author | blanchet |
Fri, 31 Aug 2012 15:04:03 +0200 | |
changeset 49045 | 7d9631754bba |
parent 49044 | c4a34ae5504d |
child 49046 | 3c5eba97d93a |
permissions | -rw-r--r-- |
49017 | 1 |
(* 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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4 |
||
5 |
Sugar on top of a BNF. |
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6 |
*) |
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||
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signature BNF_SUGAR = |
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sig |
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10 |
end; |
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11 |
||
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structure BNF_Sugar : BNF_SUGAR = |
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struct |
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||
15 |
open BNF_Util |
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open BNF_FP_Util |
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open BNF_Sugar_Tactics |
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|
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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_disjointN = "disc_disjoint" |
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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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fun mk_half_pairs [] = [] |
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| mk_half_pairs (x :: xs) = fold_rev (cons o pair x) xs (mk_half_pairs xs); |
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|
49028 | 35 |
fun index_of_half_row _ 0 = 0 |
36 |
| index_of_half_row n j = index_of_half_row n (j - 1) + n - j; |
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37 |
||
38 |
fun index_of_half_cell n j k = index_of_half_row n j + k - (j + 1); |
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val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq; |
41 |
||
49043 | 42 |
fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs; |
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|
49025 | 44 |
fun prepare_sugar prep_term (((raw_ctrs, raw_caseof), disc_names), sel_namess) no_defs_lthy = |
49017 | 45 |
let |
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(* TODO: sanity checks on arguments *) |
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|
49025 | 48 |
(* TODO: normalize types of constructors w.r.t. each other *) |
49 |
||
50 |
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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49022 | 55 |
|
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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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49025 | 59 |
val (As, B) = |
60 |
no_defs_lthy |
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61 |
|> mk_TFrees (length As0) |
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||> the_single o fst o mk_TFrees 1; |
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63 |
||
64 |
fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T); |
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65 |
||
66 |
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 |
69 |
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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49022 | 74 |
end; |
75 |
||
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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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79 |
||
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val ms = map length ctr_Tss; |
81 |
||
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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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||
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fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs); |
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||
87 |
val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |> |
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49025 | 88 |
mk_Freess "x" ctr_Tss |
89 |
||>> mk_Freess "y" ctr_Tss |
|
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||>> mk_Frees "f" caseofB_Ts |
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49032 | 91 |
||>> mk_Frees "g" caseofB_Ts |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T |
49032 | 93 |
||>> yield_singleton (mk_Frees "w") T |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT; |
95 |
||
96 |
val q = Free (fst p', B --> HOLogic.boolT); |
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49025 | 98 |
val xctrs = map2 (curry Term.list_comb) ctrs xss; |
99 |
val yctrs = map2 (curry Term.list_comb) ctrs yss; |
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49032 | 100 |
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49043 | 101 |
val xfs = map2 (curry Term.list_comb) fs xss; |
102 |
val xgs = map2 (curry Term.list_comb) gs xss; |
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103 |
||
104 |
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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106 |
||
107 |
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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49022 | 111 |
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fun mk_sel_caseof_args k xs x T = |
49025 | 113 |
map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks; |
114 |
||
115 |
fun disc_spec b exist_xs_v_eq_ctr = |
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49032 | 116 |
mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr); |
49025 | 117 |
|
49028 | 118 |
fun sel_spec b x xs k = |
49025 | 119 |
let val T' = fastype_of x in |
49032 | 120 |
mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v, |
121 |
Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v) |
|
49022 | 122 |
end; |
123 |
||
49028 | 124 |
val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) = |
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no_defs_lthy |
49025 | 126 |
|> 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; |
134 |
||
49025 | 135 |
(*transforms defined frees into consts (and more)*) |
136 |
val phi = Proof_Context.export_morphism lthy lthy'; |
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137 |
||
49028 | 138 |
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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140 |
||
141 |
val discs0 = map (Morphism.term phi) raw_discs; |
|
142 |
val selss0 = map (map (Morphism.term phi)) raw_selss; |
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|
49028 | 144 |
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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146 |
||
147 |
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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49025 | 149 |
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49032 | 150 |
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 _ _ [] [] = [] |
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| 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 | 163 |
in |
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map4 mk_goal xctrs yctrs xss yss |
49017 | 165 |
end; |
166 |
||
49019 | 167 |
val goal_half_distincts = |
49028 | 168 |
map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq) (mk_half_pairs xctrs); |
49019 | 169 |
|
49043 | 170 |
val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs; |
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val goals = [goal_exhaust] :: goal_injectss @ [goal_half_distincts, goal_cases]; |
49019 | 173 |
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174 |
fun after_qed thmss lthy = |
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175 |
let |
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val ([exhaust_thm], (inject_thmss, [half_distinct_thms, case_thms])) = |
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(hd thmss, chop n (tl thmss)); |
49019 | 178 |
|
49043 | 179 |
val inject_thms = flat inject_thmss; |
180 |
||
49032 | 181 |
val exhaust_thm' = |
182 |
let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in |
|
183 |
Drule.instantiate' [] [SOME (certify lthy v)] |
|
184 |
(Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm)) |
|
185 |
end; |
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186 |
||
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val other_half_distinct_thms = map (fn thm => thm RS not_sym) half_distinct_thms; |
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val distinct_thms = interleave half_distinct_thms other_half_distinct_thms; |
49019 | 189 |
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val nchotomy_thm = |
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let |
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val goal = |
49022 | 193 |
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v', |
49029 | 194 |
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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198 |
|
49030 | 199 |
val sel_thmss = |
49025 | 200 |
let |
49028 | 201 |
fun mk_thm k xs goal_case case_thm x sel_def = |
49025 | 202 |
let |
203 |
val T = fastype_of x; |
|
204 |
val cTs = |
|
205 |
map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree) |
|
206 |
(rev (Term.add_tfrees goal_case [])); |
|
49032 | 207 |
val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T); |
49025 | 208 |
in |
209 |
Local_Defs.fold lthy [sel_def] |
|
210 |
(Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm) |
|
211 |
end; |
|
49028 | 212 |
fun mk_thms k xs goal_case case_thm sel_defs = |
213 |
map2 (mk_thm k xs goal_case case_thm) xs sel_defs; |
|
49025 | 214 |
in |
49030 | 215 |
map5 mk_thms ks xss goal_cases case_thms sel_defss |
49025 | 216 |
end; |
217 |
||
49030 | 218 |
val discD_thms = map (fn def => def RS iffD1) disc_defs; |
49028 | 219 |
val discI_thms = |
49030 | 220 |
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs; |
49028 | 221 |
val not_disc_thms = |
49030 | 222 |
map2 (fn m => fn def => funpow m (fn thm => allI RS thm) |
223 |
(Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]}))) |
|
49028 | 224 |
ms disc_defs; |
225 |
||
49027 | 226 |
val disc_thms = |
227 |
let |
|
228 |
fun get_distinct_thm k k' = |
|
49028 | 229 |
if k > k' then nth half_distinct_thms (index_of_half_cell n (k' - 1) (k - 1)) |
230 |
else nth other_half_distinct_thms (index_of_half_cell n (k' - 1) (k' - 1)) |
|
231 |
fun mk_thm ((k, discI), not_disc) k' = |
|
232 |
if k = k' then refl RS discI else get_distinct_thm k k' RS not_disc; |
|
49027 | 233 |
in |
49028 | 234 |
map_product mk_thm (ks ~~ discI_thms ~~ not_disc_thms) ks |
49027 | 235 |
end; |
49025 | 236 |
|
49028 | 237 |
val disc_disjoint_thms = |
238 |
let |
|
239 |
fun get_disc_thm k k' = nth disc_thms ((k' - 1) * n + (k - 1)); |
|
240 |
fun mk_goal ((_, disc), (_, disc')) = |
|
49029 | 241 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
242 |
HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v)))); |
|
49028 | 243 |
fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac); |
244 |
||
49030 | 245 |
val bundles = ks ~~ ms ~~ discD_thms ~~ discs; |
49028 | 246 |
val half_pairs = mk_half_pairs bundles; |
247 |
||
248 |
val goal_halves = map mk_goal half_pairs; |
|
249 |
val half_thms = |
|
49030 | 250 |
map2 (fn ((((k, m), discD), _), (((k', _), _), _)) => |
251 |
prove (mk_half_disc_disjoint_tac m discD (get_disc_thm k k'))) |
|
49028 | 252 |
half_pairs goal_halves; |
253 |
||
254 |
val goal_other_halves = map (mk_goal o swap) half_pairs; |
|
255 |
val other_half_thms = |
|
256 |
map2 (prove o mk_other_half_disc_disjoint_tac) half_thms goal_other_halves; |
|
257 |
in |
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258 |
interleave half_thms other_half_thms |
49028 | 259 |
end; |
49025 | 260 |
|
49029 | 261 |
val disc_exhaust_thm = |
262 |
let |
|
263 |
fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)]; |
|
264 |
val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs)); |
|
265 |
in |
|
266 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms) |
|
267 |
end; |
|
49025 | 268 |
|
49030 | 269 |
val ctr_sel_thms = |
270 |
let |
|
271 |
fun mk_goal ctr disc sels = |
|
272 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
|
49032 | 273 |
mk_Trueprop_eq ((null sels ? swap) |
274 |
(Term.list_comb (ctr, map (fn sel => sel $ v) sels), v)))); |
|
49030 | 275 |
val goals = map3 mk_goal ctrs discs selss; |
276 |
in |
|
277 |
map4 (fn goal => fn m => fn discD => fn sel_thms => |
|
278 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
279 |
mk_ctr_sel_tac ctxt m discD sel_thms)) |
|
280 |
goals ms discD_thms sel_thmss |
|
281 |
end; |
|
49025 | 282 |
|
49031 | 283 |
val case_disc_thm = |
284 |
let |
|
285 |
fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels); |
|
286 |
fun mk_rhs _ [f] [sels] = mk_core f sels |
|
287 |
| mk_rhs (disc :: discs) (f :: fs) (sels :: selss) = |
|
288 |
Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $ |
|
289 |
(disc $ v) $ mk_core f sels $ mk_rhs discs fs selss; |
|
49043 | 290 |
val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss); |
49031 | 291 |
in |
292 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
293 |
mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thms sel_thmss) |
|
294 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
295 |
end; |
|
49025 | 296 |
|
49033 | 297 |
val (case_cong_thm, weak_case_cong_thm) = |
49032 | 298 |
let |
299 |
fun mk_prem xctr xs f g = |
|
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300 |
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr), |
49032 | 301 |
mk_Trueprop_eq (f, g))); |
49033 | 302 |
|
303 |
val v_eq_w = mk_Trueprop_eq (v, w); |
|
49043 | 304 |
val caseof_fs = mk_caseofB_term eta_fs; |
305 |
val caseof_gs = mk_caseofB_term eta_gs; |
|
49032 | 306 |
|
307 |
val goal = |
|
49033 | 308 |
Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs, |
309 |
mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w)); |
|
310 |
val goal_weak = |
|
311 |
Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w)); |
|
49032 | 312 |
in |
49033 | 313 |
(Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
314 |
mk_case_cong_tac ctxt exhaust_thm' case_thms), |
|
315 |
Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1))) |
|
316 |
|> pairself (singleton (Proof_Context.export names_lthy lthy)) |
|
49032 | 317 |
end; |
49025 | 318 |
|
49044 | 319 |
val (split_thm, split_asm_thm) = |
49043 | 320 |
let |
49044 | 321 |
fun mk_conjunct xctr xs f_xs = |
49043 | 322 |
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs)); |
49044 | 323 |
fun mk_disjunct xctr xs f_xs = |
324 |
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr), |
|
325 |
HOLogic.mk_not (q $ f_xs))); |
|
326 |
||
327 |
val lhs = q $ (mk_caseofB_term eta_fs $ v); |
|
328 |
||
49043 | 329 |
val goal = |
49044 | 330 |
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs)); |
331 |
val goal_asm = |
|
332 |
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj |
|
333 |
(map3 mk_disjunct xctrs xss xfs))); |
|
334 |
||
335 |
val split_thm = |
|
336 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
337 |
mk_split_tac ctxt exhaust_thm' case_thms inject_thms distinct_thms) |
|
338 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
339 |
val split_asm_thm = |
|
340 |
Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} => |
|
341 |
mk_split_asm_tac ctxt split_thm) |
|
342 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
49043 | 343 |
in |
49044 | 344 |
(split_thm, split_asm_thm) |
49043 | 345 |
end; |
49025 | 346 |
|
49043 | 347 |
(* TODO: case syntax *) |
348 |
(* TODO: attributes (simp, case_names, etc.) *) |
|
49025 | 349 |
|
49019 | 350 |
fun note thmN thms = |
351 |
snd o Local_Theory.note |
|
352 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), thms); |
|
353 |
in |
|
354 |
lthy |
|
49025 | 355 |
|> note case_congN [case_cong_thm] |
49031 | 356 |
|> note case_discsN [case_disc_thm] |
49025 | 357 |
|> note casesN case_thms |
358 |
|> note ctr_selsN ctr_sel_thms |
|
49027 | 359 |
|> note discsN disc_thms |
49025 | 360 |
|> note disc_disjointN disc_disjoint_thms |
49029 | 361 |
|> note disc_exhaustN [disc_exhaust_thm] |
49043 | 362 |
|> note distinctN distinct_thms |
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
363 |
|> note exhaustN [exhaust_thm] |
49043 | 364 |
|> note injectN inject_thms |
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
365 |
|> note nchotomyN [nchotomy_thm] |
49030 | 366 |
|> note selsN (flat sel_thmss) |
49043 | 367 |
|> note splitN [split_thm] |
368 |
|> note split_asmN [split_asm_thm] |
|
49033 | 369 |
|> note weak_case_cong_thmsN [weak_case_cong_thm] |
49019 | 370 |
end; |
49017 | 371 |
in |
49025 | 372 |
(goals, after_qed, lthy') |
49017 | 373 |
end; |
374 |
||
375 |
val parse_binding_list = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]"; |
|
376 |
||
49019 | 377 |
val bnf_sugar_cmd = (fn (goalss, after_qed, lthy) => |
378 |
Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
379 |
prepare_sugar Syntax.read_term; |
49017 | 380 |
|
381 |
val _ = |
|
382 |
Outer_Syntax.local_theory_to_proof @{command_spec "bnf_sugar"} "adds sugar on top of a BNF" |
|
49023 | 383 |
(((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term -- |
384 |
parse_binding_list -- (Parse.$$$ "[" |-- Parse.list parse_binding_list --| Parse.$$$ "]")) |
|
385 |
>> bnf_sugar_cmd); |
|
49017 | 386 |
|
387 |
end; |