author | blanchet |
Sat, 08 Sep 2012 21:04:26 +0200 | |
changeset 49200 | 73f9aede57a4 |
parent 49199 | 7c9a3c67c55d |
child 49201 | c69c2c18dccb |
permissions | -rw-r--r-- |
49112 | 1 |
(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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Sugar for constructing LFPs and GFPs. |
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*) |
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signature BNF_FP_SUGAR = |
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sig |
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end; |
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structure BNF_FP_Sugar : BNF_FP_SUGAR = |
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struct |
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open BNF_Util |
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open BNF_Wrap |
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open BNF_FP_Util |
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open BNF_LFP |
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open BNF_GFP |
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open BNF_FP_Sugar_Tactics |
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val caseN = "case"; |
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fun retype_free (Free (s, _)) T = Free (s, T); |
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||
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); |
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs; |
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fun mk_doubly_uncurried_fun f xss = |
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mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); |
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||
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fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; |
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fun merge_type_arg_constrained ctxt (T, c) (T', c') = |
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if T = T' then |
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(case (c, c') of |
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(_, NONE) => (T, c) |
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| (NONE, _) => (T, c') |
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| _ => |
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if c = c' then |
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(T, c) |
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else |
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error ("Inconsistent sort constraints for type variable " ^ |
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quote (Syntax.string_of_typ ctxt T))) |
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else |
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cannot_merge_types (); |
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||
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fun merge_type_args_constrained ctxt (cAs, cAs') = |
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if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' |
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else cannot_merge_types (); |
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||
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fun type_args_constrained_of (((cAs, _), _), _) = cAs; |
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val type_args_of = map fst o type_args_constrained_of; |
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fun type_binder_of (((_, b), _), _) = b; |
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fun mixfix_of ((_, mx), _) = mx; |
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fun ctr_specs_of (_, ctr_specs) = ctr_specs; |
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fun disc_of (((disc, _), _), _) = disc; |
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fun ctr_of (((_, ctr), _), _) = ctr; |
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fun args_of ((_, args), _) = args; |
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fun ctr_mixfix_of (_, mx) = mx; |
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fun prepare_datatype prepare_typ gfp specs fake_lthy lthy = |
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let |
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val constrained_As = |
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map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs |
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|> Library.foldr1 (merge_type_args_constrained lthy); |
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val As = map fst constrained_As; |
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val As' = map dest_TFree As; |
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val _ = (case duplicates (op =) As of [] => () |
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| A :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy A))); |
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(* TODO: use sort constraints on type args *) |
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||
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val N = length specs; |
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fun mk_fake_T b = |
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Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), |
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As); |
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val bs = map type_binder_of specs; |
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val fake_Ts = map mk_fake_T bs; |
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val mixfixes = map mixfix_of specs; |
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val _ = (case duplicates Binding.eq_name bs of [] => () |
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| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); |
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val ctr_specss = map ctr_specs_of specs; |
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val disc_binderss = map (map disc_of) ctr_specss; |
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val ctr_binderss = map (map ctr_of) ctr_specss; |
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val ctr_argsss = map (map args_of) ctr_specss; |
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val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; |
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val sel_bindersss = map (map (map fst)) ctr_argsss; |
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val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; |
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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; |
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val _ = (case subtract (op =) As' rhs_As' of |
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[] => () |
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| A' :: _ => error ("Extra type variables on rhs: " ^ |
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quote (Syntax.string_of_typ lthy (TFree A')))); |
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val ((Cs, Xs), _) = |
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lthy |
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|> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs |
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|> mk_TFrees N |
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||>> mk_TFrees N; |
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fun is_same_recT (T as Type (s, Us)) (Type (s', Us')) = |
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s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ |
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quote (Syntax.string_of_typ fake_lthy T))) |
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| is_same_recT _ _ = false; |
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fun freeze_recXs (T as Type (s, Us)) = |
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(case find_index (is_same_recT T) fake_Ts of |
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~1 => Type (s, map freeze_recXs Us) |
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| i => nth Xs i) |
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| freeze_recXs T = T; |
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val ctr_TsssXs = map (map (map freeze_recXs)) fake_ctr_Tsss; |
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val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; |
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val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; |
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val ((raw_unfs, raw_flds, raw_fp_iters, raw_fp_recs, unf_flds, fld_unfs, fld_injects), lthy') = |
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fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs mixfixes As' eqs lthy; |
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val timer = time (Timer.startRealTimer ()); |
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fun mk_unf_or_fld get_T Ts t = |
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let val Type (_, Ts0) = get_T (fastype_of t) in |
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Term.subst_atomic_types (Ts0 ~~ Ts) t |
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end; |
49119 | 136 |
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val mk_unf = mk_unf_or_fld domain_type; |
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val mk_fld = mk_unf_or_fld range_type; |
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val unfs = map (mk_unf As) raw_unfs; |
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val flds = map (mk_fld As) raw_flds; |
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val fp_Ts = map (domain_type o fastype_of) unfs; |
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val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fp_Ts)))) ctr_TsssXs; |
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fun mk_fp_iter_or_rec Ts Us t = |
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let |
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val (binders, body) = strip_type (fastype_of t); |
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val Type (_, Ts0) = if gfp then body else List.last binders; |
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val Us0 = map (if gfp then domain_type else body_type) (fst (split_last binders)); |
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in |
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
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end; |
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||
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val fp_iters = map (mk_fp_iter_or_rec As Cs) raw_fp_iters; |
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val fp_recs = map (mk_fp_iter_or_rec As Cs) raw_fp_recs; |
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fun pour_sugar_on_type ((((((((((((((b, fp_T), C), fld), unf), fp_iter), fp_rec), fld_unf), |
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unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss) |
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no_defs_lthy = |
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let |
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val n = length ctr_Tss; |
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val ks = 1 upto n; |
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val ms = map length ctr_Tss; |
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||
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val unf_T = domain_type (fastype_of fld); |
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val prod_Ts = map HOLogic.mk_tupleT ctr_Tss; |
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val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss; |
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val ((((u, v), fs), xss), _) = |
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lthy |
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|> yield_singleton (mk_Frees "u") unf_T |
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||>> yield_singleton (mk_Frees "v") fp_T |
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||>> mk_Frees "f" case_Ts |
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||>> mk_Freess "x" ctr_Tss; |
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val ctr_rhss = |
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map2 (fn k => fn xs => |
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fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss; |
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||
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val case_binder = Binding.suffix_name ("_" ^ caseN) b; |
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val case_rhs = |
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fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); |
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val (((raw_ctrs, raw_ctr_defs), (raw_case, raw_case_def)), (lthy', lthy)) = no_defs_lthy |
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|> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => |
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Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) |
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ctr_binders ctr_mixfixes ctr_rhss |
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||>> (Local_Theory.define ((case_binder, NoSyn), ((Thm.def_binding case_binder, []), |
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case_rhs)) #>> apsnd snd) |
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||> `Local_Theory.restore; |
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(*transforms defined frees into consts (and more)*) |
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val phi = Proof_Context.export_morphism lthy lthy'; |
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val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; |
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val case_def = Morphism.thm phi raw_case_def; |
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val ctrs = map (Morphism.term phi) raw_ctrs; |
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val casex = Morphism.term phi raw_case; |
49121 | 202 |
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fun exhaust_tac {context = ctxt, ...} = |
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let |
49135 | 205 |
val fld_iff_unf_thm = |
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let |
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val goal = |
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fold_rev Logic.all [u, v] |
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(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); |
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in |
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Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
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mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, fp_T]) |
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(certify lthy fld) (certify lthy unf) fld_unf unf_fld) |
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49135 | 214 |
|> Thm.close_derivation |
215 |
|> Morphism.thm phi |
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end; |
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||
218 |
val sumEN_thm' = |
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Local_Defs.unfold lthy @{thms all_unit_eq} |
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(Drule.instantiate' (map (SOME o certifyT lthy) prod_Ts) [] (mk_sumEN n)) |
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|> Morphism.thm phi; |
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in |
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mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' |
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end; |
49121 | 225 |
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49126 | 226 |
val inject_tacss = |
227 |
map2 (fn 0 => K [] |
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| _ => fn ctr_def => [fn {context = ctxt, ...} => |
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mk_inject_tac ctxt ctr_def fld_inject]) |
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ms ctr_defs; |
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231 |
||
49127 | 232 |
val half_distinct_tacss = |
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map (map (fn (def, def') => fn {context = ctxt, ...} => |
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mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); |
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||
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val case_tacs = |
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map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => |
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mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; |
49121 | 239 |
|
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val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; |
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49176 | 242 |
(* (co)iterators, (co)recursors, (co)induction *) |
243 |
||
244 |
val is_recT = member (op =) fp_Ts; |
|
245 |
||
246 |
val ns = map length ctr_Tsss; |
|
247 |
val mss = map (map length) ctr_Tsss; |
|
248 |
val Css = map2 replicate ns Cs; |
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249 |
||
49200 | 250 |
fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) = |
251 |
if member (op =) Cs U then Us else [T] |
|
252 |
| dest_rec_pair T = [T]; |
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253 |
||
49199 | 254 |
fun sugar_datatype no_defs_lthy = |
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255 |
let |
49176 | 256 |
val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter)))); |
257 |
val y_prod_Tss = map2 dest_sumTN ns fp_y_Ts; |
|
258 |
val y_Tsss = map2 (map2 dest_tupleT) mss y_prod_Tss; |
|
259 |
val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css; |
|
260 |
val iter_T = flat g_Tss ---> fp_T --> C; |
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49146 | 261 |
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49199 | 262 |
val fp_z_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_rec)))); |
263 |
val z_prod_Tss = map2 dest_sumTN ns fp_z_Ts; |
|
264 |
val z_Tsss = map2 (map2 dest_tupleT) mss z_prod_Tss; |
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49200 | 265 |
val z_Tssss = map (map (map dest_rec_pair)) z_Tsss; |
266 |
val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css; |
|
49199 | 267 |
val rec_T = flat h_Tss ---> fp_T --> C; |
268 |
||
49176 | 269 |
val ((gss, ysss), _) = |
49199 | 270 |
no_defs_lthy |
49176 | 271 |
|> mk_Freess "f" g_Tss |
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||>> mk_Freesss "x" y_Tsss; |
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273 |
|
49199 | 274 |
val hss = map2 (map2 retype_free) gss h_Tss; |
49200 | 275 |
val (zssss, _) = |
49199 | 276 |
no_defs_lthy |
49200 | 277 |
|> mk_Freessss "x" z_Tssss; |
49199 | 278 |
|
279 |
val iter_binder = Binding.suffix_name ("_" ^ iterN) b; |
|
280 |
val rec_binder = Binding.suffix_name ("_" ^ recN) b; |
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281 |
||
282 |
val iter_free = Free (Binding.name_of iter_binder, iter_T); |
|
283 |
val rec_free = Free (Binding.name_of rec_binder, rec_T); |
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284 |
||
285 |
val iter_spec = |
|
286 |
mk_Trueprop_eq (fold (fn gs => fn t => Term.list_comb (t, gs)) gss iter_free, |
|
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Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss)); |
|
288 |
val rec_spec = |
|
289 |
mk_Trueprop_eq (fold (fn hs => fn t => Term.list_comb (t, hs)) hss rec_free, |
|
49200 | 290 |
Term.list_comb (fp_rec, |
291 |
map2 (mk_sum_caseN oo map2 mk_doubly_uncurried_fun) hss zssss)); |
|
49199 | 292 |
|
293 |
val (([raw_iter, raw_rec], [raw_iter_def, raw_rec_def]), (lthy', lthy)) = no_defs_lthy |
|
294 |
|> apfst split_list o fold_map (fn (b, spec) => |
|
295 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) |
|
296 |
#>> apsnd snd) [(iter_binder, iter_spec), (rec_binder, rec_spec)] |
|
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||> `Local_Theory.restore; |
|
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in |
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lthy |
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300 |
end; |
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|
49199 | 302 |
fun sugar_codatatype no_defs_lthy = no_defs_lthy; |
49119 | 303 |
in |
49199 | 304 |
wrap_datatype tacss ((ctrs, casex), (disc_binders, sel_binderss)) lthy' |
305 |
|> (if gfp then sugar_codatatype else sugar_datatype) |
|
49119 | 306 |
end; |
49167 | 307 |
|
308 |
val lthy'' = |
|
49176 | 309 |
fold pour_sugar_on_type (bs ~~ fp_Ts ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~ |
310 |
fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ |
|
311 |
disc_binderss ~~ sel_bindersss) lthy'; |
|
49167 | 312 |
|
313 |
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ |
|
314 |
(if gfp then "co" else "") ^ "datatype")); |
|
49112 | 315 |
in |
49167 | 316 |
(timer; lthy'') |
49112 | 317 |
end; |
318 |
||
49199 | 319 |
fun datatype_cmd info specs lthy = |
49121 | 320 |
let |
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(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a |
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locale and shadows an existing global type*) |
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val fake_thy = Theory.copy |
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#> fold (fn spec => perhaps (try (Sign.add_type lthy |
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(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs; |
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val fake_lthy = Proof_Context.background_theory fake_thy lthy; |
49121 | 327 |
in |
49199 | 328 |
prepare_datatype Syntax.read_typ info specs fake_lthy lthy |
49121 | 329 |
end; |
49119 | 330 |
|
49129 | 331 |
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder |
49119 | 332 |
|
49112 | 333 |
val parse_ctr_arg = |
49119 | 334 |
Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" || |
49129 | 335 |
(Parse.typ >> pair no_binder); |
49112 | 336 |
|
337 |
val parse_single_spec = |
|
338 |
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix -- |
|
49119 | 339 |
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding -- |
340 |
Scan.repeat parse_ctr_arg -- Parse.opt_mixfix)); |
|
49112 | 341 |
|
342 |
val _ = |
|
343 |
Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes" |
|
49199 | 344 |
(Parse.and_list1 parse_single_spec >> datatype_cmd false); |
49112 | 345 |
|
346 |
val _ = |
|
347 |
Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes" |
|
49199 | 348 |
(Parse.and_list1 parse_single_spec >> datatype_cmd true); |
49112 | 349 |
|
350 |
end; |