author | blanchet |
Fri, 31 Aug 2012 16:07:06 +0200 | |
changeset 49054 | ee0a1d449f89 |
parent 49053 | a6df36ecc2a8 |
child 49055 | 631512830082 |
permissions | -rw-r--r-- |
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(* Title: HOL/Codatatype/Tools/bnf_sugar.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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Sugar on top of a BNF. |
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*) |
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signature BNF_SUGAR = |
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sig |
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end; |
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structure BNF_Sugar : BNF_SUGAR = |
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struct |
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open BNF_Util |
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open BNF_FP_Util |
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open BNF_Sugar_Tactics |
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val is_N = "is_"; |
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val un_N = "un_"; |
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fun mk_un_N 1 1 suf = un_N ^ suf |
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| mk_un_N _ l suf = un_N ^ suf ^ string_of_int l; |
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val case_congN = "case_cong"; |
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val case_discsN = "case_discs"; |
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val casesN = "cases"; |
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val ctr_selsN = "ctr_sels"; |
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val disc_exclusN = "disc_exclus"; |
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val disc_exhaustN = "disc_exhaust"; |
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val discsN = "discs"; |
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val distinctN = "distinct"; |
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val selsN = "sels"; |
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val splitN = "split"; |
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val split_asmN = "split_asm"; |
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val weak_case_cong_thmsN = "weak_case_cong"; |
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val default_name = @{binding _}; |
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fun mk_half_pairss' _ [] = [] |
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| mk_half_pairss' pad (y :: ys) = |
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pad @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: pad) ys); |
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fun mk_half_pairss ys = mk_half_pairss' [[]] ys; |
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val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq; |
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fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs; |
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fun name_of_ctr t = |
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case head_of t of |
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Const (s, _) => s |
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| Free (s, _) => s |
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| _ => error "Cannot extract name of constructor"; |
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fun prepare_sugar prep_term (((raw_ctrs, raw_caseof), raw_disc_names), raw_sel_namess) |
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no_defs_lthy = |
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let |
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(* TODO: sanity checks on arguments *) |
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(* TODO: normalize types of constructors w.r.t. each other *) |
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val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs; |
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val caseof0 = prep_term no_defs_lthy raw_caseof; |
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val n = length ctrs0; |
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val ks = 1 upto n; |
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val raw_disc_names' = |
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raw_disc_names @ replicate (length ctrs0 - length raw_disc_names) default_name; |
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val disc_names = |
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map2 (fn ctr => fn disc => |
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if Binding.eq_name (disc, default_name) then |
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Binding.name (prefix is_N (Long_Name.base_name (name_of_ctr ctr))) |
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else |
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disc) ctrs0 raw_disc_names'; |
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val sel_namess = |
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map2 (fn ctr => fn sels => |
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let val m = length sels in |
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map2 (fn l => fn sel => |
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if Binding.eq_name (sel, default_name) then |
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Binding.name (mk_un_N m l (Long_Name.base_name (name_of_ctr ctr))) |
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else |
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sel) (1 upto m) sels |
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end) ctrs0 raw_sel_namess; |
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val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0))); |
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val b = Binding.qualified_name T_name; |
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val (As, B) = |
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no_defs_lthy |
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|> mk_TFrees (length As0) |
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||> the_single o fst o mk_TFrees 1; |
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fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T); |
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fun mk_ctr Ts ctr = |
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let val Ts0 = snd (dest_Type (body_type (fastype_of ctr))) in |
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Term.subst_atomic_types (Ts0 ~~ Ts) ctr |
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end; |
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fun mk_caseof Ts T = |
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let val (binders, body) = strip_type (fastype_of caseof0) in |
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Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0 |
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end; |
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val T = Type (T_name, As); |
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val ctrs = map (mk_ctr As) ctrs0; |
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val ctr_Tss = map (binder_types o fastype_of) ctrs; |
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val ms = map length ctr_Tss; |
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val caseofB = mk_caseof As B; |
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val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss; |
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fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs); |
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val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |> |
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mk_Freess "x" ctr_Tss |
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||>> mk_Freess "y" ctr_Tss |
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||>> mk_Frees "f" caseofB_Ts |
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||>> mk_Frees "g" caseofB_Ts |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T |
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||>> yield_singleton (mk_Frees "w") T |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT; |
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val q = Free (fst p', B --> HOLogic.boolT); |
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val xctrs = map2 (curry Term.list_comb) ctrs xss; |
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val yctrs = map2 (curry Term.list_comb) ctrs yss; |
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val xfs = map2 (curry Term.list_comb) fs xss; |
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val xgs = map2 (curry Term.list_comb) gs xss; |
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val eta_fs = map2 eta_expand_caseof_arg xss xfs; |
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val eta_gs = map2 eta_expand_caseof_arg xss xgs; |
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val caseofB_fs = Term.list_comb (caseofB, eta_fs); |
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val exist_xs_v_eq_ctrs = |
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map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss; |
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fun mk_sel_caseof_args k xs x T = |
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map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks; |
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fun disc_spec b exist_xs_v_eq_ctr = |
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mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr); |
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fun sel_spec b x xs k = |
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let val T' = fastype_of x in |
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mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v, |
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Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v) |
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end; |
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val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) = |
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no_defs_lthy |
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|> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr => |
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Specification.definition (SOME (b, NONE, NoSyn), |
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((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs |
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||>> apfst (apsnd split_list o split_list) o fold_map3 (fn bs => fn xs => fn k => |
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apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x => |
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Specification.definition (SOME (b, NONE, NoSyn), |
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((Thm.def_binding b, []), sel_spec b x xs k))) bs xs) sel_namess xss ks |
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||> `Local_Theory.restore; |
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||
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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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||
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val disc_defs = map (Morphism.thm phi) raw_disc_defs; |
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val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss; |
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||
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val discs0 = map (Morphism.term phi) raw_discs; |
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val selss0 = map (map (Morphism.term phi)) raw_selss; |
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fun mk_disc_or_sel Ts t = |
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Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t; |
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||
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val discs = map (mk_disc_or_sel As) discs0; |
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val selss = map (map (mk_disc_or_sel As)) selss0; |
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fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p); |
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val goal_exhaust = |
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let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in |
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mk_imp_p (map2 mk_prem xctrs xss) |
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end; |
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val goal_injectss = |
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let |
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fun mk_goal _ _ [] [] = [] |
49025 | 191 |
| mk_goal xctr yctr xs ys = |
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[mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr), |
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Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))]; |
49017 | 194 |
in |
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map4 mk_goal xctrs yctrs xss yss |
49017 | 196 |
end; |
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val goal_half_distinctss = |
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map (map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq)) (mk_half_pairss xctrs); |
49019 | 200 |
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val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs; |
49025 | 202 |
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val goals = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases]; |
49019 | 204 |
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205 |
fun after_qed thmss lthy = |
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let |
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val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) = |
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(hd thmss, apsnd (chop (n * n)) (chop n (tl thmss))); |
49019 | 209 |
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49032 | 210 |
val exhaust_thm' = |
211 |
let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in |
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212 |
Drule.instantiate' [] [SOME (certify lthy v)] |
|
213 |
(Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm)) |
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214 |
end; |
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215 |
||
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val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss; |
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49052 | 218 |
val (distinct_thmsss', distinct_thmsss) = |
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map2 (map2 append) (Library.chop_groups n half_distinct_thmss) |
49052 | 220 |
(transpose (Library.chop_groups n other_half_distinct_thmss)) |
221 |
|> `transpose; |
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val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss); |
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val nchotomy_thm = |
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let |
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val goal = |
49022 | 227 |
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v', |
49029 | 228 |
Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs)); |
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in |
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Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm) |
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end; |
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232 |
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49030 | 233 |
val sel_thmss = |
49025 | 234 |
let |
49028 | 235 |
fun mk_thm k xs goal_case case_thm x sel_def = |
49025 | 236 |
let |
237 |
val T = fastype_of x; |
|
238 |
val cTs = |
|
239 |
map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree) |
|
240 |
(rev (Term.add_tfrees goal_case [])); |
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49032 | 241 |
val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T); |
49025 | 242 |
in |
243 |
Local_Defs.fold lthy [sel_def] |
|
244 |
(Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm) |
|
245 |
end; |
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49028 | 246 |
fun mk_thms k xs goal_case case_thm sel_defs = |
247 |
map2 (mk_thm k xs goal_case case_thm) xs sel_defs; |
|
49025 | 248 |
in |
49030 | 249 |
map5 mk_thms ks xss goal_cases case_thms sel_defss |
49025 | 250 |
end; |
251 |
||
49030 | 252 |
val discD_thms = map (fn def => def RS iffD1) disc_defs; |
49028 | 253 |
val discI_thms = |
49030 | 254 |
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs; |
49028 | 255 |
val not_disc_thms = |
49030 | 256 |
map2 (fn m => fn def => funpow m (fn thm => allI RS thm) |
257 |
(Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]}))) |
|
49028 | 258 |
ms disc_defs; |
259 |
||
49050 | 260 |
val (disc_thmss', disc_thmss) = |
49027 | 261 |
let |
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262 |
fun mk_thm discI _ [] = refl RS discI |
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| mk_thm _ not_disc [distinct] = distinct RS not_disc; |
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fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss; |
49027 | 265 |
in |
49052 | 266 |
map3 mk_thms discI_thms not_disc_thms distinct_thmsss' |
49050 | 267 |
|> `transpose |
49027 | 268 |
end; |
49025 | 269 |
|
49053 | 270 |
val disc_exclus_thms = |
49028 | 271 |
let |
272 |
fun mk_goal ((_, disc), (_, disc')) = |
|
49029 | 273 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
274 |
HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v)))); |
|
49028 | 275 |
fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac); |
276 |
||
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val bundles = ms ~~ discD_thms ~~ discs; |
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278 |
val half_pairss = mk_half_pairss bundles; |
49028 | 279 |
|
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val goal_halvess = map (map mk_goal) half_pairss; |
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val half_thmss = |
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map3 (fn [] => K (K []) |
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283 |
| [(((m, discD), _), _)] => fn disc_thm => fn [goal] => |
49053 | 284 |
[prove (mk_half_disc_exclus_tac m discD disc_thm) goal]) |
49050 | 285 |
half_pairss (flat disc_thmss') goal_halvess; |
49028 | 286 |
|
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287 |
val goal_other_halvess = map (map (mk_goal o swap)) half_pairss; |
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288 |
val other_half_thmss = |
49053 | 289 |
map2 (map2 (prove o mk_other_half_disc_exclus_tac)) half_thmss goal_other_halvess; |
49028 | 290 |
in |
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291 |
interleave (flat half_thmss) (flat other_half_thmss) |
49028 | 292 |
end; |
49025 | 293 |
|
49029 | 294 |
val disc_exhaust_thm = |
295 |
let |
|
296 |
fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)]; |
|
297 |
val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs)); |
|
298 |
in |
|
299 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms) |
|
300 |
end; |
|
49025 | 301 |
|
49030 | 302 |
val ctr_sel_thms = |
303 |
let |
|
304 |
fun mk_goal ctr disc sels = |
|
305 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
|
49032 | 306 |
mk_Trueprop_eq ((null sels ? swap) |
307 |
(Term.list_comb (ctr, map (fn sel => sel $ v) sels), v)))); |
|
49030 | 308 |
val goals = map3 mk_goal ctrs discs selss; |
309 |
in |
|
310 |
map4 (fn goal => fn m => fn discD => fn sel_thms => |
|
311 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
312 |
mk_ctr_sel_tac ctxt m discD sel_thms)) |
|
313 |
goals ms discD_thms sel_thmss |
|
314 |
end; |
|
49025 | 315 |
|
49031 | 316 |
val case_disc_thm = |
317 |
let |
|
318 |
fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels); |
|
319 |
fun mk_rhs _ [f] [sels] = mk_core f sels |
|
320 |
| mk_rhs (disc :: discs) (f :: fs) (sels :: selss) = |
|
321 |
Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $ |
|
322 |
(disc $ v) $ mk_core f sels $ mk_rhs discs fs selss; |
|
49043 | 323 |
val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss); |
49031 | 324 |
in |
325 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
49050 | 326 |
mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss) |
49031 | 327 |
|> singleton (Proof_Context.export names_lthy lthy) |
328 |
end; |
|
49025 | 329 |
|
49033 | 330 |
val (case_cong_thm, weak_case_cong_thm) = |
49032 | 331 |
let |
332 |
fun mk_prem xctr xs f g = |
|
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333 |
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr), |
49032 | 334 |
mk_Trueprop_eq (f, g))); |
49033 | 335 |
|
336 |
val v_eq_w = mk_Trueprop_eq (v, w); |
|
49043 | 337 |
val caseof_fs = mk_caseofB_term eta_fs; |
338 |
val caseof_gs = mk_caseofB_term eta_gs; |
|
49032 | 339 |
|
340 |
val goal = |
|
49033 | 341 |
Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs, |
342 |
mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w)); |
|
343 |
val goal_weak = |
|
344 |
Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w)); |
|
49032 | 345 |
in |
49049 | 346 |
(Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms), |
49033 | 347 |
Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1))) |
348 |
|> pairself (singleton (Proof_Context.export names_lthy lthy)) |
|
49032 | 349 |
end; |
49025 | 350 |
|
49044 | 351 |
val (split_thm, split_asm_thm) = |
49043 | 352 |
let |
49044 | 353 |
fun mk_conjunct xctr xs f_xs = |
49043 | 354 |
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs)); |
49044 | 355 |
fun mk_disjunct xctr xs f_xs = |
356 |
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr), |
|
357 |
HOLogic.mk_not (q $ f_xs))); |
|
358 |
||
359 |
val lhs = q $ (mk_caseofB_term eta_fs $ v); |
|
360 |
||
49043 | 361 |
val goal = |
49044 | 362 |
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs)); |
363 |
val goal_asm = |
|
364 |
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj |
|
365 |
(map3 mk_disjunct xctrs xss xfs))); |
|
366 |
||
367 |
val split_thm = |
|
49049 | 368 |
Skip_Proof.prove lthy [] [] goal |
49052 | 369 |
(fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss) |
49044 | 370 |
|> singleton (Proof_Context.export names_lthy lthy) |
371 |
val split_asm_thm = |
|
372 |
Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} => |
|
373 |
mk_split_asm_tac ctxt split_thm) |
|
374 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
49043 | 375 |
in |
49044 | 376 |
(split_thm, split_asm_thm) |
49043 | 377 |
end; |
49025 | 378 |
|
49043 | 379 |
(* TODO: case syntax *) |
380 |
(* TODO: attributes (simp, case_names, etc.) *) |
|
49025 | 381 |
|
49052 | 382 |
val notes = |
383 |
[(case_congN, [case_cong_thm]), |
|
384 |
(case_discsN, [case_disc_thm]), |
|
385 |
(casesN, case_thms), |
|
386 |
(ctr_selsN, ctr_sel_thms), |
|
387 |
(discsN, (flat disc_thmss)), |
|
49053 | 388 |
(disc_exclusN, disc_exclus_thms), |
49052 | 389 |
(disc_exhaustN, [disc_exhaust_thm]), |
390 |
(distinctN, distinct_thms), |
|
391 |
(exhaustN, [exhaust_thm]), |
|
392 |
(injectN, (flat inject_thmss)), |
|
393 |
(nchotomyN, [nchotomy_thm]), |
|
394 |
(selsN, (flat sel_thmss)), |
|
395 |
(splitN, [split_thm]), |
|
396 |
(split_asmN, [split_asm_thm]), |
|
397 |
(weak_case_cong_thmsN, [weak_case_cong_thm])] |
|
398 |
|> map (fn (thmN, thms) => |
|
399 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); |
|
49019 | 400 |
in |
49052 | 401 |
lthy |> Local_Theory.notes notes |> snd |
49019 | 402 |
end; |
49017 | 403 |
in |
49025 | 404 |
(goals, after_qed, lthy') |
49017 | 405 |
end; |
406 |
||
407 |
val parse_binding_list = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]"; |
|
408 |
||
49019 | 409 |
val bnf_sugar_cmd = (fn (goalss, after_qed, lthy) => |
410 |
Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo |
|
49020
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diff
changeset
|
411 |
prepare_sugar Syntax.read_term; |
49017 | 412 |
|
413 |
val _ = |
|
414 |
Outer_Syntax.local_theory_to_proof @{command_spec "bnf_sugar"} "adds sugar on top of a BNF" |
|
49023 | 415 |
(((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term -- |
416 |
parse_binding_list -- (Parse.$$$ "[" |-- Parse.list parse_binding_list --| Parse.$$$ "]")) |
|
417 |
>> bnf_sugar_cmd); |
|
49017 | 418 |
|
419 |
end; |