author | blanchet |
Thu, 24 Oct 2013 15:32:34 +0200 | |
changeset 54198 | 4fadf746f2d5 |
parent 53690 | a3ad5a0350f9 |
child 54241 | 357988ad95ec |
permissions | -rw-r--r-- |
49636 | 1 |
(* Title: HOL/BNF/Tools/bnf_fp_def_sugar_tactics.ML |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
2 |
Author: Jasmin Blanchette, TU Muenchen |
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
3 |
Copyright 2012 |
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
4 |
|
49389 | 5 |
Tactics for datatype and codatatype sugar. |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
6 |
*) |
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
7 |
|
49636 | 8 |
signature BNF_FP_DEF_SUGAR_TACTICS = |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
9 |
sig |
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
10 |
val sum_prod_thms_map: thm list |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
11 |
val sum_prod_thms_set: thm list |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
12 |
val sum_prod_thms_rel: thm list |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
13 |
|
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
14 |
val mk_coinduct_tac: Proof.context -> thm list -> int -> int list -> thm -> thm list -> |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
15 |
thm list -> thm list -> thm list list -> thm list list list -> thm list list list -> tactic |
52349 | 16 |
val mk_coiter_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic |
49501 | 17 |
val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> |
18 |
tactic |
|
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
19 |
val mk_disc_coiter_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic |
49161
a8e74375d971
fixed (n + 1)st bug in "mk_exhaust_tac" -- arose with uncurried constructors
blanchet
parents:
49160
diff
changeset
|
20 |
val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic |
49127 | 21 |
val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic |
49590 | 22 |
val mk_induct_tac: Proof.context -> int -> int list -> int list list -> int list list list -> |
23 |
thm list -> thm -> thm list -> thm list list -> tactic |
|
49126 | 24 |
val mk_inject_tac: Proof.context -> thm -> thm -> tactic |
52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52195
diff
changeset
|
25 |
val mk_iter_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
26 |
end; |
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
27 |
|
49636 | 28 |
structure BNF_FP_Def_Sugar_Tactics : BNF_FP_DEF_SUGAR_TACTICS = |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
29 |
struct |
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
30 |
|
49125 | 31 |
open BNF_Tactics |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
32 |
open BNF_Util |
51850
106afdf5806c
renamed a few FP-related files, to make it clear that these are not the sum of LFP + GFP but rather shared basic libraries
blanchet
parents:
51843
diff
changeset
|
33 |
open BNF_FP_Util |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
34 |
|
49590 | 35 |
val basic_simp_thms = @{thms simp_thms(7,8,12,14,22,24)}; |
36 |
val more_simp_thms = basic_simp_thms @ @{thms simp_thms(11,15,16,21)}; |
|
37 |
||
49683 | 38 |
val sum_prod_thms_map = @{thms id_apply map_pair_simp prod.cases sum.cases sum_map.simps}; |
49585
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
39 |
val sum_prod_thms_set0 = |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
40 |
@{thms SUP_empty Sup_empty Sup_insert UN_insert Un_empty_left Un_empty_right Un_iff |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
41 |
Union_Un_distrib collect_def[abs_def] image_def o_apply map_pair_simp |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
42 |
mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps sum_set_simps}; |
5c4a12550491
generate high-level "maps", "sets", and "rels" properties
blanchet
parents:
49542
diff
changeset
|
43 |
val sum_prod_thms_set = @{thms UN_compreh_eq_eq} @ sum_prod_thms_set0; |
51893
596baae88a88
got rid of the set based relator---use (binary) predicate based relator instead
traytel
parents:
51850
diff
changeset
|
44 |
val sum_prod_thms_rel = @{thms prod_rel_simp sum_rel_simps id_apply}; |
49368 | 45 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49683
diff
changeset
|
46 |
val ss_if_True_False = simpset_of (ss_only @{thms if_True if_False} @{context}); |
49589 | 47 |
|
49590 | 48 |
fun mk_proj T k = |
49 |
let val binders = binder_types T in |
|
50 |
fold_rev (fn T => fn t => Abs (Name.uu, T, t)) binders (Bound (length binders - k)) |
|
51 |
end; |
|
52 |
||
49668 | 53 |
fun hhf_concl_conv cv ctxt ct = |
54 |
(case Thm.term_of ct of |
|
55 |
Const (@{const_name all}, _) $ Abs _ => |
|
56 |
Conv.arg_conv (Conv.abs_conv (hhf_concl_conv cv o snd) ctxt) ct |
|
57 |
| _ => Conv.concl_conv ~1 cv ct); |
|
58 |
||
49590 | 59 |
fun inst_as_projs ctxt k thm = |
49368 | 60 |
let |
49384 | 61 |
val fs = |
49368 | 62 |
Term.add_vars (prop_of thm) [] |
63 |
|> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false); |
|
49384 | 64 |
val cfs = |
49590 | 65 |
map (fn f as (_, T) => (certify ctxt (Var f), certify ctxt (mk_proj T k))) fs; |
49368 | 66 |
in |
49384 | 67 |
Drule.cterm_instantiate cfs thm |
49368 | 68 |
end; |
69 |
||
49590 | 70 |
val inst_as_projs_tac = PRIMITIVE oo inst_as_projs; |
49368 | 71 |
|
49501 | 72 |
fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' = |
52324 | 73 |
unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN HEADGOAL (rtac sumEN') THEN |
52659
58b87aa4dc3b
eliminate duplicated theorems (thanks to "Auto solve_direct" in jEdit)
traytel
parents:
52349
diff
changeset
|
74 |
unfold_thms_tac ctxt @{thms split_paired_all} THEN |
52324 | 75 |
HEADGOAL (EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, |
76 |
REPEAT_DETERM o dtac meta_spec, etac meta_mp, atac]) (1 upto n))); |
|
49125 | 77 |
|
49501 | 78 |
fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor = |
52324 | 79 |
HEADGOAL (rtac iffI THEN' |
80 |
EVERY' (map3 (fn cTs => fn cx => fn th => |
|
81 |
dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN' |
|
82 |
SELECT_GOAL (unfold_thms_tac ctxt [th]) THEN' |
|
83 |
atac) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])); |
|
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
84 |
|
49501 | 85 |
fun mk_half_distinct_tac ctxt ctor_inject ctr_defs = |
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49501
diff
changeset
|
86 |
unfold_thms_tac ctxt (ctor_inject :: @{thms sum.inject} @ ctr_defs) THEN |
52324 | 87 |
HEADGOAL (rtac @{thm sum.distinct(1)}); |
49127 | 88 |
|
49501 | 89 |
fun mk_inject_tac ctxt ctr_def ctor_inject = |
52324 | 90 |
unfold_thms_tac ctxt [ctr_def] THEN HEADGOAL (rtac (ctor_inject RS ssubst)) THEN |
91 |
unfold_thms_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN HEADGOAL (rtac refl); |
|
49126 | 92 |
|
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
93 |
val iter_unfold_thms = |
52195 | 94 |
@{thms comp_def convol_def fst_conv id_def prod_case_Pair_iden snd_conv |
95 |
split_conv unit_case_Unity} @ sum_prod_thms_map; |
|
49205 | 96 |
|
53329 | 97 |
fun mk_iter_tac pre_map_defs map_idents iter_defs ctor_iter ctr_def ctxt = |
98 |
unfold_thms_tac ctxt (ctr_def :: ctor_iter :: iter_defs @ pre_map_defs @ map_idents @ |
|
52324 | 99 |
iter_unfold_thms) THEN HEADGOAL (rtac refl); |
49205 | 100 |
|
52349 | 101 |
val coiter_unfold_thms = @{thms id_def} @ sum_prod_thms_map; |
49683 | 102 |
|
53329 | 103 |
fun mk_coiter_tac coiter_defs map_idents ctor_dtor_coiter pre_map_def ctr_def ctxt = |
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
104 |
unfold_thms_tac ctxt (ctr_def :: coiter_defs) THEN |
52324 | 105 |
HEADGOAL (rtac (ctor_dtor_coiter RS trans) THEN' |
106 |
asm_simp_tac (put_simpset ss_if_True_False ctxt)) THEN_MAYBE |
|
53329 | 107 |
(unfold_thms_tac ctxt (pre_map_def :: map_idents @ coiter_unfold_thms) THEN |
52324 | 108 |
HEADGOAL (rtac refl ORELSE' rtac (@{thm unit_eq} RS arg_cong))); |
49213 | 109 |
|
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
110 |
fun mk_disc_coiter_iff_tac case_splits' coiters discs ctxt = |
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
111 |
EVERY (map3 (fn case_split_tac => fn coiter_thm => fn disc => |
52324 | 112 |
HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [coiter_thm] THEN |
113 |
HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN |
|
114 |
(if is_refl disc then all_tac else HEADGOAL (rtac disc))) |
|
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51798
diff
changeset
|
115 |
(map rtac case_splits' @ [K all_tac]) coiters discs); |
49482 | 116 |
|
51798 | 117 |
fun solve_prem_prem_tac ctxt = |
49429
64ac3471005a
cleaner way of dealing with the set functions of sums and products
blanchet
parents:
49428
diff
changeset
|
118 |
REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE' |
51798 | 119 |
hyp_subst_tac ctxt ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN' |
49429
64ac3471005a
cleaner way of dealing with the set functions of sums and products
blanchet
parents:
49428
diff
changeset
|
120 |
(rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI}); |
49426 | 121 |
|
53290 | 122 |
fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_maps pre_set_defs = |
52324 | 123 |
HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp, |
53290 | 124 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ set_maps @ sum_prod_thms_set0)), |
52324 | 125 |
solve_prem_prem_tac ctxt]) (rev kks))); |
49368 | 126 |
|
53290 | 127 |
fun mk_induct_discharge_prem_tac ctxt nn n set_maps pre_set_defs m k kks = |
49429
64ac3471005a
cleaner way of dealing with the set functions of sums and products
blanchet
parents:
49428
diff
changeset
|
128 |
let val r = length kks in |
52324 | 129 |
HEADGOAL (EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt, |
130 |
REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)]) THEN |
|
49391 | 131 |
EVERY [REPEAT_DETERM_N r |
52324 | 132 |
(HEADGOAL (rotate_tac ~1 THEN' dtac meta_mp THEN' rotate_tac 1) THEN prefer_tac 2), |
133 |
if r > 0 then ALLGOALS Goal.norm_hhf_tac else all_tac, HEADGOAL atac, |
|
53290 | 134 |
mk_induct_leverage_prem_prems_tac ctxt nn kks set_maps pre_set_defs] |
49391 | 135 |
end; |
49368 | 136 |
|
53290 | 137 |
fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' set_maps pre_set_defss = |
49590 | 138 |
let val n = Integer.sum ns in |
52324 | 139 |
unfold_thms_tac ctxt ctr_defs THEN |
140 |
HEADGOAL (rtac ctor_induct' THEN' inst_as_projs_tac ctxt) THEN |
|
53290 | 141 |
EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_maps) pre_set_defss |
51766
f19a4d0ab1bf
renamed "set_natural" to "set_map", reflecting {Bl,Po,Tr} concensus
blanchet
parents:
51717
diff
changeset
|
142 |
mss (unflat mss (1 upto n)) kkss) |
49368 | 143 |
end; |
144 |
||
52966 | 145 |
fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def dtor_ctor ctr_def discs sels = |
51798 | 146 |
hyp_subst_tac ctxt THEN' |
49665 | 147 |
CONVERSION (hhf_concl_conv |
148 |
(Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' |
|
49642
9f884142334c
fixed simplification of prod and sum relators to avoid issues with e.g. codata ('a, 'b) k = K "'a + 'b"
blanchet
parents:
49639
diff
changeset
|
149 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
150 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels @ sum_prod_thms_rel)) THEN' |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
151 |
(atac ORELSE' REPEAT o etac conjE THEN' |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
152 |
full_simp_tac |
52324 | 153 |
(ss_only (@{thm prod.inject} :: no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' |
154 |
REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' REPEAT o rtac conjI THEN' |
|
53570
773302e7741d
made tactic handle gracefully the case: codatatype ('a, 's) scheduler2 = Combine2 "'s => 'a" "'s => ('a, 's) scheduler2"
blanchet
parents:
53329
diff
changeset
|
155 |
REPEAT o (rtac refl ORELSE' atac)); |
49590 | 156 |
|
52966 | 157 |
fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = |
54198
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
158 |
let |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
159 |
val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
160 |
|> distinct Thm.eq_thm_prop; |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
161 |
in |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
162 |
hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN' |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
163 |
full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
164 |
end; |
49590 | 165 |
|
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
166 |
fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def dtor_ctor exhaust ctr_defs |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
167 |
discss selss = |
49590 | 168 |
let val ks = 1 upto n in |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
169 |
EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk, dtac |
52324 | 170 |
meta_spec, dtac meta_mp, atac, rtac exhaust, K (HEADGOAL (inst_as_projs_tac ctxt)), |
51798 | 171 |
hyp_subst_tac ctxt] @ |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
172 |
map4 (fn k => fn ctr_def => fn discs => fn sels => |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
173 |
EVERY' ([rtac exhaust, K (inst_as_projs_tac ctxt 2)] @ |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
174 |
map2 (fn k' => fn discs' => |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
175 |
if k' = k then |
52966 | 176 |
mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def dtor_ctor ctr_def discs sels |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
177 |
else |
52966 | 178 |
mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss) |
49590 | 179 |
end; |
180 |
||
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
181 |
fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs dtor_ctors exhausts ctr_defss |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
182 |
discsss selsss = |
52324 | 183 |
HEADGOAL (rtac dtor_coinduct' THEN' |
184 |
EVERY' (map8 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn) |
|
185 |
(1 upto nn) ns pre_rel_defs dtor_ctors exhausts ctr_defss discsss selsss)); |
|
49590 | 186 |
|
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
187 |
end; |