author | blanchet |
Tue, 04 Sep 2012 23:42:33 +0200 | |
changeset 49135 | de13b454fa31 |
parent 49134 | 846264f80f16 |
child 49146 | e32b1f748854 |
permissions | -rw-r--r-- |
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(* 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 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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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_typ ((_, 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 mixfix_of_ctr (_, mx) = mx; |
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val uncurry_fs = |
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map2 (fn f => fn xs => HOLogic.tupled_lambda (HOLogic.mk_tuple xs) (Term.list_comb (f, xs))); |
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fun prepare_data 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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| T :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy T))); |
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(* TODO: check that no type variables occur in the rhss that's not in the lhss *) |
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(* TODO: use sort constraints on type args *) |
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val N = length specs; |
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fun mk_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 Ts = map mk_T bs; |
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val mixfixes = map mixfix_of_typ 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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||
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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 mixfix_of_ctr) ctr_specss; |
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val sel_bindersss = map (map (map fst)) ctr_argsss; |
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val ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; |
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val (Bs, C) = |
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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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||> the_single o fst o mk_TFrees 1; |
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fun freeze_rec (T as Type (s, Ts')) = |
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(case find_index (curry (op =) T) Ts of |
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~1 => Type (s, map freeze_rec Ts') |
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| i => nth Bs i) |
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| freeze_rec T = T; |
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||
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val ctr_TsssBs = map (map (map freeze_rec)) ctr_Tsss; |
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val sum_prod_TsBs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssBs; |
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val eqs = map dest_TFree Bs ~~ sum_prod_TsBs; |
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val ((raw_unfs, raw_flds, unf_flds, fld_unfs, fld_injects), lthy') = |
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fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs As' eqs lthy; |
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fun mk_unf_or_fld get_foldedT Ts t = |
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let val Type (_, Ts0) = get_foldedT (fastype_of t) in |
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Term.subst_atomic_types (Ts0 ~~ Ts) t |
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end; |
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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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fun pour_sugar_on_type ((((((((((b, T), fld), unf), fld_unf), unf_fld), fld_inject), |
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ctr_binders), ctr_Tss), disc_binders), sel_binderss) no_defs_lthy = |
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let |
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val n = length ctr_binders; |
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val ks = 1 upto n; |
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val ms = map length ctr_Tss; |
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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 ((((fs, u), v), xss), _) = |
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lthy |
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|> mk_Frees "f" case_Ts |
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||>> yield_singleton (mk_Frees "u") unf_T |
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||>> yield_singleton (mk_Frees "v") T |
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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 (uncurry_fs 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_map2 (fn b => fn rhs => |
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Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) |
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ctr_binders 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; |
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fun exhaust_tac {context = ctxt, ...} = |
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let |
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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, T]) (certify lthy fld) |
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(certify lthy unf) fld_unf unf_fld) |
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|> Thm.close_derivation |
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|> Morphism.thm phi |
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end; |
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||
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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 ms ctr_defs fld_iff_unf_thm sumEN_thm' |
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end; |
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val inject_tacss = |
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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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||
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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; |
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val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; |
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fun sugar_lfp lthy = |
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let |
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(*### |
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val iter_Tss = map ( ) ctr_Tss |
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val iter_Ts = map (fn Ts => Ts ---> C) iter_Tss; |
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val iter_fs = map2 (fn Free (s, _) => fn T => Free (s, T)) fs iter_Ts |
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val uncurried_fs = |
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map2 (fn f => fn xs => |
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HOLogic.tupled_lambda (HOLogic.mk_tuple xs) (Term.list_comb (f, xs))) fs xss; |
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*) |
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in |
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lthy |
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end; |
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fun sugar_gfp lthy = lthy; |
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in |
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wrap_data tacss ((ctrs, casex), (disc_binders, sel_binderss)) lthy' |
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|> (if gfp then sugar_gfp else sugar_lfp) |
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end; |
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in |
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lthy' |
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|> fold pour_sugar_on_type (bs ~~ Ts ~~ flds ~~ unfs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ |
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ctr_binderss ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss) |
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end; |
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||
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fun data_cmd info specs lthy = |
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let |
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val fake_lthy = |
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Proof_Context.theory_of lthy |
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|> Theory.copy |
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|> Sign.add_types_global (map (fn spec => |
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(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of_typ spec)) specs) |
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|> Proof_Context.init_global |
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in |
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prepare_data Syntax.read_typ info specs fake_lthy lthy |
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end; |
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val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder |
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val parse_ctr_arg = |
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Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" || |
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(Parse.typ >> pair no_binder); |
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val parse_single_spec = |
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Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix -- |
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(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding -- |
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Scan.repeat parse_ctr_arg -- Parse.opt_mixfix)); |
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val _ = |
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Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes" |
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(Parse.and_list1 parse_single_spec >> data_cmd false); |
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val _ = |
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Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes" |
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(Parse.and_list1 parse_single_spec >> data_cmd true); |
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end; |