(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Sugar for constructing LFPs and GFPs.
*)
signature BNF_FP_SUGAR =
sig
end;
structure BNF_FP_Sugar : BNF_FP_SUGAR =
struct
open BNF_Util
open BNF_Wrap
open BNF_FP_Util
open BNF_LFP
open BNF_GFP
open BNF_FP_Sugar_Tactics
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
fun merge_type_arg_constrained ctxt (T, c) (T', c') =
if T = T' then
(case (c, c') of
(_, NONE) => (T, c)
| (NONE, _) => (T, c')
| _ =>
if c = c' then
(T, c)
else
error ("Inconsistent sort constraints for type variable " ^
quote (Syntax.string_of_typ ctxt T)))
else
cannot_merge_types ();
fun merge_type_args_constrained ctxt (cAs, cAs') =
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
else cannot_merge_types ();
fun type_args_constrained_of (((cAs, _), _), _) = cAs;
val type_args_of = map fst o type_args_constrained_of;
fun type_name_of (((_, b), _), _) = b;
fun mixfix_of_typ ((_, mx), _) = mx;
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
fun disc_of (((disc, _), _), _) = disc;
fun ctr_of (((_, ctr), _), _) = ctr;
fun args_of ((_, args), _) = args;
fun mixfix_of_ctr (_, mx) = mx;
val lfp_info = bnf_lfp;
val gfp_info = bnf_gfp;
fun prepare_data prepare_typ construct specs fake_lthy lthy =
let
val constrained_As =
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
|> Library.foldr1 (merge_type_args_constrained lthy);
val As = map fst constrained_As;
val _ = (case duplicates (op =) As of [] => ()
| T :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy T)));
(* TODO: check that no type variables occur in the rhss that's not in the lhss *)
(* TODO: use sort constraints on type args *)
val N = length specs;
fun mk_T b =
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
As);
val bs = map type_name_of specs;
val Ts = map mk_T bs;
val mixfixes = map mixfix_of_typ specs;
val _ = (case duplicates Binding.eq_name bs of [] => ()
| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
val ctr_specss = map ctr_specs_of specs;
val disc_namess = map (map disc_of) ctr_specss;
val ctr_namess = map (map ctr_of) ctr_specss;
val ctr_argsss = map (map args_of) ctr_specss;
val ctr_mixfixess = map (map mixfix_of_ctr) ctr_specss;
val sel_namesss = map (map (map fst)) ctr_argsss;
val ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
val (Bs, C) =
lthy
|> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
|> mk_TFrees N
||> the_single o fst o mk_TFrees 1;
fun freeze_rec (T as Type (s, Ts')) =
(case find_index (curry (op =) T) Ts of
~1 => Type (s, map freeze_rec Ts')
| i => nth Bs i)
| freeze_rec T = T;
val ctr_TsssBs = map (map (map freeze_rec)) ctr_Tsss;
val sum_prod_TsBs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssBs;
val eqs = map dest_TFree Bs ~~ sum_prod_TsBs;
val ((raw_flds, raw_unfs, fld_unfs, unf_flds), lthy') = fp_bnf construct bs eqs lthy;
fun mk_fld_or_unf get_foldedT Ts t =
let val Type (_, Ts0) = get_foldedT (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
val mk_fld = mk_fld_or_unf range_type;
val mk_unf = mk_fld_or_unf domain_type;
val flds = map (mk_fld As) raw_flds;
val unfs = map (mk_unf As) raw_unfs;
fun wrap_type ((((((((T, fld), unf), fld_unf), unf_fld), ctr_names), ctr_Tss), disc_names),
sel_namess) no_defs_lthy =
let
val n = length ctr_names;
val ks = 1 upto n;
val ms = map length ctr_Tss;
val unf_T = domain_type (fastype_of fld);
val prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
val (((u, v), xss), _) =
lthy
|> yield_singleton (mk_Frees "u") unf_T
||>> yield_singleton (mk_Frees "v") T
||>> mk_Freess "x" ctr_Tss;
val rhss =
map2 (fn k => fn xs =>
fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss;
val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
|> apfst split_list o fold_map2 (fn b => fn rhs =>
Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
ctr_names rhss
||> `Local_Theory.restore;
val raw_caseof =
Const (@{const_name undefined}, map (fn Ts => Ts ---> C) ctr_Tss ---> T --> C);
(*transforms defined frees into consts (and more)*)
val phi = Proof_Context.export_morphism lthy lthy';
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
val ctrs = map (Morphism.term phi) raw_ctrs;
val caseof = Morphism.term phi raw_caseof;
val fld_iff_unf_thm =
let
val goal =
fold_rev Logic.all [u, v]
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
in
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, T]) (certify lthy fld)
(certify lthy unf) fld_unf unf_fld)
|> Thm.close_derivation
end;
val sumEN_thm = mk_sumEN n;
val sumEN_thm' =
let val cTs = map (SOME o certifyT lthy) prod_Ts in
Local_Defs.unfold lthy @{thms all_unit_eq} (Drule.instantiate' cTs [] sumEN_thm)
end;
fun exhaust_tac {context = ctxt, ...} =
mk_exhaust_tac ctxt n ms ctr_defs fld_iff_unf_thm sumEN_thm';
(* ### *)
fun cheat_tac {context = ctxt, ...} = Skip_Proof.cheat_tac (Proof_Context.theory_of ctxt);
val inject_tacss = map (fn 0 => [] | _ => [cheat_tac]) ms;
val half_distinct_tacss = map (map (K cheat_tac)) (mk_half_pairss ks);
val case_tacs = map (K cheat_tac) ks;
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
in
wrap_data tacss ((ctrs, caseof), (disc_names, sel_namess)) lthy'
end;
in
lthy'
|> fold wrap_type (Ts ~~ flds ~~ unfs ~~ fld_unfs ~~ unf_flds ~~ ctr_namess ~~ ctr_Tsss ~~
disc_namess ~~ sel_namesss)
end;
fun data_cmd info specs lthy =
let
val fake_lthy =
Proof_Context.theory_of lthy
|> Theory.copy
|> Sign.add_types_global (map (fn spec =>
(type_name_of spec, length (type_args_constrained_of spec), mixfix_of_typ spec)) specs)
|> Proof_Context.init_global
in
prepare_data Syntax.read_typ info specs fake_lthy lthy
end;
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_name
val parse_ctr_arg =
Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
(Parse.typ >> pair no_name);
val parse_single_spec =
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
val _ =
Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
(Parse.and_list1 parse_single_spec >> data_cmd lfp_info);
val _ =
Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
(Parse.and_list1 parse_single_spec >> data_cmd gfp_info);
end;