src/Pure/Proof/extraction.ML
author wenzelm
Tue Jun 01 12:33:50 2004 +0200 (2004-06-01)
changeset 14854 61bdf2ae4dc5
parent 14472 cba7c0a3ffb3
child 14981 e73f8140af78
permissions -rw-r--r--
removed obsolete sort 'logic';
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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 : (Sign.sg -> 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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  val parsers: OuterSyntax.parser list
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  val setup: (theory -> theory) list
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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
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     ((Pattern.eta_contract lhs, (next, r)), net, K false)};
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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 (rs2 \\ rs1, {next = next, rs = rs1, net = net});
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fun condrew sign rules procs =
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  let
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    val tsig = Sign.tsig_of sign;
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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 = get_first (fn (_, (prems, (tm1, tm2))) =>
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      let
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        fun ren t = if_none (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 (subst_vars env o inc o ren)) prems;
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        val env' = Envir.Envir
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          {maxidx = foldl Int.max
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            (~1, map (Int.max o pairself maxidx_of_term) prems'),
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           iTs = Vartab.make Tenv, asol = Vartab.make tenv};
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        val env'' = foldl (fn (env, p) =>
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          Pattern.unify (sign, env, [pairself 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.compare o pairself fst)
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          (Net.match_term rules (Pattern.eta_contract tm)));
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  in rew end;
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val chtype = change_type o Some;
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fun add_prefix a b = NameSpace.pack (a :: NameSpace.unpack b);
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fun corr_name s vs =
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  add_prefix "extr" (space_implode "_" (s :: vs)) ^ "_correctness";
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fun extr_name s vs = add_prefix "extr" (space_implode "_" (s :: vs));
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fun msg d s = priority (implode (replicate d " ") ^ s);
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fun vars_of t = rev (foldl_aterms
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  (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t));
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fun vfs_of t = vars_of t @ sort (make_ord atless) (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 (Term.add_vars ([], t), 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 (Term.add_frees ([], t), 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 ExtractionArgs =
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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 : (Sign.sg -> 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 prep_ext = 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 sg (x : T) = ();
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end;
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structure ExtractionData = TheoryDataFun(ExtractionArgs);
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fun read_condeq thy =
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  let val sg = sign_of (add_syntax thy)
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  in fn s =>
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    let val t = Logic.varify (term_of (read_cterm sg (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 (map (prep_eq thy) eqns, realizes_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 (eqns', typeof_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 ":" mem explode 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 sg vs Ts t =
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  let
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    val {typeof_eqns, ...} = ExtractionData.get_sg sg;
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    fun err () = error ("Unable to determine type of extracted program for\n" ^
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      Sign.string_of_term sg t)
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  in case strip_abs_body (freeze_thaw (condrew sg (#net typeof_eqns)
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    [typeof_proc (Sign.defaultS sg) 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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         (map (prep_rlz thy) (rev rs), realizers),
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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 = flat (map (fst o snd) types);
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    val rtypes = map fst types;
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    val eqns = Net.merge (#net realizes_eqns, #net typeof_eqns, K false);
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    val thy' = add_syntax thy;
berghofe@13402
   318
    val sign = sign_of thy';
berghofe@13402
   319
    val tsg = Sign.tsig_of sign;
berghofe@13402
   320
    val rd = ProofSyntax.read_proof thy' false
berghofe@13402
   321
  in fn (thm, (vs, s1, s2)) =>
berghofe@13402
   322
    let
berghofe@13402
   323
      val name = Thm.name_of_thm thm;
berghofe@13402
   324
      val _ = assert (name <> "") "add_realizers: unnamed theorem";
berghofe@13402
   325
      val prop = Pattern.rewrite_term tsg
berghofe@13402
   326
        (map (Logic.dest_equals o prop_of) defs) [] (prop_of thm);
berghofe@13402
   327
      val vars = vars_of prop;
berghofe@13732
   328
      val vars' = filter_out (fn v =>
berghofe@13732
   329
        tname_of (body_type (fastype_of v)) mem rtypes) vars;
berghofe@13402
   330
      val T = etype_of sign vs [] prop;
berghofe@13402
   331
      val (T', thw) = Type.freeze_thaw_type
berghofe@13732
   332
        (if T = nullT then nullT else map fastype_of vars' ---> T);
berghofe@13402
   333
      val t = map_term_types thw (term_of (read_cterm sign (s1, T')));
berghofe@13732
   334
      val r' = freeze_thaw (condrew sign eqns
berghofe@13732
   335
        (procs @ [typeof_proc (Sign.defaultS sign) vs, rlz_proc]))
berghofe@13402
   336
          (Const ("realizes", T --> propT --> propT) $
berghofe@13732
   337
            (if T = nullT then t else list_comb (t, vars')) $ prop);
berghofe@13732
   338
      val r = foldr forall_intr (map (get_var_type r') vars, r');
berghofe@13402
   339
      val prf = Reconstruct.reconstruct_proof sign r (rd s2);
berghofe@13402
   340
    in (name, (vs, (t, prf))) end
berghofe@13402
   341
  end;
berghofe@13402
   342
berghofe@13402
   343
val add_realizers_i = gen_add_realizers
berghofe@13402
   344
  (fn _ => fn (name, (vs, t, prf)) => (name, (vs, (t, prf))));
berghofe@13402
   345
val add_realizers = gen_add_realizers prep_realizer;
berghofe@13402
   346
berghofe@13714
   347
fun realizes_of thy vs t prop =
berghofe@13714
   348
  let
berghofe@13714
   349
    val thy' = add_syntax thy;
berghofe@13714
   350
    val sign = sign_of thy';
berghofe@13732
   351
    val {realizes_eqns, typeof_eqns, defs, types, ...} =
berghofe@13714
   352
      ExtractionData.get thy';
berghofe@13732
   353
    val procs = flat (map (fst o snd) types);
berghofe@13714
   354
    val eqns = Net.merge (#net realizes_eqns, #net typeof_eqns, K false);
berghofe@13714
   355
    val prop' = Pattern.rewrite_term (Sign.tsig_of sign)
berghofe@13714
   356
      (map (Logic.dest_equals o prop_of) defs) [] prop;
berghofe@13732
   357
  in freeze_thaw (condrew sign eqns
berghofe@13732
   358
    (procs @ [typeof_proc (Sign.defaultS sign) vs, rlz_proc]))
berghofe@13714
   359
      (Const ("realizes", fastype_of t --> propT --> propT) $ t $ prop')
berghofe@13714
   360
  end;
berghofe@13714
   361
berghofe@13402
   362
(** expanding theorems / definitions **)
berghofe@13402
   363
berghofe@13402
   364
fun add_expand_thm (thy, thm) =
berghofe@13402
   365
  let
berghofe@13402
   366
    val {realizes_eqns, typeof_eqns, types, realizers,
berghofe@13402
   367
      defs, expand, prep} = ExtractionData.get thy;
berghofe@13402
   368
berghofe@13402
   369
    val name = Thm.name_of_thm thm;
berghofe@13402
   370
    val _ = assert (name <> "") "add_expand_thms: unnamed theorem";
berghofe@13402
   371
berghofe@13402
   372
    val is_def =
berghofe@13402
   373
      (case strip_comb (fst (Logic.dest_equals (prop_of thm))) of
berghofe@13402
   374
         (Const _, ts) => forall is_Var ts andalso null (duplicates ts)
berghofe@13402
   375
           andalso exists (fn thy =>
berghofe@13402
   376
               is_some (Symtab.lookup (#axioms (rep_theory thy), name)))
berghofe@13402
   377
             (thy :: ancestors_of thy)
berghofe@13402
   378
       | _ => false) handle TERM _ => false;
berghofe@13402
   379
berghofe@13402
   380
    val name = Thm.name_of_thm thm;
berghofe@13402
   381
    val _ = assert (name <> "") "add_expand_thms: unnamed theorem";
berghofe@13402
   382
  in
berghofe@13402
   383
    (ExtractionData.put (if is_def then
berghofe@13402
   384
        {realizes_eqns = realizes_eqns,
berghofe@13402
   385
         typeof_eqns = add_rule (([],
berghofe@13402
   386
           Logic.dest_equals (prop_of (Drule.abs_def thm))), typeof_eqns),
berghofe@13402
   387
         types = types,
berghofe@13402
   388
         realizers = realizers, defs = gen_ins eq_thm (thm, defs),
berghofe@13402
   389
         expand = expand, prep = prep}
berghofe@13402
   390
      else
berghofe@13402
   391
        {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns, types = types,
berghofe@13402
   392
         realizers = realizers, defs = defs,
berghofe@13402
   393
         expand = (name, prop_of thm) ins expand, prep = prep}) thy, thm)
berghofe@13402
   394
  end;
berghofe@13402
   395
berghofe@13402
   396
fun add_expand_thms thms thy = foldl (fst o add_expand_thm) (thy, thms);
berghofe@13402
   397
berghofe@13732
   398
(** types with computational content **)
berghofe@13732
   399
berghofe@13732
   400
fun add_types tys thy =
berghofe@13732
   401
  let val {realizes_eqns, typeof_eqns, types, realizers,
berghofe@13732
   402
    defs, expand, prep} = ExtractionData.get thy;
berghofe@13732
   403
  in
berghofe@13732
   404
    ExtractionData.put
berghofe@13732
   405
      {realizes_eqns = realizes_eqns, typeof_eqns = typeof_eqns,
berghofe@13732
   406
       types = map (apfst (Sign.intern_tycon (sign_of thy))) tys @ types,
berghofe@13732
   407
       realizers = realizers, defs = defs, expand = expand, prep = prep} thy
berghofe@13732
   408
  end;
berghofe@13732
   409
berghofe@13402
   410
berghofe@13402
   411
(**** extract program ****)
berghofe@13402
   412
berghofe@13402
   413
val dummyt = Const ("dummy", dummyT);
berghofe@13402
   414
berghofe@13402
   415
fun extract thms thy =
berghofe@13402
   416
  let
berghofe@13402
   417
    val sg = sign_of (add_syntax thy);
berghofe@13402
   418
    val tsg = Sign.tsig_of sg;
berghofe@13402
   419
    val {realizes_eqns, typeof_eqns, types, realizers, defs, expand, prep} =
berghofe@13402
   420
      ExtractionData.get thy;
berghofe@13732
   421
    val procs = flat (map (fst o snd) types);
berghofe@13732
   422
    val rtypes = map fst types;
berghofe@13402
   423
    val typroc = typeof_proc (Sign.defaultS sg);
berghofe@13402
   424
    val prep = if_none prep (K I) sg o ProofRewriteRules.elim_defs sg false defs o
berghofe@13402
   425
      Reconstruct.expand_proof sg (("", None) :: map (apsnd Some) expand);
berghofe@13402
   426
    val rrews = Net.merge (#net realizes_eqns, #net typeof_eqns, K false);
berghofe@13402
   427
berghofe@13402
   428
    fun find_inst prop Ts ts vs =
berghofe@13402
   429
      let
berghofe@13732
   430
        val rvs = relevant_vars rtypes prop;
berghofe@13402
   431
        val vars = vars_of prop;
berghofe@13402
   432
        val n = Int.min (length vars, length ts);
berghofe@13402
   433
berghofe@13402
   434
        fun add_args ((Var ((a, i), _), t), (vs', tye)) =
berghofe@13402
   435
          if a mem rvs then
berghofe@13402
   436
            let val T = etype_of sg vs Ts t
berghofe@13402
   437
            in if T = nullT then (vs', tye)
berghofe@13402
   438
               else (a :: vs', (("'" ^ a, i), T) :: tye)
berghofe@13402
   439
            end
berghofe@13402
   440
          else (vs', tye)
berghofe@13402
   441
berghofe@13402
   442
      in foldr add_args (take (n, vars) ~~ take (n, ts), ([], [])) end;
berghofe@13402
   443
berghofe@13402
   444
    fun find vs = apsome snd o find_first (curry eq_set vs o fst);
berghofe@13402
   445
    fun find' s = map snd o filter (equal s o fst)
berghofe@13402
   446
berghofe@13732
   447
    fun app_rlz_rews Ts vs t = strip_abs (length Ts) (freeze_thaw
berghofe@13732
   448
      (condrew sg rrews (procs @ [typroc vs, rlz_proc])) (list_abs
berghofe@13732
   449
        (map (pair "x") (rev Ts), t)));
berghofe@13732
   450
berghofe@13732
   451
    fun realizes_null vs prop = app_rlz_rews [] vs
berghofe@13732
   452
      (Const ("realizes", nullT --> propT --> propT) $ nullt $ prop);
berghofe@13402
   453
berghofe@13402
   454
    fun corr d defs vs ts Ts hs (PBound i) _ _ = (defs, PBound i)
berghofe@13402
   455
berghofe@13402
   456
      | corr d defs vs ts Ts hs (Abst (s, Some T, prf)) (Abst (_, _, prf')) t =
berghofe@13402
   457
          let val (defs', corr_prf) = corr d defs vs [] (T :: Ts)
berghofe@13402
   458
            (dummyt :: hs) prf (incr_pboundvars 1 0 prf')
berghofe@13402
   459
            (case t of Some (Abs (_, _, u)) => Some u | _ => None)
berghofe@13402
   460
          in (defs', Abst (s, Some T, corr_prf)) end
berghofe@13402
   461
berghofe@13402
   462
      | corr d defs vs ts Ts hs (AbsP (s, Some prop, prf)) (AbsP (_, _, prf')) t =
berghofe@13402
   463
          let
berghofe@13402
   464
            val T = etype_of sg vs Ts prop;
berghofe@13402
   465
            val u = if T = nullT then 
berghofe@13402
   466
                (case t of Some u => Some (incr_boundvars 1 u) | None => None)
berghofe@13402
   467
              else (case t of Some (Abs (_, _, u)) => Some u | _ => None);
berghofe@13402
   468
            val (defs', corr_prf) = corr d defs vs [] (T :: Ts) (prop :: hs)
berghofe@13402
   469
              (incr_pboundvars 0 1 prf) (incr_pboundvars 0 1 prf') u;
berghofe@13402
   470
            val rlz = Const ("realizes", T --> propT --> propT)
berghofe@13402
   471
          in (defs',
berghofe@13732
   472
            if T = nullT then AbsP ("R",
berghofe@13732
   473
              Some (app_rlz_rews Ts vs (rlz $ nullt $ prop)),
berghofe@13732
   474
                prf_subst_bounds [nullt] corr_prf)
berghofe@13402
   475
            else Abst (s, Some T, AbsP ("R",
berghofe@13732
   476
              Some (app_rlz_rews (T :: Ts) vs
berghofe@13732
   477
                (rlz $ Bound 0 $ incr_boundvars 1 prop)), corr_prf)))
berghofe@13402
   478
          end
berghofe@13402
   479
berghofe@13402
   480
      | corr d defs vs ts Ts hs (prf % Some t) (prf' % _) t' =
berghofe@13732
   481
          let
berghofe@13732
   482
            val (Us, T) = strip_type (fastype_of1 (Ts, t));
berghofe@13732
   483
            val (defs', corr_prf) = corr d defs vs (t :: ts) Ts hs prf prf'
berghofe@13732
   484
              (if tname_of T mem rtypes then t'
berghofe@13732
   485
               else (case t' of Some (u $ _) => Some u | _ => None));
berghofe@13732
   486
            val u = if not (tname_of T mem rtypes) then t else
berghofe@13732
   487
              let
berghofe@13732
   488
                val eT = etype_of sg vs Ts t;
berghofe@13732
   489
                val (r, Us') = if eT = nullT then (nullt, Us) else
berghofe@13732
   490
                  (Bound (length Us), eT :: Us);
berghofe@13732
   491
                val u = list_comb (incr_boundvars (length Us') t,
berghofe@13732
   492
                  map Bound (length Us - 1 downto 0));
berghofe@13732
   493
                val u' = (case assoc (types, tname_of T) of
berghofe@13732
   494
                    Some ((_, Some f)) => f r eT u T
berghofe@13732
   495
                  | _ => Const ("realizes", eT --> T --> T) $ r $ u)
berghofe@13732
   496
              in app_rlz_rews Ts vs (list_abs (map (pair "x") Us', u')) end
berghofe@13732
   497
          in (defs', corr_prf % Some u) end
berghofe@13402
   498
berghofe@13402
   499
      | corr d defs vs ts Ts hs (prf1 %% prf2) (prf1' %% prf2') t =
berghofe@13402
   500
          let
berghofe@13402
   501
            val prop = Reconstruct.prop_of' hs prf2';
berghofe@13402
   502
            val T = etype_of sg vs Ts prop;
berghofe@13402
   503
            val (defs1, f, u) = if T = nullT then (defs, t, None) else
berghofe@13402
   504
              (case t of
berghofe@13402
   505
                 Some (f $ u) => (defs, Some f, Some u)
berghofe@13402
   506
               | _ =>
berghofe@13402
   507
                 let val (defs1, u) = extr d defs vs [] Ts hs prf2'
berghofe@13402
   508
                 in (defs1, None, Some u) end)
berghofe@13402
   509
            val (defs2, corr_prf1) = corr d defs1 vs [] Ts hs prf1 prf1' f;
berghofe@13402
   510
            val (defs3, corr_prf2) = corr d defs2 vs [] Ts hs prf2 prf2' u;
berghofe@13402
   511
          in
berghofe@13402
   512
            if T = nullT then (defs3, corr_prf1 %% corr_prf2) else
berghofe@13402
   513
              (defs3, corr_prf1 % u %% corr_prf2)
berghofe@13402
   514
          end
berghofe@13402
   515
berghofe@13402
   516
      | corr d defs vs ts Ts hs (prf0 as PThm ((name, _), prf, prop, Some Ts')) _ _ =
berghofe@13402
   517
          let
berghofe@13402
   518
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   519
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye;
berghofe@13402
   520
            val T = etype_of sg vs' [] prop;
berghofe@13402
   521
            val defs' = if T = nullT then defs
berghofe@13402
   522
              else fst (extr d defs vs ts Ts hs prf0)
berghofe@13402
   523
          in
berghofe@13609
   524
            if T = nullT andalso realizes_null vs' prop aconv prop then (defs, prf0)
berghofe@13402
   525
            else case Symtab.lookup (realizers, name) of
berghofe@13402
   526
              None => (case find vs' (find' name defs') of
berghofe@13402
   527
                None =>
berghofe@13402
   528
                  let
berghofe@13402
   529
                    val _ = assert (T = nullT) "corr: internal error";
berghofe@13402
   530
                    val _ = msg d ("Building correctness proof for " ^ quote name ^
berghofe@13402
   531
                      (if null vs' then ""
berghofe@13402
   532
                       else " (relevant variables: " ^ commas_quote vs' ^ ")"));
berghofe@13402
   533
                    val prf' = prep (Reconstruct.reconstruct_proof sg prop prf);
berghofe@13402
   534
                    val (defs'', corr_prf) =
berghofe@13402
   535
                      corr (d + 1) defs' vs' [] [] [] prf' prf' None;
berghofe@13732
   536
                    val corr_prop = Reconstruct.prop_of corr_prf;
berghofe@13732
   537
                    val corr_prf' = foldr forall_intr_prf
berghofe@13732
   538
                      (map (get_var_type corr_prop) (vfs_of prop), proof_combt
berghofe@13793
   539
                         (PThm ((corr_name name vs', []), corr_prf, corr_prop,
berghofe@13732
   540
                             Some (map TVar (term_tvars corr_prop))), vfs_of corr_prop))
berghofe@13402
   541
                  in
berghofe@13732
   542
                    ((name, (vs', ((nullt, nullt), (corr_prf, corr_prf')))) :: defs'',
berghofe@13402
   543
                     prf_subst_TVars tye' corr_prf')
berghofe@13402
   544
                  end
berghofe@13732
   545
              | Some (_, (_, prf')) => (defs', prf_subst_TVars tye' prf'))
berghofe@13402
   546
            | Some rs => (case find vs' rs of
berghofe@13402
   547
                Some (_, prf') => (defs', prf_subst_TVars tye' prf')
berghofe@13402
   548
              | None => error ("corr: no realizer for instance of theorem " ^
berghofe@13402
   549
                  quote name ^ ":\n" ^ Sign.string_of_term sg (Envir.beta_norm
berghofe@13402
   550
                    (Reconstruct.prop_of (proof_combt (prf0, ts))))))
berghofe@13402
   551
          end
berghofe@13402
   552
berghofe@13402
   553
      | corr d defs vs ts Ts hs (prf0 as PAxm (s, prop, Some Ts')) _ _ =
berghofe@13402
   554
          let
berghofe@13402
   555
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   556
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   557
          in
berghofe@13609
   558
            if etype_of sg vs' [] prop = nullT andalso
berghofe@13609
   559
              realizes_null vs' prop aconv prop then (defs, prf0)
berghofe@13609
   560
            else case find vs' (Symtab.lookup_multi (realizers, s)) of
berghofe@13402
   561
              Some (_, prf) => (defs, prf_subst_TVars tye' prf)
berghofe@13402
   562
            | None => error ("corr: no realizer for instance of axiom " ^
berghofe@13402
   563
                quote s ^ ":\n" ^ Sign.string_of_term sg (Envir.beta_norm
berghofe@13402
   564
                  (Reconstruct.prop_of (proof_combt (prf0, ts)))))
berghofe@13402
   565
          end
berghofe@13402
   566
berghofe@13402
   567
      | corr d defs vs ts Ts hs _ _ _ = error "corr: bad proof"
berghofe@13402
   568
berghofe@13402
   569
    and extr d defs vs ts Ts hs (PBound i) = (defs, Bound i)
berghofe@13402
   570
berghofe@13402
   571
      | extr d defs vs ts Ts hs (Abst (s, Some T, prf)) =
berghofe@13402
   572
          let val (defs', t) = extr d defs vs []
berghofe@13402
   573
            (T :: Ts) (dummyt :: hs) (incr_pboundvars 1 0 prf)
berghofe@13402
   574
          in (defs', Abs (s, T, t)) end
berghofe@13402
   575
berghofe@13402
   576
      | extr d defs vs ts Ts hs (AbsP (s, Some t, prf)) =
berghofe@13402
   577
          let
berghofe@13402
   578
            val T = etype_of sg vs Ts t;
berghofe@13402
   579
            val (defs', t) = extr d defs vs [] (T :: Ts) (t :: hs)
berghofe@13402
   580
              (incr_pboundvars 0 1 prf)
berghofe@13402
   581
          in (defs',
berghofe@13402
   582
            if T = nullT then subst_bound (nullt, t) else Abs (s, T, t))
berghofe@13402
   583
          end
berghofe@13402
   584
berghofe@13402
   585
      | extr d defs vs ts Ts hs (prf % Some t) =
berghofe@13402
   586
          let val (defs', u) = extr d defs vs (t :: ts) Ts hs prf
berghofe@13732
   587
          in (defs',
berghofe@13732
   588
            if tname_of (body_type (fastype_of1 (Ts, t))) mem rtypes then u
berghofe@13732
   589
            else u $ t)
berghofe@13732
   590
          end
berghofe@13402
   591
berghofe@13402
   592
      | extr d defs vs ts Ts hs (prf1 %% prf2) =
berghofe@13402
   593
          let
berghofe@13402
   594
            val (defs', f) = extr d defs vs [] Ts hs prf1;
berghofe@13402
   595
            val prop = Reconstruct.prop_of' hs prf2;
berghofe@13402
   596
            val T = etype_of sg vs Ts prop
berghofe@13402
   597
          in
berghofe@13402
   598
            if T = nullT then (defs', f) else
berghofe@13402
   599
              let val (defs'', t) = extr d defs' vs [] Ts hs prf2
berghofe@13402
   600
              in (defs'', f $ t) end
berghofe@13402
   601
          end
berghofe@13402
   602
berghofe@13402
   603
      | extr d defs vs ts Ts hs (prf0 as PThm ((s, _), prf, prop, Some Ts')) =
berghofe@13402
   604
          let
berghofe@13402
   605
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   606
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   607
          in
berghofe@13402
   608
            case Symtab.lookup (realizers, s) of
berghofe@13402
   609
              None => (case find vs' (find' s defs) of
berghofe@13402
   610
                None =>
berghofe@13402
   611
                  let
berghofe@13402
   612
                    val _ = msg d ("Extracting " ^ quote s ^
berghofe@13402
   613
                      (if null vs' then ""
berghofe@13402
   614
                       else " (relevant variables: " ^ commas_quote vs' ^ ")"));
berghofe@13402
   615
                    val prf' = prep (Reconstruct.reconstruct_proof sg prop prf);
berghofe@13402
   616
                    val (defs', t) = extr (d + 1) defs vs' [] [] [] prf';
berghofe@13402
   617
                    val (defs'', corr_prf) =
berghofe@13402
   618
                      corr (d + 1) defs' vs' [] [] [] prf' prf' (Some t);
berghofe@13402
   619
berghofe@13402
   620
                    val nt = Envir.beta_norm t;
berghofe@13732
   621
                    val args = filter_out (fn v => tname_of (body_type
berghofe@13732
   622
                      (fastype_of v)) mem rtypes) (vfs_of prop);
berghofe@13402
   623
                    val args' = filter (fn v => Logic.occs (v, nt)) args;
berghofe@13402
   624
                    val t' = mkabs (args', nt);
berghofe@13402
   625
                    val T = fastype_of t';
berghofe@13732
   626
                    val cname = extr_name s vs';
berghofe@13402
   627
                    val c = Const (cname, T);
berghofe@13402
   628
                    val u = mkabs (args, list_comb (c, args'));
berghofe@13402
   629
                    val eqn = Logic.mk_equals (c, t');
berghofe@13402
   630
                    val rlz =
berghofe@13402
   631
                      Const ("realizes", fastype_of nt --> propT --> propT);
berghofe@13732
   632
                    val lhs = app_rlz_rews [] vs' (rlz $ nt $ prop);
berghofe@13732
   633
                    val rhs = app_rlz_rews [] vs' (rlz $ list_comb (c, args') $ prop);
berghofe@13732
   634
                    val f = app_rlz_rews [] vs'
berghofe@13732
   635
                      (Abs ("x", T, rlz $ list_comb (Bound 0, args') $ prop));
berghofe@13402
   636
berghofe@13732
   637
                    val corr_prf' =
berghofe@13732
   638
                      chtype [] equal_elim_axm %> lhs %> rhs %%
berghofe@13732
   639
                       (chtype [propT] symmetric_axm %> rhs %> lhs %%
berghofe@13732
   640
                         (chtype [propT, T] combination_axm %> f %> f %> c %> t' %%
berghofe@13732
   641
                           (chtype [T --> propT] reflexive_axm %> f) %%
berghofe@13732
   642
                           PAxm (cname ^ "_def", eqn,
berghofe@13732
   643
                             Some (map TVar (term_tvars eqn))))) %% corr_prf;
berghofe@13732
   644
                    val corr_prop = Reconstruct.prop_of corr_prf';
berghofe@13732
   645
                    val corr_prf'' = foldr forall_intr_prf
berghofe@13732
   646
                      (map (get_var_type corr_prop) (vfs_of prop), proof_combt
berghofe@13732
   647
                        (PThm ((corr_name s vs', []), corr_prf', corr_prop,
berghofe@13732
   648
                          Some (map TVar (term_tvars corr_prop))), vfs_of corr_prop));
berghofe@13402
   649
                  in
berghofe@13732
   650
                    ((s, (vs', ((t', u), (corr_prf', corr_prf'')))) :: defs'',
berghofe@13402
   651
                     subst_TVars tye' u)
berghofe@13402
   652
                  end
berghofe@13402
   653
              | Some ((_, u), _) => (defs, subst_TVars tye' u))
berghofe@13402
   654
            | Some rs => (case find vs' rs of
berghofe@13402
   655
                Some (t, _) => (defs, subst_TVars tye' t)
berghofe@13402
   656
              | None => error ("extr: no realizer for instance of theorem " ^
berghofe@13402
   657
                  quote s ^ ":\n" ^ Sign.string_of_term sg (Envir.beta_norm
berghofe@13402
   658
                    (Reconstruct.prop_of (proof_combt (prf0, ts))))))
berghofe@13402
   659
          end
berghofe@13402
   660
berghofe@13402
   661
      | extr d defs vs ts Ts hs (prf0 as PAxm (s, prop, Some Ts')) =
berghofe@13402
   662
          let
berghofe@13402
   663
            val (vs', tye) = find_inst prop Ts ts vs;
berghofe@13402
   664
            val tye' = (map fst (term_tvars prop) ~~ Ts') @ tye
berghofe@13402
   665
          in
berghofe@13402
   666
            case find vs' (Symtab.lookup_multi (realizers, s)) of
berghofe@13402
   667
              Some (t, _) => (defs, subst_TVars tye' t)
berghofe@13609
   668
            | None => error ("extr: no realizer for instance of axiom " ^
berghofe@13402
   669
                quote s ^ ":\n" ^ Sign.string_of_term sg (Envir.beta_norm
berghofe@13402
   670
                  (Reconstruct.prop_of (proof_combt (prf0, ts)))))
berghofe@13402
   671
          end
berghofe@13402
   672
berghofe@13402
   673
      | extr d defs vs ts Ts hs _ = error "extr: bad proof";
berghofe@13402
   674
berghofe@13732
   675
    fun prep_thm (thm, vs) =
berghofe@13402
   676
      let
berghofe@13402
   677
        val {prop, der = (_, prf), sign, ...} = rep_thm thm;
berghofe@13402
   678
        val name = Thm.name_of_thm thm;
berghofe@13402
   679
        val _ = assert (name <> "") "extraction: unnamed theorem";
berghofe@13732
   680
        val _ = assert (etype_of sg vs [] prop <> nullT) ("theorem " ^
berghofe@13402
   681
          quote name ^ " has no computational content")
berghofe@13732
   682
      in (Reconstruct.reconstruct_proof sign prop prf, vs) end;
berghofe@13402
   683
berghofe@13732
   684
    val defs = foldl (fn (defs, (prf, vs)) =>
berghofe@13732
   685
      fst (extr 0 defs vs [] [] [] prf)) ([], map prep_thm thms);
berghofe@13402
   686
    val {path, ...} = Sign.rep_sg sg;
berghofe@13402
   687
berghofe@13732
   688
    fun add_def ((s, (vs, ((t, u), (prf, _)))), thy) =
berghofe@13732
   689
      (case Sign.const_type (sign_of thy) (extr_name s vs) of
berghofe@13732
   690
         None =>
berghofe@13732
   691
           let
berghofe@13732
   692
             val corr_prop = Reconstruct.prop_of prf;
berghofe@13732
   693
             val ft = fst (Type.freeze_thaw t);
berghofe@13732
   694
             val fu = fst (Type.freeze_thaw u);
berghofe@13732
   695
             val thy' = if t = nullt then thy else thy |>
berghofe@13732
   696
               Theory.add_consts_i [(extr_name s vs, fastype_of ft, NoSyn)] |>
berghofe@13732
   697
               fst o PureThy.add_defs_i false [((extr_name s vs ^ "_def",
berghofe@13732
   698
                 Logic.mk_equals (head_of (strip_abs_body fu), ft)), [])];
berghofe@13732
   699
           in
berghofe@13732
   700
             fst (PureThy.store_thm ((corr_name s vs,
berghofe@13732
   701
               Thm.varifyT (funpow (length (term_vars corr_prop))
berghofe@13732
   702
                 (forall_elim_var 0) (forall_intr_frees
berghofe@13732
   703
                   (ProofChecker.thm_of_proof thy'
berghofe@13732
   704
                     (fst (Proofterm.freeze_thaw_prf prf)))))), []) thy')
berghofe@13732
   705
           end
berghofe@13732
   706
       | Some _ => thy);
berghofe@13402
   707
berghofe@13402
   708
  in thy |>
berghofe@13402
   709
    Theory.absolute_path |>
berghofe@13402
   710
    curry (foldr add_def) defs |>
berghofe@13402
   711
    Theory.add_path (NameSpace.pack (if_none path []))
berghofe@13402
   712
  end;
berghofe@13402
   713
berghofe@13402
   714
berghofe@13402
   715
(**** interface ****)
berghofe@13402
   716
berghofe@13402
   717
structure P = OuterParse and K = OuterSyntax.Keyword;
berghofe@13402
   718
berghofe@13732
   719
val parse_vars = Scan.optional (P.$$$ "(" |-- P.list1 P.name --| P.$$$ ")") [];
berghofe@13732
   720
berghofe@13402
   721
val realizersP =
berghofe@13402
   722
  OuterSyntax.command "realizers"
berghofe@13402
   723
  "specify realizers for primitive axioms / theorems, together with correctness proof"
berghofe@13402
   724
  K.thy_decl
berghofe@13732
   725
    (Scan.repeat1 (P.xname -- parse_vars --| P.$$$ ":" -- P.string -- P.string) >>
berghofe@13402
   726
     (fn xs => Toplevel.theory (fn thy => add_realizers
berghofe@13402
   727
       (map (fn (((a, vs), s1), s2) =>
berghofe@13402
   728
         (PureThy.get_thm thy a, (vs, s1, s2))) xs) thy)));
berghofe@13402
   729
berghofe@13402
   730
val realizabilityP =
berghofe@13402
   731
  OuterSyntax.command "realizability"
berghofe@13402
   732
  "add equations characterizing realizability" K.thy_decl
berghofe@13402
   733
  (Scan.repeat1 P.string >> (Toplevel.theory o add_realizes_eqns));
berghofe@13402
   734
berghofe@13402
   735
val typeofP =
berghofe@13402
   736
  OuterSyntax.command "extract_type"
berghofe@13402
   737
  "add equations characterizing type of extracted program" K.thy_decl
berghofe@13402
   738
  (Scan.repeat1 P.string >> (Toplevel.theory o add_typeof_eqns));
berghofe@13402
   739
berghofe@13402
   740
val extractP =
berghofe@13402
   741
  OuterSyntax.command "extract" "extract terms from proofs" K.thy_decl
berghofe@13732
   742
    (Scan.repeat1 (P.xname -- parse_vars) >> (fn xs => Toplevel.theory
berghofe@13732
   743
      (fn thy => extract (map (apfst (PureThy.get_thm thy)) xs) thy)));
berghofe@13402
   744
berghofe@13402
   745
val parsers = [realizersP, realizabilityP, typeofP, extractP];
berghofe@13402
   746
berghofe@13402
   747
val setup =
berghofe@13402
   748
  [ExtractionData.init,
berghofe@13402
   749
berghofe@13732
   750
   add_types [("prop", ([], None))],
berghofe@13732
   751
berghofe@13402
   752
   add_typeof_eqns
berghofe@13402
   753
     ["(typeof (PROP P)) == (Type (TYPE(Null))) ==>  \
berghofe@13402
   754
    \  (typeof (PROP Q)) == (Type (TYPE('Q))) ==>  \
berghofe@13402
   755
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE('Q)))",
berghofe@13402
   756
berghofe@13402
   757
      "(typeof (PROP Q)) == (Type (TYPE(Null))) ==>  \
berghofe@13402
   758
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE(Null)))",
berghofe@13402
   759
berghofe@13402
   760
      "(typeof (PROP P)) == (Type (TYPE('P))) ==>  \
berghofe@13402
   761
    \  (typeof (PROP Q)) == (Type (TYPE('Q))) ==>  \
berghofe@13402
   762
    \    (typeof (PROP P ==> PROP Q)) == (Type (TYPE('P => 'Q)))",
berghofe@13402
   763
berghofe@13402
   764
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE(Null))) ==>  \
berghofe@13402
   765
    \    (typeof (!!x. PROP P (x))) == (Type (TYPE(Null)))",
berghofe@13402
   766
berghofe@13402
   767
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE('P))) ==>  \
berghofe@13402
   768
    \    (typeof (!!x::'a. PROP P (x))) == (Type (TYPE('a => 'P)))",
berghofe@13402
   769
berghofe@13402
   770
      "(%x. typeof (f (x))) == (%x. Type (TYPE('f))) ==>  \
berghofe@13402
   771
    \    (typeof (f)) == (Type (TYPE('f)))"],
berghofe@13402
   772
berghofe@13402
   773
   add_realizes_eqns
berghofe@13402
   774
     ["(typeof (PROP P)) == (Type (TYPE(Null))) ==>  \
berghofe@13402
   775
    \    (realizes (r) (PROP P ==> PROP Q)) ==  \
berghofe@13402
   776
    \    (PROP realizes (Null) (PROP P) ==> PROP realizes (r) (PROP Q))",
berghofe@13402
   777
berghofe@13402
   778
      "(typeof (PROP P)) == (Type (TYPE('P))) ==>  \
berghofe@13402
   779
    \  (typeof (PROP Q)) == (Type (TYPE(Null))) ==>  \
berghofe@13402
   780
    \    (realizes (r) (PROP P ==> PROP Q)) ==  \
berghofe@13402
   781
    \    (!!x::'P. PROP realizes (x) (PROP P) ==> PROP realizes (Null) (PROP Q))",
berghofe@13402
   782
berghofe@13402
   783
      "(realizes (r) (PROP P ==> PROP Q)) ==  \
berghofe@13402
   784
    \  (!!x. PROP realizes (x) (PROP P) ==> PROP realizes (r (x)) (PROP Q))",
berghofe@13402
   785
berghofe@13402
   786
      "(%x. typeof (PROP P (x))) == (%x. Type (TYPE(Null))) ==>  \
berghofe@13402
   787
    \    (realizes (r) (!!x. PROP P (x))) ==  \
berghofe@13402
   788
    \    (!!x. PROP realizes (Null) (PROP P (x)))",
berghofe@13402
   789
berghofe@13402
   790
      "(realizes (r) (!!x. PROP P (x))) ==  \
berghofe@13402
   791
    \  (!!x. PROP realizes (r (x)) (PROP P (x)))"],
berghofe@13402
   792
berghofe@13402
   793
   Attrib.add_attributes
berghofe@13402
   794
     [("extraction_expand",
berghofe@13402
   795
       (Attrib.no_args add_expand_thm, K Attrib.undef_local_attribute),
berghofe@13402
   796
       "specify theorems / definitions to be expanded during extraction")]];
berghofe@13402
   797
berghofe@13714
   798
val etype_of = etype_of o sign_of o add_syntax;
berghofe@13714
   799
berghofe@13402
   800
end;
berghofe@13402
   801
berghofe@13402
   802
OuterSyntax.add_parsers Extraction.parsers;