author | wenzelm |
Mon, 12 Dec 2011 20:55:57 +0100 | |
changeset 45821 | c2f6c50e3d42 |
parent 45743 | 857b7fcb0365 |
child 45822 | 843dc212f69e |
permissions | -rw-r--r-- |
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haftmann
parents:
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changeset
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1 |
(* Title: HOL/Tools/Datatype/datatype_abs_proofs.ML |
11539 | 2 |
Author: Stefan Berghofer, TU Muenchen |
5177 | 3 |
|
45821 | 4 |
Datatype package: proofs and definitions independent of concrete |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
5 |
representation of datatypes (i.e. requiring only abstract |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
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changeset
|
6 |
properties: injectivity / distinctness of constructors and induction). |
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*) |
8 |
||
9 |
signature DATATYPE_ABS_PROOFS = |
|
10 |
sig |
|
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include DATATYPE_COMMON |
12 |
val prove_casedist_thms : config -> string list -> |
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descr list -> (string * sort) list -> thm -> |
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attribute list -> theory -> thm list * theory |
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val prove_primrec_thms : config -> string list -> |
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descr list -> (string * sort) list -> |
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(string -> thm list) -> thm list list -> thm list list * thm list list -> |
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thm -> theory -> (string list * thm list) * theory |
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val prove_case_thms : config -> string list -> |
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parents:
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descr list -> (string * sort) list -> |
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string list -> thm list -> theory -> (thm list list * string list) * theory |
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val prove_split_thms : config -> string list -> |
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haftmann
parents:
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descr list -> (string * sort) list -> |
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thm list list -> thm list list -> thm list -> thm list list -> theory -> |
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(thm * thm) list * theory |
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val prove_nchotomys : config -> string list -> descr list -> |
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(string * sort) list -> thm list -> theory -> thm list * theory |
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val prove_weak_case_congs : string list -> descr list -> |
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(string * sort) list -> theory -> thm list * theory |
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val prove_case_congs : string list -> |
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descr list -> (string * sort) list -> |
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thm list -> thm list list -> theory -> thm list * theory |
5177 | 33 |
end; |
34 |
||
33968
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modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
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parents:
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35 |
structure Datatype_Abs_Proofs: DATATYPE_ABS_PROOFS = |
5177 | 36 |
struct |
37 |
||
38 |
(************************ case distinction theorems ***************************) |
|
39 |
||
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fun prove_casedist_thms (config : Datatype_Aux.config) |
41 |
new_type_names descr sorts induct case_names_exhausts thy = |
|
5177 | 42 |
let |
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val _ = Datatype_Aux.message config "Proving case distinction theorems ..."; |
5177 | 44 |
|
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val descr' = flat descr; |
41423 | 46 |
val recTs = Datatype_Aux.get_rec_types descr' sorts; |
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val newTs = take (length (hd descr)) recTs; |
5177 | 48 |
|
44058 | 49 |
val maxidx = Thm.maxidx_of induct; |
8305 | 50 |
val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
5177 | 51 |
|
33063 | 52 |
fun prove_casedist_thm (i, (T, t)) = |
5177 | 53 |
let |
54 |
val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => |
|
35364 | 55 |
Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps; |
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val P = |
57 |
Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $ |
|
58 |
Var (("P", 0), HOLogic.boolT)); |
|
59 |
val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs); |
|
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val cert = cterm_of thy; |
45700 | 61 |
val insts' = map cert induct_Ps ~~ map cert insts; |
62 |
val induct' = |
|
63 |
refl RS |
|
64 |
(nth (Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i RSN (2, rev_mp)); |
|
17985 | 65 |
in |
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Skip_Proof.prove_global thy [] |
67 |
(Logic.strip_imp_prems t) |
|
68 |
(Logic.strip_imp_concl t) |
|
69 |
(fn {prems, ...} => |
|
70 |
EVERY |
|
71 |
[rtac induct' 1, |
|
72 |
REPEAT (rtac TrueI 1), |
|
73 |
REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), |
|
74 |
REPEAT (rtac TrueI 1)]) |
|
5177 | 75 |
end; |
76 |
||
45700 | 77 |
val casedist_thms = |
78 |
map_index prove_casedist_thm (newTs ~~ Datatype_Prop.make_casedists descr sorts); |
|
18314 | 79 |
in |
80 |
thy |
|
41423 | 81 |
|> Datatype_Aux.store_thms_atts "exhaust" new_type_names |
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(map single case_names_exhausts) casedist_thms |
18314 | 83 |
end; |
5177 | 84 |
|
85 |
||
86 |
(*************************** primrec combinators ******************************) |
|
87 |
||
41423 | 88 |
fun prove_primrec_thms (config : Datatype_Aux.config) new_type_names descr sorts |
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injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy = |
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let |
41423 | 91 |
val _ = Datatype_Aux.message config "Constructing primrec combinators ..."; |
5661 | 92 |
|
93 |
val big_name = space_implode "_" new_type_names; |
|
32124 | 94 |
val thy0 = Sign.add_path big_name thy; |
5177 | 95 |
|
32952 | 96 |
val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr' sorts; |
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val used = fold Term.add_tfree_namesT recTs []; |
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val newTs = take (length (hd descr)) recTs; |
5177 | 100 |
|
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
5177 | 102 |
|
5661 | 103 |
val big_rec_name' = big_name ^ "_rec_set"; |
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val rec_set_names' = |
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if length descr' = 1 then [big_rec_name'] |
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else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr'); |
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val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; |
5177 | 108 |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
109 |
val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr sorts used; |
5177 | 110 |
|
45700 | 111 |
val rec_set_Ts = |
112 |
map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); |
|
5177 | 113 |
|
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val rec_fns = |
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map (uncurry (Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts)); |
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val rec_sets' = |
117 |
map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts); |
|
118 |
val rec_sets = |
|
119 |
map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts); |
|
5177 | 120 |
|
121 |
(* introduction rules for graph of primrec function *) |
|
122 |
||
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fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) = |
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let |
33338 | 125 |
fun mk_prem (dt, U) (j, k, prems, t1s, t2s) = |
45700 | 126 |
let val free1 = Datatype_Aux.mk_Free "x" U j in |
127 |
(case (Datatype_Aux.strip_dtyp dt, strip_type U) of |
|
128 |
((_, Datatype_Aux.DtRec m), (Us, _)) => |
|
129 |
let |
|
130 |
val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k; |
|
131 |
val i = length Us; |
|
132 |
in |
|
133 |
(j + 1, k + 1, |
|
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HOLogic.mk_Trueprop (HOLogic.list_all |
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(map (pair "x") Us, nth rec_sets' m $ |
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Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems, |
|
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free1 :: t1s, free2 :: t2s) |
|
138 |
end |
|
45821 | 139 |
| _ => (j + 1, k, prems, free1 :: t1s, t2s)) |
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end; |
141 |
||
41423 | 142 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
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val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []); |
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|
45700 | 145 |
in |
146 |
(rec_intr_ts @ |
|
147 |
[Logic.list_implies (prems, HOLogic.mk_Trueprop |
|
148 |
(rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ |
|
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list_comb (nth rec_fns l, t1s @ t2s)))], l + 1) |
|
5177 | 150 |
end; |
151 |
||
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val (rec_intr_ts, _) = |
153 |
fold (fn ((d, T), set_name) => |
|
154 |
fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0); |
|
5177 | 155 |
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156 |
val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = |
33278 | 157 |
thy0 |
158 |
|> Sign.map_naming Name_Space.conceal |
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159 |
|> Inductive.add_inductive_global |
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{quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name', |
161 |
coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false} |
|
28965 | 162 |
(map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
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(map dest_Free rec_fns) |
33278 | 164 |
(map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] |
165 |
||> Sign.restore_naming thy0 |
|
166 |
||> Theory.checkpoint; |
|
5177 | 167 |
|
168 |
(* prove uniqueness and termination of primrec combinators *) |
|
169 |
||
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val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ..."; |
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|
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fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) = |
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let |
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val distinct_tac = |
45700 | 175 |
if i < length newTs then |
176 |
full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1 |
|
177 |
else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1; |
|
5177 | 178 |
|
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val inject = |
180 |
map (fn r => r RS iffD1) |
|
181 |
(if i < length newTs then nth constr_inject i else injects_of tname); |
|
5177 | 182 |
|
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fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) = |
5177 | 184 |
let |
45700 | 185 |
val k = length (filter Datatype_Aux.is_rec_type cargs); |
186 |
in |
|
187 |
(EVERY |
|
188 |
[DETERM tac, |
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REPEAT (etac ex1E 1), rtac ex1I 1, |
190 |
DEPTH_SOLVE_1 (ares_tac [intr] 1), |
|
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191 |
REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1), |
5177 | 192 |
etac elim 1, |
193 |
REPEAT_DETERM_N j distinct_tac, |
|
21021 | 194 |
TRY (dresolve_tac inject 1), |
5177 | 195 |
REPEAT (etac conjE 1), hyp_subst_tac 1, |
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196 |
REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), |
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TRY (hyp_subst_tac 1), |
198 |
rtac refl 1, |
|
199 |
REPEAT_DETERM_N (n - j - 1) distinct_tac], |
|
200 |
intrs, j + 1) |
|
201 |
end; |
|
202 |
||
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val (tac', intrs', _) = |
204 |
fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0); |
|
5177 | 205 |
in (tac', intrs') end; |
206 |
||
207 |
val rec_unique_thms = |
|
208 |
let |
|
45700 | 209 |
val rec_unique_ts = |
210 |
map (fn (((set_t, T1), T2), i) => |
|
211 |
Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ |
|
212 |
absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2))) |
|
213 |
(rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); |
|
214 |
val cert = cterm_of thy1; |
|
215 |
val insts = |
|
216 |
map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t) |
|
217 |
((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); |
|
218 |
val induct' = cterm_instantiate (map cert induct_Ps ~~ map cert insts) induct; |
|
219 |
val (tac, _) = |
|
220 |
fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts) |
|
221 |
(((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1 THEN |
|
222 |
rewrite_goals_tac [mk_meta_eq @{thm choice_eq}], rec_intrs)); |
|
41423 | 223 |
in |
224 |
Datatype_Aux.split_conj_thm (Skip_Proof.prove_global thy1 [] [] |
|
225 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) (K tac)) |
|
5177 | 226 |
end; |
227 |
||
35410 | 228 |
val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms; |
5177 | 229 |
|
230 |
(* define primrec combinators *) |
|
231 |
||
45700 | 232 |
val big_reccomb_name = space_implode "_" new_type_names ^ "_rec"; |
233 |
val reccomb_names = |
|
234 |
map (Sign.full_bname thy1) |
|
235 |
(if length descr' = 1 then [big_reccomb_name] |
|
45821 | 236 |
else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr')); |
45700 | 237 |
val reccombs = |
238 |
map (fn ((name, T), T') => list_comb (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) |
|
5177 | 239 |
(reccomb_names ~~ recTs ~~ rec_result_Ts); |
240 |
||
18358 | 241 |
val (reccomb_defs, thy2) = |
242 |
thy1 |
|
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243 |
|> Sign.add_consts_i (map (fn ((name, T), T') => |
45700 | 244 |
(Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) |
245 |
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
|
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|
246 |
|> (Global_Theory.add_defs false o map Thm.no_attributes) |
45700 | 247 |
(map |
248 |
(fn ((((name, comb), set), T), T') => |
|
249 |
(Binding.name (Long_Name.base_name name ^ "_def"), |
|
250 |
Logic.mk_equals (comb, absfree ("x", T) |
|
251 |
(Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T') |
|
252 |
(set $ Free ("x", T) $ Free ("y", T')))))) |
|
253 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |
|
32124 | 254 |
||> Sign.parent_path |
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|
255 |
||> Theory.checkpoint; |
5177 | 256 |
|
257 |
||
258 |
(* prove characteristic equations for primrec combinators *) |
|
259 |
||
41423 | 260 |
val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ..."; |
5177 | 261 |
|
45700 | 262 |
val rec_thms = |
263 |
map (fn t => |
|
264 |
Skip_Proof.prove_global thy2 [] [] t |
|
265 |
(fn _ => EVERY |
|
266 |
[rewrite_goals_tac reccomb_defs, |
|
267 |
rtac @{thm the1_equality} 1, |
|
268 |
resolve_tac rec_unique_thms 1, |
|
269 |
resolve_tac rec_intrs 1, |
|
270 |
REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) |
|
271 |
(Datatype_Prop.make_primrecs new_type_names descr sorts thy2); |
|
5177 | 272 |
in |
18314 | 273 |
thy2 |
24712
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wenzelm
parents:
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diff
changeset
|
274 |
|> Sign.add_path (space_implode "_" new_type_names) |
39557
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renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
38864
diff
changeset
|
275 |
|> Global_Theory.add_thmss [((Binding.name "recs", rec_thms), [Nitpick_Simps.add])] |
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parents:
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|
276 |
||> Sign.parent_path |
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parents:
28110
diff
changeset
|
277 |
||> Theory.checkpoint |
32906 | 278 |
|-> (fn thms => pair (reccomb_names, flat thms)) |
5177 | 279 |
end; |
280 |
||
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|
281 |
|
5177 | 282 |
(***************************** case combinators *******************************) |
283 |
||
41423 | 284 |
fun prove_case_thms (config : Datatype_Aux.config) |
285 |
new_type_names descr sorts reccomb_names primrec_thms thy = |
|
5177 | 286 |
let |
41423 | 287 |
val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ..."; |
5661 | 288 |
|
32124 | 289 |
val thy1 = Sign.add_path (space_implode "_" new_type_names) thy; |
5177 | 290 |
|
32952 | 291 |
val descr' = flat descr; |
41423 | 292 |
val recTs = Datatype_Aux.get_rec_types descr' sorts; |
45738 | 293 |
val used = fold Term.add_tfree_namesT recTs []; |
33957 | 294 |
val newTs = take (length (hd descr)) recTs; |
43324
2b47822868e4
discontinued Name.variant to emphasize that this is old-style / indirect;
wenzelm
parents:
42375
diff
changeset
|
295 |
val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS); |
5177 | 296 |
|
41423 | 297 |
fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' sorts dt) ---> T'; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
298 |
|
45700 | 299 |
val case_dummy_fns = |
300 |
map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => |
|
301 |
let |
|
302 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
|
303 |
val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs) |
|
304 |
in Const (@{const_name undefined}, Ts @ Ts' ---> T') end) constrs) descr'; |
|
5177 | 305 |
|
28965 | 306 |
val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names; |
5177 | 307 |
|
308 |
(* define case combinators via primrec combinators *) |
|
309 |
||
45700 | 310 |
val (case_defs, thy2) = |
311 |
fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) => |
|
312 |
let |
|
313 |
val (fns1, fns2) = split_list (map (fn ((_, cargs), j) => |
|
314 |
let |
|
315 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
|
316 |
val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs); |
|
317 |
val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts'); |
|
318 |
val frees = take (length cargs) frees'; |
|
319 |
val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j; |
|
320 |
in |
|
321 |
(free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees))) |
|
322 |
end) (constrs ~~ (1 upto length constrs))); |
|
323 |
||
324 |
val caseT = map (snd o dest_Free) fns1 @ [T] ---> T'; |
|
325 |
val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns); |
|
326 |
val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); |
|
327 |
val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); |
|
328 |
val def = |
|
329 |
(Binding.name (Long_Name.base_name name ^ "_def"), |
|
330 |
Logic.mk_equals (list_comb (Const (name, caseT), fns1), |
|
331 |
list_comb (reccomb, (flat (take i case_dummy_fns)) @ |
|
332 |
fns2 @ (flat (drop (i + 1) case_dummy_fns))))); |
|
333 |
val ([def_thm], thy') = |
|
334 |
thy |
|
335 |
|> Sign.declare_const_global decl |> snd |
|
336 |
|> (Global_Theory.add_defs false o map Thm.no_attributes) [def]; |
|
337 |
||
338 |
in (defs @ [def_thm], thy') end) |
|
339 |
(hd descr ~~ newTs ~~ case_names ~~ take (length newTs) reccomb_names) ([], thy1) |
|
28361
232fcbba2e4e
explicit checkpoint for low-level (global) theory operations, admits concurrent proofs;
wenzelm
parents:
28110
diff
changeset
|
340 |
||> Theory.checkpoint; |
5177 | 341 |
|
45700 | 342 |
val case_thms = |
343 |
(map o map) (fn t => |
|
344 |
Skip_Proof.prove_global thy2 [] [] t |
|
345 |
(fn _ => |
|
346 |
EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])) |
|
347 |
(Datatype_Prop.make_cases new_type_names descr sorts thy2); |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
348 |
in |
18314 | 349 |
thy2 |
33459 | 350 |
|> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms) |
32124 | 351 |
|> Sign.parent_path |
41423 | 352 |
|> Datatype_Aux.store_thmss "cases" new_type_names case_thms |
18314 | 353 |
|-> (fn thmss => pair (thmss, case_names)) |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
354 |
end; |
5177 | 355 |
|
356 |
||
357 |
(******************************* case splitting *******************************) |
|
358 |
||
41423 | 359 |
fun prove_split_thms (config : Datatype_Aux.config) |
360 |
new_type_names descr sorts constr_inject dist_rewrites casedist_thms case_thms thy = |
|
5177 | 361 |
let |
41423 | 362 |
val _ = Datatype_Aux.message config "Proving equations for case splitting ..."; |
5177 | 363 |
|
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31604
diff
changeset
|
364 |
val descr' = flat descr; |
41423 | 365 |
val recTs = Datatype_Aux.get_rec_types descr' sorts; |
33957 | 366 |
val newTs = take (length (hd descr)) recTs; |
5177 | 367 |
|
45700 | 368 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) = |
5177 | 369 |
let |
17985 | 370 |
val cert = cterm_of thy; |
5177 | 371 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); |
45700 | 372 |
val exhaustion' = cterm_instantiate [(cert lhs, cert (Free ("x", T)))] exhaustion; |
373 |
val tac = |
|
374 |
EVERY [rtac exhaustion' 1, |
|
375 |
ALLGOALS (asm_simp_tac (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]; |
|
5177 | 376 |
in |
45700 | 377 |
(Skip_Proof.prove_global thy [] [] t1 (K tac), |
378 |
Skip_Proof.prove_global thy [] [] t2 (K tac)) |
|
5177 | 379 |
end; |
380 |
||
45700 | 381 |
val split_thm_pairs = |
382 |
map prove_split_thms |
|
383 |
((Datatype_Prop.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ |
|
384 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); |
|
5177 | 385 |
|
386 |
val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs |
|
387 |
||
388 |
in |
|
18314 | 389 |
thy |
41423 | 390 |
|> Datatype_Aux.store_thms "split" new_type_names split_thms |
391 |
||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms |
|
18314 | 392 |
|-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) |
5177 | 393 |
end; |
394 |
||
8601 | 395 |
fun prove_weak_case_congs new_type_names descr sorts thy = |
396 |
let |
|
397 |
fun prove_weak_case_cong t = |
|
45700 | 398 |
Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
399 |
(fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1]); |
|
8601 | 400 |
|
45700 | 401 |
val weak_case_congs = |
402 |
map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs new_type_names descr sorts thy); |
|
8601 | 403 |
|
41423 | 404 |
in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end; |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
405 |
|
5177 | 406 |
(************************* additional theorems for TFL ************************) |
407 |
||
41423 | 408 |
fun prove_nchotomys (config : Datatype_Aux.config) |
409 |
new_type_names descr sorts casedist_thms thy = |
|
5177 | 410 |
let |
41423 | 411 |
val _ = Datatype_Aux.message config "Proving additional theorems for TFL ..."; |
5177 | 412 |
|
413 |
fun prove_nchotomy (t, exhaustion) = |
|
414 |
let |
|
415 |
(* For goal i, select the correct disjunct to attack, then prove it *) |
|
45700 | 416 |
fun tac i 0 = EVERY [TRY (rtac disjI1 i), hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] |
417 |
| tac i n = rtac disjI2 i THEN tac i (n - 1); |
|
418 |
in |
|
419 |
Skip_Proof.prove_global thy [] [] t |
|
420 |
(fn _ => |
|
421 |
EVERY [rtac allI 1, |
|
422 |
Datatype_Aux.exh_tac (K exhaustion) 1, |
|
423 |
ALLGOALS (fn i => tac i (i - 1))]) |
|
5177 | 424 |
end; |
425 |
||
426 |
val nchotomys = |
|
45700 | 427 |
map prove_nchotomy (Datatype_Prop.make_nchotomys descr sorts ~~ casedist_thms); |
5177 | 428 |
|
41423 | 429 |
in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end; |
5177 | 430 |
|
431 |
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = |
|
432 |
let |
|
433 |
fun prove_case_cong ((t, nchotomy), case_rewrites) = |
|
434 |
let |
|
45700 | 435 |
val Const ("==>", _) $ tm $ _ = t; |
436 |
val Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma) = tm; |
|
22578 | 437 |
val cert = cterm_of thy; |
5177 | 438 |
val nchotomy' = nchotomy RS spec; |
29264 | 439 |
val [v] = Term.add_vars (concl_of nchotomy') []; |
45700 | 440 |
val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy'; |
5177 | 441 |
in |
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
442 |
Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
45700 | 443 |
(fn {prems, ...} => |
444 |
let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) in |
|
445 |
EVERY [ |
|
446 |
simp_tac (HOL_ss addsimps [hd prems]) 1, |
|
17985 | 447 |
cut_facts_tac [nchotomy''] 1, |
448 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), |
|
449 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] |
|
20046 | 450 |
end) |
5177 | 451 |
end; |
452 |
||
45700 | 453 |
val case_congs = |
454 |
map prove_case_cong (Datatype_Prop.make_case_congs |
|
455 |
new_type_names descr sorts thy ~~ nchotomys ~~ case_thms); |
|
5177 | 456 |
|
41423 | 457 |
in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end; |
458 |
||
459 |
||
460 |
open Datatype_Aux; |
|
5177 | 461 |
|
462 |
end; |