--- a/src/HOL/Tools/datatype_realizer.ML Wed Jun 10 16:22:54 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,230 +0,0 @@
-(* Title: HOL/Tools/datatype_realizer.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Porgram extraction from proofs involving datatypes:
-Realizers for induction and case analysis
-*)
-
-signature DATATYPE_REALIZER =
-sig
- val add_dt_realizers: string list -> theory -> theory
- val setup: theory -> theory
-end;
-
-structure DatatypeRealizer : DATATYPE_REALIZER =
-struct
-
-open DatatypeAux;
-
-fun subsets i j = if i <= j then
- let val is = subsets (i+1) j
- in map (fn ks => i::ks) is @ is end
- else [[]];
-
-fun forall_intr_prf (t, prf) =
- let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
- in Abst (a, SOME T, Proofterm.prf_abstract_over t prf) end;
-
-fun prf_of thm =
- Reconstruct.reconstruct_proof (Thm.theory_of_thm thm) (Thm.prop_of thm) (Thm.proof_of thm);
-
-fun prf_subst_vars inst =
- Proofterm.map_proof_terms (subst_vars ([], inst)) I;
-
-fun is_unit t = snd (strip_type (fastype_of t)) = HOLogic.unitT;
-
-fun tname_of (Type (s, _)) = s
- | tname_of _ = "";
-
-fun mk_realizes T = Const ("realizes", T --> HOLogic.boolT --> HOLogic.boolT);
-
-fun make_ind sorts ({descr, rec_names, rec_rewrites, induction, ...} : datatype_info) is thy =
- let
- val recTs = get_rec_types descr sorts;
- val pnames = if length descr = 1 then ["P"]
- else map (fn i => "P" ^ string_of_int i) (1 upto length descr);
-
- val rec_result_Ts = map (fn ((i, _), P) =>
- if i mem is then TFree ("'" ^ P, HOLogic.typeS) else HOLogic.unitT)
- (descr ~~ pnames);
-
- fun make_pred i T U r x =
- if i mem is then
- Free (List.nth (pnames, i), T --> U --> HOLogic.boolT) $ r $ x
- else Free (List.nth (pnames, i), U --> HOLogic.boolT) $ x;
-
- fun mk_all i s T t =
- if i mem is then list_all_free ([(s, T)], t) else t;
-
- val (prems, rec_fns) = split_list (flat (fst (fold_map
- (fn ((i, (_, _, constrs)), T) => fold_map (fn (cname, cargs) => fn j =>
- let
- val Ts = map (typ_of_dtyp descr sorts) cargs;
- val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
- val recs = filter (is_rec_type o fst o fst) (cargs ~~ tnames ~~ Ts);
- val frees = tnames ~~ Ts;
-
- fun mk_prems vs [] =
- let
- val rT = nth (rec_result_Ts) i;
- val vs' = filter_out is_unit vs;
- val f = mk_Free "f" (map fastype_of vs' ---> rT) j;
- val f' = Envir.eta_contract (list_abs_free
- (map dest_Free vs, if i mem is then list_comb (f, vs')
- else HOLogic.unit));
- in (HOLogic.mk_Trueprop (make_pred i rT T (list_comb (f, vs'))
- (list_comb (Const (cname, Ts ---> T), map Free frees))), f')
- end
- | mk_prems vs (((dt, s), T) :: ds) =
- let
- val k = body_index dt;
- val (Us, U) = strip_type T;
- val i = length Us;
- val rT = nth (rec_result_Ts) k;
- val r = Free ("r" ^ s, Us ---> rT);
- val (p, f) = mk_prems (vs @ [r]) ds
- in (mk_all k ("r" ^ s) (Us ---> rT) (Logic.mk_implies
- (list_all (map (pair "x") Us, HOLogic.mk_Trueprop
- (make_pred k rT U (app_bnds r i)
- (app_bnds (Free (s, T)) i))), p)), f)
- end
-
- in (apfst (curry list_all_free frees) (mk_prems (map Free frees) recs), j + 1) end)
- constrs) (descr ~~ recTs) 1)));
-
- fun mk_proj j [] t = t
- | mk_proj j (i :: is) t = if null is then t else
- if (j: int) = i then HOLogic.mk_fst t
- else mk_proj j is (HOLogic.mk_snd t);
-
- val tnames = DatatypeProp.make_tnames recTs;
- val fTs = map fastype_of rec_fns;
- val ps = map (fn ((((i, _), T), U), s) => Abs ("x", T, make_pred i U T
- (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Bound 0) (Bound 0)))
- (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names);
- val r = if null is then Extraction.nullt else
- foldr1 HOLogic.mk_prod (List.mapPartial (fn (((((i, _), T), U), s), tname) =>
- if i mem is then SOME
- (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Free (tname, T))
- else NONE) (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names ~~ tnames));
- val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
- (map (fn ((((i, _), T), U), tname) =>
- make_pred i U T (mk_proj i is r) (Free (tname, T)))
- (descr ~~ recTs ~~ rec_result_Ts ~~ tnames)));
- val cert = cterm_of thy;
- val inst = map (pairself cert) (map head_of (HOLogic.dest_conj
- (HOLogic.dest_Trueprop (concl_of induction))) ~~ ps);
-
- val thm = OldGoals.simple_prove_goal_cterm (cert (Logic.list_implies (prems, concl)))
- (fn prems =>
- [rewrite_goals_tac (map mk_meta_eq [fst_conv, snd_conv]),
- rtac (cterm_instantiate inst induction) 1,
- ALLGOALS ObjectLogic.atomize_prems_tac,
- rewrite_goals_tac (@{thm o_def} :: map mk_meta_eq rec_rewrites),
- REPEAT ((resolve_tac prems THEN_ALL_NEW (fn i =>
- REPEAT (etac allE i) THEN atac i)) 1)]);
-
- val ind_name = Thm.get_name induction;
- val vs = map (fn i => List.nth (pnames, i)) is;
- val (thm', thy') = thy
- |> Sign.root_path
- |> PureThy.store_thm
- (Binding.qualified_name (space_implode "_" (ind_name :: vs @ ["correctness"])), thm)
- ||> Sign.restore_naming thy;
-
- val ivs = rev (Term.add_vars (Logic.varify (DatatypeProp.make_ind [descr] sorts)) []);
- val rvs = rev (Thm.fold_terms Term.add_vars thm' []);
- val ivs1 = map Var (filter_out (fn (_, T) =>
- tname_of (body_type T) mem ["set", "bool"]) ivs);
- val ivs2 = map (fn (ixn, _) => Var (ixn, valOf (AList.lookup (op =) rvs ixn))) ivs;
-
- val prf = List.foldr forall_intr_prf
- (List.foldr (fn ((f, p), prf) =>
- (case head_of (strip_abs_body f) of
- Free (s, T) =>
- let val T' = Logic.varifyT T
- in Abst (s, SOME T', Proofterm.prf_abstract_over
- (Var ((s, 0), T')) (AbsP ("H", SOME p, prf)))
- end
- | _ => AbsP ("H", SOME p, prf)))
- (Proofterm.proof_combP
- (prf_of thm', map PBound (length prems - 1 downto 0))) (rec_fns ~~ prems_of thm)) ivs2;
-
- val r' = if null is then r else Logic.varify (List.foldr (uncurry lambda)
- r (map Logic.unvarify ivs1 @ filter_out is_unit
- (map (head_of o strip_abs_body) rec_fns)));
-
- in Extraction.add_realizers_i [(ind_name, (vs, r', prf))] thy' end;
-
-
-fun make_casedists sorts ({index, descr, case_name, case_rewrites, exhaustion, ...} : datatype_info) thy =
- let
- val cert = cterm_of thy;
- val rT = TFree ("'P", HOLogic.typeS);
- val rT' = TVar (("'P", 0), HOLogic.typeS);
-
- fun make_casedist_prem T (cname, cargs) =
- let
- val Ts = map (typ_of_dtyp descr sorts) cargs;
- val frees = Name.variant_list ["P", "y"] (DatatypeProp.make_tnames Ts) ~~ Ts;
- val free_ts = map Free frees;
- val r = Free ("r" ^ Long_Name.base_name cname, Ts ---> rT)
- in (r, list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop
- (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))),
- HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $
- list_comb (r, free_ts)))))
- end;
-
- val SOME (_, _, constrs) = AList.lookup (op =) descr index;
- val T = List.nth (get_rec_types descr sorts, index);
- val (rs, prems) = split_list (map (make_casedist_prem T) constrs);
- val r = Const (case_name, map fastype_of rs ---> T --> rT);
-
- val y = Var (("y", 0), Logic.legacy_varifyT T);
- val y' = Free ("y", T);
-
- val thm = OldGoals.prove_goalw_cterm [] (cert (Logic.list_implies (prems,
- HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $
- list_comb (r, rs @ [y'])))))
- (fn prems =>
- [rtac (cterm_instantiate [(cert y, cert y')] exhaustion) 1,
- ALLGOALS (EVERY'
- [asm_simp_tac (HOL_basic_ss addsimps case_rewrites),
- resolve_tac prems, asm_simp_tac HOL_basic_ss])]);
-
- val exh_name = Thm.get_name exhaustion;
- val (thm', thy') = thy
- |> Sign.root_path
- |> PureThy.store_thm (Binding.qualified_name (exh_name ^ "_P_correctness"), thm)
- ||> Sign.restore_naming thy;
-
- val P = Var (("P", 0), rT' --> HOLogic.boolT);
- val prf = forall_intr_prf (y, forall_intr_prf (P,
- List.foldr (fn ((p, r), prf) =>
- forall_intr_prf (Logic.legacy_varify r, AbsP ("H", SOME (Logic.varify p),
- prf))) (Proofterm.proof_combP (prf_of thm',
- map PBound (length prems - 1 downto 0))) (prems ~~ rs)));
- val r' = Logic.legacy_varify (Abs ("y", Logic.legacy_varifyT T,
- list_abs (map dest_Free rs, list_comb (r,
- map Bound ((length rs - 1 downto 0) @ [length rs])))));
-
- in Extraction.add_realizers_i
- [(exh_name, (["P"], r', prf)),
- (exh_name, ([], Extraction.nullt, prf_of exhaustion))] thy'
- end;
-
-fun add_dt_realizers names thy =
- if ! Proofterm.proofs < 2 then thy
- else let
- val _ = message "Adding realizers for induction and case analysis ..."
- val infos = map (DatatypePackage.the_datatype thy) names;
- val info :: _ = infos;
- in
- thy
- |> fold_rev (make_ind (#sorts info) info) (subsets 0 (length (#descr info) - 1))
- |> fold_rev (make_casedists (#sorts info)) infos
- end;
-
-val setup = DatatypePackage.interpretation add_dt_realizers;
-
-end;