _ => NONE));
berghofe@13732
   531
            val u = if not (tname_of T mem rtypes) then t else
berghofe@13732
   532
              let
wenzelm@16458
   533
                val eT = etype_of thy' vs Ts t;
berghofe@13732
   534
                val (r, Us') = if eT = nullT then (nullt, Us) else
berghofe@13732
   535
                  (Bound (length Us), eT :: Us);
berghofe@13732
   536
                val u = list_comb (incr_boundvars (length Us') t,
berghofe@13732
   537
                  map Bound (length Us - 1 downto 0));
wenzelm@16865
   538
                val u' = (case assoc_string (types, tname_of T) of
skalberg@15531
   539
                    SOME ((_, SOME f)) => f r eT u T
berghofe@13732
   540
                  | _ => Const ("realizes", eT --> T --> T) $ r $ u)
berghofe@13732
   541
              in app_rlz_rews Ts vs (list_abs (map (pair "x") Us', u')) end
skalberg@15531
   542
          in (defs', corr_prf % SOME u) end
berghofe@13402
   543
berghofe@13402
   544
      | corr d defs vs ts Ts hs (prf1 %% prf2) (prf1' %% prf2') t =
berghofe@13402
   545
          let
berghofe@13402
   546
            val prop = Reconstruct.prop_of' hs prf2';
wenzelm@16458
   547
            val T = etype_of thy' vs Ts prop;
skalberg@15531
   548
            val (defs1, f, u) = if T = nullT then (defs, t, NONE) else
berghofe@13402
   549
              (case t of
skalberg@15531
   550
                 SOME (f $ u) => (defs, SOME f, SOME u)
berghofe@13402
   551
               | _ =>
berghofe@13402
   552
                 let val (defs1, u) = extr d defs vs [] Ts hs prf2'
skalberg@15531
   553
                 in (defs1, NONE, SOME u) end)
berghofe@13402
   554
            val (defs2, corr_prf1) = corr d defs1 vs [] Ts hs prf1 prf1' f;
berghofe@13402
   555
            val (defs3, corr_prf2) = corr d defs2 vs [] Ts hs prf2 prf2' u;
berghofe@13402
   556
          in
berghofe@13402
   557
            if T = nullT then (defs3, corr_prf1 %% corr_prf2) else
berghofe@13402
   558
              (defs3, corr_prf1 % u %% corr_prf2)
berghofe@13402
   559
          end
berghofe@13402
   560
skalberg@15531
   561
      | corr d defs vs ts Ts hs (prf0 as PThm ((name, _), prf, prop, SOME Ts')) _ _ =
berghofe@13402
   562
          let
berghofe@13402
   563
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   564
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye;
wenzelm@16458
   565
            val T = etype_of thy' vs' [] prop;
berghofe@13402
   566
            val defs' = if T = nullT then defs
berghofe@13402
   567
              else fst (extr d defs vs ts Ts hs prf0)
berghofe@13402
   568
          in
berghofe@13609
   569
            if T = nullT andalso realizes_null vs' prop aconv prop then (defs, prf0)
berghofe@13402
   570
            else case Symtab.lookup (realizers, name) of
skalberg@15531
   571
              NONE => (case find vs' (find' name defs') of
skalberg@15531
   572
                NONE =>
berghofe@13402
   573
                  let
berghofe@13402
   574
                    val _ = assert (T = nullT) "corr: internal error";
berghofe@13402
   575
                    val _ = msg d ("Building correctness proof for " ^ quote name ^
berghofe@13402
   576
                      (if null vs' then ""
berghofe@13402
   577
                       else " (relevant variables: " ^ commas_quote vs' ^ ")"));
wenzelm@16458
   578
                    val prf' = prep (Reconstruct.reconstruct_proof thy' prop prf);
berghofe@13402
   579
                    val (defs'', corr_prf) =
skalberg@15531
   580
                      corr (d + 1) defs' vs' [] [] [] prf' prf' NONE;
berghofe@13732
   581
                    val corr_prop = Reconstruct.prop_of corr_prf;
skalberg@15574
   582
                    val corr_prf' = foldr forall_intr_prf
skalberg@15574
   583
                      (proof_combt
berghofe@13793
   584
                         (PThm ((corr_name name vs', []), corr_prf, corr_prop,
skalberg@15531
   585
                             SOME (map TVar (term_tvars corr_prop))), vfs_of corr_prop))
skalberg@15574
   586
		      (map (get_var_type corr_prop) (vfs_of prop))
berghofe@13402
   587
                  in
berghofe@13732
   588
                    ((name, (vs', ((nullt, nullt), (corr_prf, corr_prf')))) :: defs'',
berghofe@13402
   589
                     prf_subst_TVars tye' corr_prf')
berghofe@13402
   590
                  end
skalberg@15531
   591
              | SOME (_, (_, prf')) => (defs', prf_subst_TVars tye' prf'))
skalberg@15531
   592
            | SOME rs => (case find vs' rs of
skalberg@15531
   593
                SOME (_, prf') => (defs', prf_subst_TVars tye' prf')
skalberg@15531
   594
              | NONE => error ("corr: no realizer for instance of theorem " ^
wenzelm@16458
   595
                  quote name ^ ":\n" ^ Sign.string_of_term thy' (Envir.beta_norm
berghofe@13402
   596
                    (Reconstruct.prop_of (proof_combt (prf0, ts))))))
berghofe@13402
   597
          end
berghofe@13402
   598
skalberg@15531
   599
      | corr d defs vs ts Ts hs (prf0 as PAxm (s, prop, SOME Ts')) _ _ =
berghofe@13402
   600
          let
berghofe@13402
   601
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   602
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   603
          in
wenzelm@16458
   604
            if etype_of thy' vs' [] prop = nullT andalso
berghofe@13609
   605
              realizes_null vs' prop aconv prop then (defs, prf0)
berghofe@13609
   606
            else case find vs' (Symtab.lookup_multi (realizers, s)) of
skalberg@15531
   607
              SOME (_, prf) => (defs, prf_subst_TVars tye' prf)
skalberg@15531
   608
            | NONE => error ("corr: no realizer for instance of axiom " ^
wenzelm@16458
   609
                quote s ^ ":\n" ^ Sign.string_of_term thy' (Envir.beta_norm
berghofe@13402
   610
                  (Reconstruct.prop_of (proof_combt (prf0, ts)))))
berghofe@13402
   611
          end
berghofe@13402
   612
berghofe@13402
   613
      | corr d defs vs ts Ts hs _ _ _ = error "corr: bad proof"
berghofe@13402
   614
berghofe@13402
   615
    and extr d defs vs ts Ts hs (PBound i) = (defs, Bound i)
berghofe@13402
   616
skalberg@15531
   617
      | extr d defs vs ts Ts hs (Abst (s, SOME T, prf)) =
berghofe@13402
   618
          let val (defs', t) = extr d defs vs []
berghofe@13402
   619
            (T :: Ts) (dummyt :: hs) (incr_pboundvars 1 0 prf)
berghofe@13402
   620
          in (defs', Abs (s, T, t)) end
berghofe@13402
   621
skalberg@15531
   622
      | extr d defs vs ts Ts hs (AbsP (s, SOME t, prf)) =
berghofe@13402
   623
          let
wenzelm@16458
   624
            val T = etype_of thy' vs Ts t;
berghofe@13402
   625
            val (defs', t) = extr d defs vs [] (T :: Ts) (t :: hs)
berghofe@13402
   626
              (incr_pboundvars 0 1 prf)
berghofe@13402
   627
          in (defs',
berghofe@13402
   628
            if T = nullT then subst_bound (nullt, t) else Abs (s, T, t))
berghofe@13402
   629
          end
berghofe@13402
   630
skalberg@15531
   631
      | extr d defs vs ts Ts hs (prf % SOME t) =
berghofe@13402
   632
          let val (defs', u) = extr d defs vs (t :: ts) Ts hs prf
berghofe@13732
   633
          in (defs',
berghofe@13732
   634
            if tname_of (body_type (fastype_of1 (Ts, t))) mem rtypes then u
berghofe@13732
   635
            else u $ t)
berghofe@13732
   636
          end
berghofe@13402
   637
berghofe@13402
   638
      | extr d defs vs ts Ts hs (prf1 %% prf2) =
berghofe@13402
   639
          let
berghofe@13402
   640
            val (defs', f) = extr d defs vs [] Ts hs prf1;
berghofe@13402
   641
            val prop = Reconstruct.prop_of' hs prf2;
wenzelm@16458
   642
            val T = etype_of thy' vs Ts prop
berghofe@13402
   643
          in
berghofe@13402
   644
            if T = nullT then (defs', f) else
berghofe@13402
   645
              let val (defs'', t) = extr d defs' vs [] Ts hs prf2
berghofe@13402
   646
              in (defs'', f $ t) end
berghofe@13402
   647
          end
berghofe@13402
   648
skalberg@15531
   649
      | extr d defs vs ts Ts hs (prf0 as PThm ((s, _), prf, prop, SOME Ts')) =
berghofe@13402
   650
          let
berghofe@13402
   651
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   652
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   653
          in
berghofe@13402
   654
            case Symtab.lookup (realizers, s) of
skalberg@15531
   655
              NONE => (case find vs' (find' s defs) of
skalberg@15531
   656
                NONE =>
berghofe@13402
   657
                  let
berghofe@13402
   658
                    val _ = msg d ("Extracting " ^ quote s ^
berghofe@13402
   659
                      (if null vs' then ""
berghofe@13402
   660
                       else " (relevant variables: " ^ commas_quote vs' ^ ")"));
wenzelm@16458
   661
                    val prf' = prep (Reconstruct.reconstruct_proof thy' prop prf);
berghofe@13402
   662
                    val (defs', t) = extr (d + 1) defs vs' [] [] [] prf';
berghofe@13402
   663
                    val (defs'', corr_prf) =
skalberg@15531
   664
                      corr (d + 1) defs' vs' [] [] [] prf' prf' (SOME t);
berghofe@13402
   665
berghofe@13402
   666
                    val nt = Envir.beta_norm t;
berghofe@13732
   667
                    val args = filter_out (fn v => tname_of (body_type
berghofe@13732
   668
                      (fastype_of v)) mem rtypes) (vfs_of prop);
skalberg@15570
   669
                    val args' = List.filter (fn v => Logic.occs (v, nt)) args;
skalberg@15574
   670
                    val t' = mkabs nt args';
berghofe@13402
   671
                    val T = fastype_of t';
berghofe@13732
   672
                    val cname = extr_name s vs';
berghofe@13402
   673
                    val c = Const (cname, T);
skalberg@15574
   674
                    val u = mkabs (list_comb (c, args')) args;
berghofe@13402
   675
                    val eqn = Logic.mk_equals (c, t');
berghofe@13402
   676
                    val rlz =
berghofe@13402
   677
                      Const ("realizes", fastype_of nt --> propT --> propT);
berghofe@13732
   678
                    val lhs = app_rlz_rews [] vs' (rlz $ nt $ prop);
berghofe@13732
   679
                    val rhs = app_rlz_rews [] vs' (rlz $ list_comb (c, args') $ prop);
berghofe@13732
   680
                    val f = app_rlz_rews [] vs'
berghofe@13732
   681
                      (Abs ("x", T, rlz $ list_comb (Bound 0, args') $ prop));
berghofe@13402
   682
berghofe@13732
   683
                    val corr_prf' =
berghofe@13732
   684
                      chtype [] equal_elim_axm %> lhs %> rhs %%
berghofe@13732
   685
                       (chtype [propT] symmetric_axm %> rhs %> lhs %%
berghofe@13732
   686
                         (chtype [propT, T] combination_axm %> f %> f %> c %> t' %%
berghofe@13732
   687
                           (chtype [T --> propT] reflexive_axm %> f) %%
berghofe@13732
   688
                           PAxm (cname ^ "_def", eqn,
skalberg@15531
   689
                             SOME (map TVar (term_tvars eqn))))) %% corr_prf;
berghofe@13732
   690
                    val corr_prop = Reconstruct.prop_of corr_prf';
skalberg@15574
   691
                    val corr_prf'' = foldr forall_intr_prf
skalberg@15574
   692
                      (proof_combt
berghofe@13732
   693
                        (PThm ((corr_name s vs', []), corr_prf', corr_prop,
skalberg@15574
   694
                          SOME (map TVar (term_tvars corr_prop))),  vfs_of corr_prop))
skalberg@15574
   695
		      (map (get_var_type corr_prop) (vfs_of prop));
berghofe@13402
   696
                  in
berghofe@13732
   697
                    ((s, (vs', ((t', u), (corr_prf', corr_prf'')))) :: defs'',
berghofe@13402
   698
                     subst_TVars tye' u)
berghofe@13402
   699
                  end
skalberg@15531
   700
              | SOME ((_, u), _) => (defs, subst_TVars tye' u))
skalberg@15531
   701
            | SOME rs => (case find vs' rs of
skalberg@15531
   702
                SOME (t, _) => (defs, subst_TVars tye' t)
skalberg@15531
   703
              | NONE => error ("extr: no realizer for instance of theorem " ^
wenzelm@16458
   704
                  quote s ^ ":\n" ^ Sign.string_of_term thy' (Envir.beta_norm
berghofe@13402
   705
                    (Reconstruct.prop_of (proof_combt (prf0, ts))))))
berghofe@13402
   706
          end
berghofe@13402
   707
skalberg@15531
   708
      | extr d defs vs ts Ts hs (prf0 as PAxm (s, prop, SOME Ts')) =
berghofe@13402
   709
          let
berghofe@13402
   710
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   711
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   712
          in
berghofe@13402
   713
            case find vs' (Symtab.lookup_multi (realizers, s)) of
skalberg@15531
   714
              SOME (t, _) => (defs, subst_TVars tye' t)
skalberg@15531
   715
            | NONE => error ("extr: no realizer for instance of axiom " ^
wenzelm@16458
   716
                quote s ^ ":\n" ^ Sign.string_of_term thy' (Envir.beta_norm
berghofe@13402
   717
                  (Reconstruct.prop_of (proof_combt (prf0, ts)))))
berghofe@13402
   718
          end
berghofe@13402
   719
berghofe@13402
   720
      | extr d defs vs ts Ts hs _ = error "extr: bad proof";
berghofe@13402
   721
berghofe@13732
   722
    fun prep_thm (thm, vs) =
berghofe@13402
   723
      let
berghofe@13402
   724
        val {prop, der = (_, prf), sign, ...} = rep_thm thm;
berghofe@13402
   725
        val name = Thm.name_of_thm thm;
berghofe@13402
   726
        val _ = assert (name <> "") "extraction: unnamed theorem";
wenzelm@16458
   727
        val _ = assert (etype_of thy' vs [] prop <> nullT) ("theorem " ^
berghofe@13402
   728
          quote name ^ " has no computational content")
berghofe@13732
   729
      in (Reconstruct.reconstruct_proof sign prop prf, vs) end;
berghofe@13402
   730
skalberg@15570
   731
    val defs = Library.foldl (fn (defs, (prf, vs)) =>
berghofe@13732
   732
      fst (extr 0 defs vs [] [] [] prf)) ([], map prep_thm thms);
berghofe@13402
   733
wenzelm@16149
   734
    fun add_def (s, (vs, ((t, u), (prf, _)))) thy =
wenzelm@16458
   735
      (case Sign.const_type thy (extr_name s vs) of
skalberg@15531
   736
         NONE =>
berghofe@13732
   737
           let
berghofe@13732
   738
             val corr_prop = Reconstruct.prop_of prf;
wenzelm@16287
   739
             val ft = Type.freeze t;
wenzelm@16287
   740
             val fu = Type.freeze u;
berghofe@13732
   741
             val thy' = if t = nullt then thy else thy |>
berghofe@13732
   742
               Theory.add_consts_i [(extr_name s vs, fastype_of ft, NoSyn)] |>
berghofe@13732
   743
               fst o PureThy.add_defs_i false [((extr_name s vs ^ "_def",
berghofe@13732
   744
                 Logic.mk_equals (head_of (strip_abs_body fu), ft)), [])];
berghofe@13732
   745
           in
berghofe@13732
   746
             fst (PureThy.store_thm ((corr_name s vs,
berghofe@13732
   747
               Thm.varifyT (funpow (length (term_vars corr_prop))
berghofe@13732
   748
                 (forall_elim_var 0) (forall_intr_frees
berghofe@13732
   749
                   (ProofChecker.thm_of_proof thy'
berghofe@13732
   750
                     (fst (Proofterm.freeze_thaw_prf prf)))))), []) thy')
berghofe@13732
   751
           end
skalberg@15531
   752
       | SOME _ => thy);
berghofe@13402
   753
wenzelm@16149
   754
  in
wenzelm@16149
   755
    thy
wenzelm@16149
   756
    |> Theory.absolute_path
wenzelm@16149
   757
    |> fold_rev add_def defs
wenzelm@16149
   758
    |> Theory.restore_naming thy
berghofe@13402
   759
  end;
berghofe@13402
   760
berghofe@13402
   761
berghofe@13402
   762
(**** interface ****)
berghofe@13402
   763
wenzelm@17057
   764
structure P = OuterParse and K = OuterKeyword;
berghofe@13402
   765
berghofe@13732
   766
val parse_vars = Scan.optional (P.$$$ "(" |-- P.list1 P.name --| P.$$$ ")") [];
berghofe@13732
   767
berghofe@13402
   768
val realizersP =
berghofe@13402
   769
  OuterSyntax.command "realizers"
berghofe@13402
   770
  "specify realizers for primitive axioms / theorems, together with correctness proof"
berghofe@13402
   771
  K.thy_decl
berghofe@13732
   772
    (Scan.repeat1 (P.xname -- parse_vars --| P.$$$ ":" -- P.string -- P.string) >>
berghofe@13402
   773
     (fn xs => Toplevel.theory (fn thy => add_realizers
berghofe@13402
   774
       (map (fn (((a, vs), s1), s2) =>
wenzelm@16486
   775
         (PureThy.get_thm thy (Name a), (vs, s1, s2))) xs) thy)));
berghofe@13402
   776
berghofe@13402
   777
val realizabilityP =
berghofe@13402
   778
  OuterSyntax.command "realizability"
berghofe@13402
   779
  "add equations characterizing realizability" K.thy_decl
berghofe@13402
   780
  (Scan.repeat1 P.string >> (Toplevel.theory o add_realizes_eqns));
berghofe@13402
   781
berghofe@13402
   782
val typeofP =
berghofe@13402
   783
  OuterSyntax.command "extract_type"
berghofe@13402
   784
  "add equations characterizing type of extracted program" K.thy_decl
berghofe@13402
   785
  (Scan.repeat1 P.string >> (Toplevel.theory o add_typeof_eqns));
berghofe@13402
   786
berghofe@13402
   787
val extractP =
berghofe@13402
   788
  OuterSyntax.command "extract" "extract terms from proofs" K.thy_decl
berghofe@13732
   789
    (Scan.repeat1 (P.xname -- parse_vars) >> (fn xs => Toplevel.theory
wenzelm@16486
   790
      (fn thy => extract (map (apfst (PureThy.get_thm thy o Name)) xs) thy)));
berghofe@13402
   791
wenzelm@15801
   792
val _ = OuterSyntax.add_parsers [realizersP, realizabilityP, typeofP, extractP];
berghofe@13402
   793
wenzelm@16458
   794
val etype_of = etype_of o add_syntax;
berghofe@13714
   795
berghofe@13402
   796
end;