author | blanchet |
Mon, 03 Sep 2012 11:54:21 +0200 | |
changeset 49075 | ed769978dc8d |
parent 49074 | d8af889dcbe3 |
child 49111 | 9d511132394e |
permissions | -rw-r--r-- |
49074 | 1 |
(* Title: HOL/Codatatype/Tools/bnf_wrap.ML |
49017 | 2 |
Author: Jasmin Blanchette, TU Muenchen |
3 |
Copyright 2012 |
|
4 |
||
49074 | 5 |
Wrapping existing datatypes. |
49017 | 6 |
*) |
7 |
||
49074 | 8 |
signature BNF_WRAP = |
49017 | 9 |
sig |
10 |
end; |
|
11 |
||
49074 | 12 |
structure BNF_Wrap : BNF_WRAP = |
49017 | 13 |
struct |
14 |
||
15 |
open BNF_Util |
|
49074 | 16 |
open BNF_Wrap_Tactics |
49017 | 17 |
|
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
18 |
val is_N = "is_"; |
49054 | 19 |
val un_N = "un_"; |
20 |
fun mk_un_N 1 1 suf = un_N ^ suf |
|
21 |
| mk_un_N _ l suf = un_N ^ suf ^ string_of_int l; |
|
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
22 |
|
49054 | 23 |
val case_congN = "case_cong"; |
24 |
val case_discsN = "case_discs"; |
|
25 |
val casesN = "cases"; |
|
26 |
val ctr_selsN = "ctr_sels"; |
|
27 |
val disc_exclusN = "disc_exclus"; |
|
28 |
val disc_exhaustN = "disc_exhaust"; |
|
29 |
val discsN = "discs"; |
|
30 |
val distinctN = "distinct"; |
|
49075 | 31 |
val exhaustN = "exhaust"; |
32 |
val injectN = "inject"; |
|
33 |
val nchotomyN = "nchotomy"; |
|
49054 | 34 |
val selsN = "sels"; |
35 |
val splitN = "split"; |
|
36 |
val split_asmN = "split_asm"; |
|
37 |
val weak_case_cong_thmsN = "weak_case_cong"; |
|
49019 | 38 |
|
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
39 |
val default_name = @{binding _}; |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
40 |
|
49056 | 41 |
fun pad_list x n xs = xs @ replicate (n - length xs) x; |
42 |
||
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
43 |
fun mk_half_pairss' _ [] = [] |
49056 | 44 |
| mk_half_pairss' indent (y :: ys) = |
45 |
indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys); |
|
49027 | 46 |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
47 |
fun mk_half_pairss ys = mk_half_pairss' [[]] ys; |
49027 | 48 |
|
49032 | 49 |
val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq; |
50 |
||
49055 | 51 |
fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T); |
52 |
||
49043 | 53 |
fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs; |
49032 | 54 |
|
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
55 |
fun name_of_ctr t = |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
56 |
case head_of t of |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
57 |
Const (s, _) => s |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
58 |
| Free (s, _) => s |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
59 |
| _ => error "Cannot extract name of constructor"; |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
60 |
|
49074 | 61 |
fun prepare_wrap prep_term ((raw_ctrs, raw_caseof), (raw_disc_names, raw_sel_namess)) |
49054 | 62 |
no_defs_lthy = |
49017 | 63 |
let |
49019 | 64 |
(* TODO: sanity checks on arguments *) |
49017 | 65 |
|
49025 | 66 |
(* TODO: normalize types of constructors w.r.t. each other *) |
67 |
||
68 |
val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs; |
|
69 |
val caseof0 = prep_term no_defs_lthy raw_caseof; |
|
49017 | 70 |
|
49054 | 71 |
val n = length ctrs0; |
72 |
val ks = 1 upto n; |
|
73 |
||
49055 | 74 |
val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0))); |
75 |
val b = Binding.qualified_name T_name; |
|
76 |
||
77 |
val (As, B) = |
|
78 |
no_defs_lthy |
|
79 |
|> mk_TFrees (length As0) |
|
80 |
||> the_single o fst o mk_TFrees 1; |
|
81 |
||
82 |
fun mk_ctr Ts ctr = |
|
83 |
let val Ts0 = snd (dest_Type (body_type (fastype_of ctr))) in |
|
84 |
Term.subst_atomic_types (Ts0 ~~ Ts) ctr |
|
85 |
end; |
|
86 |
||
87 |
val T = Type (T_name, As); |
|
88 |
val ctrs = map (mk_ctr As) ctrs0; |
|
89 |
val ctr_Tss = map (binder_types o fastype_of) ctrs; |
|
90 |
||
91 |
val ms = map length ctr_Tss; |
|
92 |
||
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
93 |
val disc_names = |
49056 | 94 |
pad_list default_name n raw_disc_names |
95 |
|> map2 (fn ctr => fn disc => |
|
49046
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
96 |
if Binding.eq_name (disc, default_name) then |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
97 |
Binding.name (prefix is_N (Long_Name.base_name (name_of_ctr ctr))) |
3c5eba97d93a
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet
parents:
49045
diff
changeset
|
98 |
else |
49056 | 99 |
disc) ctrs0; |
100 |
||
49054 | 101 |
val sel_namess = |
49056 | 102 |
pad_list [] n raw_sel_namess |
103 |
|> map3 (fn ctr => fn m => map2 (fn l => fn sel => |
|
104 |
if Binding.eq_name (sel, default_name) then |
|
105 |
Binding.name (mk_un_N m l (Long_Name.base_name (name_of_ctr ctr))) |
|
106 |
else |
|
107 |
sel) (1 upto m) o pad_list default_name m) ctrs0 ms; |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
108 |
|
49028 | 109 |
fun mk_caseof Ts T = |
110 |
let val (binders, body) = strip_type (fastype_of caseof0) in |
|
111 |
Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0 |
|
49022 | 112 |
end; |
113 |
||
49028 | 114 |
val caseofB = mk_caseof As B; |
49025 | 115 |
val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss; |
116 |
||
49043 | 117 |
fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs); |
118 |
||
119 |
val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |> |
|
49025 | 120 |
mk_Freess "x" ctr_Tss |
121 |
||>> mk_Freess "y" ctr_Tss |
|
122 |
||>> mk_Frees "f" caseofB_Ts |
|
49032 | 123 |
||>> mk_Frees "g" caseofB_Ts |
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
124 |
||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T |
49032 | 125 |
||>> yield_singleton (mk_Frees "w") T |
49043 | 126 |
||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT; |
127 |
||
128 |
val q = Free (fst p', B --> HOLogic.boolT); |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
129 |
|
49025 | 130 |
val xctrs = map2 (curry Term.list_comb) ctrs xss; |
131 |
val yctrs = map2 (curry Term.list_comb) ctrs yss; |
|
49032 | 132 |
|
49043 | 133 |
val xfs = map2 (curry Term.list_comb) fs xss; |
134 |
val xgs = map2 (curry Term.list_comb) gs xss; |
|
135 |
||
136 |
val eta_fs = map2 eta_expand_caseof_arg xss xfs; |
|
137 |
val eta_gs = map2 eta_expand_caseof_arg xss xgs; |
|
138 |
||
139 |
val caseofB_fs = Term.list_comb (caseofB, eta_fs); |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
140 |
|
49025 | 141 |
val exist_xs_v_eq_ctrs = |
142 |
map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss; |
|
49022 | 143 |
|
49032 | 144 |
fun mk_sel_caseof_args k xs x T = |
49025 | 145 |
map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks; |
146 |
||
147 |
fun disc_spec b exist_xs_v_eq_ctr = |
|
49032 | 148 |
mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr); |
49025 | 149 |
|
49028 | 150 |
fun sel_spec b x xs k = |
49025 | 151 |
let val T' = fastype_of x in |
49032 | 152 |
mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v, |
153 |
Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v) |
|
49022 | 154 |
end; |
155 |
||
49028 | 156 |
val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) = |
49022 | 157 |
no_defs_lthy |
49025 | 158 |
|> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr => |
49022 | 159 |
Specification.definition (SOME (b, NONE, NoSyn), |
49025 | 160 |
((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs |
49028 | 161 |
||>> apfst (apsnd split_list o split_list) o fold_map3 (fn bs => fn xs => fn k => |
49025 | 162 |
apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x => |
49022 | 163 |
Specification.definition (SOME (b, NONE, NoSyn), |
49028 | 164 |
((Thm.def_binding b, []), sel_spec b x xs k))) bs xs) sel_namess xss ks |
49022 | 165 |
||> `Local_Theory.restore; |
166 |
||
49025 | 167 |
(*transforms defined frees into consts (and more)*) |
168 |
val phi = Proof_Context.export_morphism lthy lthy'; |
|
169 |
||
49028 | 170 |
val disc_defs = map (Morphism.thm phi) raw_disc_defs; |
171 |
val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss; |
|
172 |
||
173 |
val discs0 = map (Morphism.term phi) raw_discs; |
|
174 |
val selss0 = map (map (Morphism.term phi)) raw_selss; |
|
49025 | 175 |
|
49028 | 176 |
fun mk_disc_or_sel Ts t = |
177 |
Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t; |
|
178 |
||
179 |
val discs = map (mk_disc_or_sel As) discs0; |
|
180 |
val selss = map (map (mk_disc_or_sel As)) selss0; |
|
49025 | 181 |
|
49032 | 182 |
fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p); |
49029 | 183 |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
184 |
val goal_exhaust = |
49032 | 185 |
let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in |
49025 | 186 |
mk_imp_p (map2 mk_prem xctrs xss) |
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
187 |
end; |
49019 | 188 |
|
49034
b77e1910af8a
make parallel list indexing possible for inject theorems
blanchet
parents:
49033
diff
changeset
|
189 |
val goal_injectss = |
49017 | 190 |
let |
49034
b77e1910af8a
make parallel list indexing possible for inject theorems
blanchet
parents:
49033
diff
changeset
|
191 |
fun mk_goal _ _ [] [] = [] |
49025 | 192 |
| mk_goal xctr yctr xs ys = |
49034
b77e1910af8a
make parallel list indexing possible for inject theorems
blanchet
parents:
49033
diff
changeset
|
193 |
[mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr), |
b77e1910af8a
make parallel list indexing possible for inject theorems
blanchet
parents:
49033
diff
changeset
|
194 |
Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))]; |
49017 | 195 |
in |
49034
b77e1910af8a
make parallel list indexing possible for inject theorems
blanchet
parents:
49033
diff
changeset
|
196 |
map4 mk_goal xctrs yctrs xss yss |
49017 | 197 |
end; |
198 |
||
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
199 |
val goal_half_distinctss = |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
200 |
map (map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq)) (mk_half_pairss xctrs); |
49019 | 201 |
|
49043 | 202 |
val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs; |
49025 | 203 |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
204 |
val goals = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases]; |
49019 | 205 |
|
206 |
fun after_qed thmss lthy = |
|
207 |
let |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
208 |
val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) = |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
209 |
(hd thmss, apsnd (chop (n * n)) (chop n (tl thmss))); |
49019 | 210 |
|
49032 | 211 |
val exhaust_thm' = |
212 |
let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in |
|
213 |
Drule.instantiate' [] [SOME (certify lthy v)] |
|
214 |
(Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm)) |
|
215 |
end; |
|
216 |
||
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
217 |
val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss; |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
218 |
|
49052 | 219 |
val (distinct_thmsss', distinct_thmsss) = |
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
220 |
map2 (map2 append) (Library.chop_groups n half_distinct_thmss) |
49052 | 221 |
(transpose (Library.chop_groups n other_half_distinct_thmss)) |
222 |
|> `transpose; |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
223 |
val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss); |
49019 | 224 |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
225 |
val nchotomy_thm = |
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
226 |
let |
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
227 |
val goal = |
49022 | 228 |
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v', |
49029 | 229 |
Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs)); |
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
230 |
in |
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
231 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm) |
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
232 |
end; |
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
49019
diff
changeset
|
233 |
|
49030 | 234 |
val sel_thmss = |
49025 | 235 |
let |
49028 | 236 |
fun mk_thm k xs goal_case case_thm x sel_def = |
49025 | 237 |
let |
238 |
val T = fastype_of x; |
|
239 |
val cTs = |
|
240 |
map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree) |
|
241 |
(rev (Term.add_tfrees goal_case [])); |
|
49032 | 242 |
val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T); |
49025 | 243 |
in |
244 |
Local_Defs.fold lthy [sel_def] |
|
245 |
(Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm) |
|
246 |
end; |
|
49028 | 247 |
fun mk_thms k xs goal_case case_thm sel_defs = |
248 |
map2 (mk_thm k xs goal_case case_thm) xs sel_defs; |
|
49025 | 249 |
in |
49030 | 250 |
map5 mk_thms ks xss goal_cases case_thms sel_defss |
49025 | 251 |
end; |
252 |
||
49030 | 253 |
val discD_thms = map (fn def => def RS iffD1) disc_defs; |
49028 | 254 |
val discI_thms = |
49030 | 255 |
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs; |
49028 | 256 |
val not_disc_thms = |
49030 | 257 |
map2 (fn m => fn def => funpow m (fn thm => allI RS thm) |
258 |
(Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]}))) |
|
49028 | 259 |
ms disc_defs; |
260 |
||
49050 | 261 |
val (disc_thmss', disc_thmss) = |
49027 | 262 |
let |
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
263 |
fun mk_thm discI _ [] = refl RS discI |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
264 |
| mk_thm _ not_disc [distinct] = distinct RS not_disc; |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
265 |
fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss; |
49027 | 266 |
in |
49052 | 267 |
map3 mk_thms discI_thms not_disc_thms distinct_thmsss' |
49050 | 268 |
|> `transpose |
49027 | 269 |
end; |
49025 | 270 |
|
49053 | 271 |
val disc_exclus_thms = |
49028 | 272 |
let |
273 |
fun mk_goal ((_, disc), (_, disc')) = |
|
49029 | 274 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
275 |
HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v)))); |
|
49028 | 276 |
fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac); |
277 |
||
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
278 |
val bundles = ms ~~ discD_thms ~~ discs; |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
279 |
val half_pairss = mk_half_pairss bundles; |
49028 | 280 |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
281 |
val goal_halvess = map (map mk_goal) half_pairss; |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
282 |
val half_thmss = |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
283 |
map3 (fn [] => K (K []) |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
284 |
| [(((m, discD), _), _)] => fn disc_thm => fn [goal] => |
49053 | 285 |
[prove (mk_half_disc_exclus_tac m discD disc_thm) goal]) |
49050 | 286 |
half_pairss (flat disc_thmss') goal_halvess; |
49028 | 287 |
|
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
288 |
val goal_other_halvess = map (map (mk_goal o swap)) half_pairss; |
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
289 |
val other_half_thmss = |
49053 | 290 |
map2 (map2 (prove o mk_other_half_disc_exclus_tac)) half_thmss goal_other_halvess; |
49028 | 291 |
in |
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
292 |
interleave (flat half_thmss) (flat other_half_thmss) |
49028 | 293 |
end; |
49025 | 294 |
|
49029 | 295 |
val disc_exhaust_thm = |
296 |
let |
|
297 |
fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)]; |
|
298 |
val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs)); |
|
299 |
in |
|
300 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms) |
|
301 |
end; |
|
49025 | 302 |
|
49030 | 303 |
val ctr_sel_thms = |
304 |
let |
|
305 |
fun mk_goal ctr disc sels = |
|
306 |
Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v), |
|
49032 | 307 |
mk_Trueprop_eq ((null sels ? swap) |
308 |
(Term.list_comb (ctr, map (fn sel => sel $ v) sels), v)))); |
|
49030 | 309 |
val goals = map3 mk_goal ctrs discs selss; |
310 |
in |
|
311 |
map4 (fn goal => fn m => fn discD => fn sel_thms => |
|
312 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
313 |
mk_ctr_sel_tac ctxt m discD sel_thms)) |
|
314 |
goals ms discD_thms sel_thmss |
|
315 |
end; |
|
49025 | 316 |
|
49031 | 317 |
val case_disc_thm = |
318 |
let |
|
319 |
fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels); |
|
320 |
fun mk_rhs _ [f] [sels] = mk_core f sels |
|
321 |
| mk_rhs (disc :: discs) (f :: fs) (sels :: selss) = |
|
322 |
Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $ |
|
323 |
(disc $ v) $ mk_core f sels $ mk_rhs discs fs selss; |
|
49043 | 324 |
val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss); |
49031 | 325 |
in |
326 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
49050 | 327 |
mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss) |
49031 | 328 |
|> singleton (Proof_Context.export names_lthy lthy) |
329 |
end; |
|
49025 | 330 |
|
49033 | 331 |
val (case_cong_thm, weak_case_cong_thm) = |
49032 | 332 |
let |
333 |
fun mk_prem xctr xs f g = |
|
49045
7d9631754bba
minor fixes (for compatibility with existing datatype package)
blanchet
parents:
49044
diff
changeset
|
334 |
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr), |
49032 | 335 |
mk_Trueprop_eq (f, g))); |
49033 | 336 |
|
337 |
val v_eq_w = mk_Trueprop_eq (v, w); |
|
49043 | 338 |
val caseof_fs = mk_caseofB_term eta_fs; |
339 |
val caseof_gs = mk_caseofB_term eta_gs; |
|
49032 | 340 |
|
341 |
val goal = |
|
49033 | 342 |
Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs, |
343 |
mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w)); |
|
344 |
val goal_weak = |
|
345 |
Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w)); |
|
49032 | 346 |
in |
49049 | 347 |
(Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms), |
49033 | 348 |
Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1))) |
349 |
|> pairself (singleton (Proof_Context.export names_lthy lthy)) |
|
49032 | 350 |
end; |
49025 | 351 |
|
49044 | 352 |
val (split_thm, split_asm_thm) = |
49043 | 353 |
let |
49044 | 354 |
fun mk_conjunct xctr xs f_xs = |
49043 | 355 |
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs)); |
49044 | 356 |
fun mk_disjunct xctr xs f_xs = |
357 |
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr), |
|
358 |
HOLogic.mk_not (q $ f_xs))); |
|
359 |
||
360 |
val lhs = q $ (mk_caseofB_term eta_fs $ v); |
|
361 |
||
49043 | 362 |
val goal = |
49044 | 363 |
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs)); |
364 |
val goal_asm = |
|
365 |
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj |
|
366 |
(map3 mk_disjunct xctrs xss xfs))); |
|
367 |
||
368 |
val split_thm = |
|
49049 | 369 |
Skip_Proof.prove lthy [] [] goal |
49052 | 370 |
(fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss) |
49044 | 371 |
|> singleton (Proof_Context.export names_lthy lthy) |
372 |
val split_asm_thm = |
|
373 |
Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} => |
|
374 |
mk_split_asm_tac ctxt split_thm) |
|
375 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
49043 | 376 |
in |
49044 | 377 |
(split_thm, split_asm_thm) |
49043 | 378 |
end; |
49025 | 379 |
|
49043 | 380 |
(* TODO: case syntax *) |
381 |
(* TODO: attributes (simp, case_names, etc.) *) |
|
49025 | 382 |
|
49052 | 383 |
val notes = |
384 |
[(case_congN, [case_cong_thm]), |
|
385 |
(case_discsN, [case_disc_thm]), |
|
386 |
(casesN, case_thms), |
|
387 |
(ctr_selsN, ctr_sel_thms), |
|
388 |
(discsN, (flat disc_thmss)), |
|
49053 | 389 |
(disc_exclusN, disc_exclus_thms), |
49052 | 390 |
(disc_exhaustN, [disc_exhaust_thm]), |
391 |
(distinctN, distinct_thms), |
|
392 |
(exhaustN, [exhaust_thm]), |
|
393 |
(injectN, (flat inject_thmss)), |
|
394 |
(nchotomyN, [nchotomy_thm]), |
|
395 |
(selsN, (flat sel_thmss)), |
|
396 |
(splitN, [split_thm]), |
|
397 |
(split_asmN, [split_asm_thm]), |
|
398 |
(weak_case_cong_thmsN, [weak_case_cong_thm])] |
|
399 |
|> map (fn (thmN, thms) => |
|
400 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); |
|
49019 | 401 |
in |
49052 | 402 |
lthy |> Local_Theory.notes notes |> snd |
49019 | 403 |
end; |
49017 | 404 |
in |
49025 | 405 |
(goals, after_qed, lthy') |
49017 | 406 |
end; |
407 |
||
49057 | 408 |
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]"; |
409 |
||
410 |
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]"; |
|
49017 | 411 |
|
49074 | 412 |
val wrap_data_cmd = (fn (goalss, after_qed, lthy) => |
49019 | 413 |
Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo |
49074 | 414 |
prepare_wrap Syntax.read_term; |
49017 | 415 |
|
416 |
val _ = |
|
49074 | 417 |
Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype" |
49023 | 418 |
(((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term -- |
49057 | 419 |
Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], [])) |
49074 | 420 |
>> wrap_data_cmd); |
49017 | 421 |
|
422 |
end; |