(* Title: HOL/Codatatype/Tools/bnf_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Sugar on top of a BNF.
*)
signature BNF_SUGAR =
sig
end;
structure BNF_Sugar : BNF_SUGAR =
struct
open BNF_Util
open BNF_FP_Util
open BNF_Sugar_Tactics
val case_congN = "case_cong"
val case_discsN = "case_discs"
val casesN = "cases"
val ctr_selsN = "ctr_sels"
val disc_disjointN = "disc_disjoint"
val distinctN = "distinct"
val disc_exhaustN = "disc_exhaust"
val selsN = "sels"
val splitN = "split"
val split_asmN = "split_asm"
val weak_case_cong_thmsN = "weak_case_cong"
fun prepare_sugar prep_term (((raw_ctrs, raw_caseof), disc_names), sel_namess) no_defs_lthy =
let
(* TODO: sanity checks on arguments *)
(* TODO: normalize types of constructors w.r.t. each other *)
val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
val caseof0 = prep_term no_defs_lthy raw_caseof;
val n = length ctrs0;
val ks = 1 upto n;
val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0)));
val b = Binding.qualified_name T_name;
val (As, B) =
no_defs_lthy
|> mk_TFrees (length As0)
||> the_single o fst o mk_TFrees 1;
fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
fun mk_ctr Ts ctr =
let
val Ts0 = snd (dest_Type (body_type (fastype_of ctr)));
in
Term.subst_atomic_types (Ts0 ~~ Ts) ctr
end;
fun mk_caseof T =
let
val (binders, body) = strip_type (fastype_of caseof0);
in
Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ As)) caseof0
end;
val T = Type (T_name, As);
val ctrs = map (mk_ctr As) ctrs0;
val ctr_Tss = map (binder_types o fastype_of) ctrs;
val caseofB = mk_caseof B;
val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
val (((((xss, yss), fs), (v, v')), p), _) = no_defs_lthy |>
mk_Freess "x" ctr_Tss
||>> mk_Freess "y" ctr_Tss
||>> mk_Frees "f" caseofB_Ts
||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
||>> yield_singleton (mk_Frees "P") HOLogic.boolT;
val xctrs = map2 (curry Term.list_comb) ctrs xss;
val yctrs = map2 (curry Term.list_comb) ctrs yss;
val eta_fs = map2 (fn f => fn xs => fold_rev Term.lambda xs (Term.list_comb (f, xs))) fs xss;
val exist_xs_v_eq_ctrs =
map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
fun mk_caseof_args k xs x T =
map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks;
fun disc_spec b exist_xs_v_eq_ctr =
HOLogic.mk_Trueprop (HOLogic.mk_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v,
exist_xs_v_eq_ctr));
fun sel_spec b x xs xctr k =
let val T' = fastype_of x in
HOLogic.mk_Trueprop (HOLogic.mk_eq (Free (Binding.name_of b, T --> T') $ v,
Term.list_comb (mk_caseof T', mk_caseof_args k xs x T') $ v))
end;
val (((discs0, (_, disc_defs0)), (selss0, (_, sel_defss0))), (lthy', lthy)) =
no_defs_lthy
|> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr =>
Specification.definition (SOME (b, NONE, NoSyn),
((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs
||>> apfst (apsnd split_list o split_list) o fold_map4 (fn bs => fn xs => fn xctr => fn k =>
apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x =>
Specification.definition (SOME (b, NONE, NoSyn),
((Thm.def_binding b, []), sel_spec b x xs xctr k))) bs xs) sel_namess xss xctrs
ks
||> `Local_Theory.restore;
(*transforms defined frees into consts (and more)*)
val phi = Proof_Context.export_morphism lthy lthy';
val disc_defs = map (Morphism.thm phi) disc_defs0;
val sel_defss = map (map (Morphism.thm phi)) sel_defss0;
val discs = map (Morphism.term phi) discs0;
val selss = map (map (Morphism.term phi)) selss0;
val goal_exhaust =
let
fun mk_imp_p Q = Logic.list_implies (Q, HOLogic.mk_Trueprop p);
fun mk_prem xctr xs =
fold_rev Logic.all xs (mk_imp_p [HOLogic.mk_Trueprop (HOLogic.mk_eq (v, xctr))]);
in
mk_imp_p (map2 mk_prem xctrs xss)
end;
val goal_injects =
let
fun mk_goal _ _ [] [] = NONE
| mk_goal xctr yctr xs ys =
SOME (HOLogic.mk_Trueprop (HOLogic.mk_eq
(HOLogic.mk_eq (xctr, yctr),
Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))));
in
map_filter I (map4 mk_goal xctrs yctrs xss yss)
end;
val goal_half_distincts =
let
fun mk_goal t u = HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (t, u)));
fun mk_goals [] = []
| mk_goals (t :: ts) = fold_rev (cons o mk_goal t) ts (mk_goals ts);
in
mk_goals xctrs
end;
val goal_cases =
let
val lhs0 = Term.list_comb (caseofB, eta_fs);
fun mk_goal k xctr xs f =
HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs0 $ xctr, Term.list_comb (f, xs)))
|> tap (tracing o prefix "HERE: " o PolyML.makestring)(*###*);
in
map4 mk_goal ks xctrs xss fs
end;
val goals = [[goal_exhaust], goal_injects, goal_half_distincts, goal_cases];
fun after_qed thmss lthy =
let
val [[exhaust_thm], inject_thms, half_distinct_thms, case_thms] = thmss;
val other_half_distinct_thms = map (fn thm => thm RS not_sym) half_distinct_thms;
val nchotomy_thm =
let
val goal =
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
in
Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
end;
val sel_thms =
let
fun mk_thm k xs goal_case case_thm x sel sel_def =
let
val T = fastype_of x;
val cTs =
map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
(rev (Term.add_tfrees goal_case []));
val cxs = map (certify lthy) (mk_caseof_args k xs x T);
in
Local_Defs.fold lthy [sel_def]
(Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
end;
fun mk_thms k xs goal_case case_thm sels sel_defs =
map3 (mk_thm k xs goal_case case_thm) xs sels sel_defs;
in
flat (map6 mk_thms ks xss goal_cases case_thms selss sel_defss)
end;
val disc_thms = [];
val disc_disjoint_thms = [];
val disc_exhaust_thms = [];
val ctr_sel_thms = [];
val case_disc_thms = [];
val case_cong_thm = TrueI;
val weak_case_cong_thms = TrueI;
val split_thms = [];
val split_asm_thms = [];
(* case syntax *)
fun note thmN thms =
snd o Local_Theory.note
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), thms);
in
lthy
|> note case_congN [case_cong_thm]
|> note case_discsN case_disc_thms
|> note casesN case_thms
|> note ctr_selsN ctr_sel_thms
|> note disc_disjointN disc_disjoint_thms
|> note disc_exhaustN disc_exhaust_thms
|> note distinctN (half_distinct_thms @ other_half_distinct_thms)
|> note exhaustN [exhaust_thm]
|> note injectN inject_thms
|> note nchotomyN [nchotomy_thm]
|> note selsN sel_thms
|> note splitN split_thms
|> note split_asmN split_asm_thms
|> note weak_case_cong_thmsN [weak_case_cong_thms]
end;
in
(goals, after_qed, lthy')
end;
val parse_binding_list = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]";
val bnf_sugar_cmd = (fn (goalss, after_qed, lthy) =>
Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
prepare_sugar Syntax.read_term;
val _ =
Outer_Syntax.local_theory_to_proof @{command_spec "bnf_sugar"} "adds sugar on top of a BNF"
(((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
parse_binding_list -- (Parse.$$$ "[" |-- Parse.list parse_binding_list --| Parse.$$$ "]"))
>> bnf_sugar_cmd);
end;