author | wenzelm |
Wed, 02 Nov 2005 14:46:51 +0100 | |
changeset 18057 | ad97e231bf8a |
parent 17985 | d5d576b72371 |
child 18083 | cf7669049df5 |
permissions | -rw-r--r-- |
2276 | 1 |
(* Title: HOLCF/domain/theorems.ML |
2445
51993fea433f
removed Holcfb.thy and Holcfb.ML, moving classical3 to HOL.ML as classical2
oheimb
parents:
2276
diff
changeset
|
2 |
ID: $Id$ |
12030 | 3 |
Author: David von Oheimb |
15742 | 4 |
New proofs/tactics by Brian Huffman |
2445
51993fea433f
removed Holcfb.thy and Holcfb.ML, moving classical3 to HOL.ML as classical2
oheimb
parents:
2276
diff
changeset
|
5 |
|
12030 | 6 |
Proof generator for domain section. |
1274 | 7 |
*) |
8 |
||
16842 | 9 |
val HOLCF_ss = simpset(); |
2446
c2a9bf6c0948
The previous log message was wrong. The correct one is:
oheimb
parents:
2445
diff
changeset
|
10 |
|
1274 | 11 |
structure Domain_Theorems = struct |
12 |
||
13 |
local |
|
14 |
||
15 |
open Domain_Library; |
|
16 |
infixr 0 ===>;infixr 0 ==>;infix 0 == ; |
|
17 |
infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<; |
|
18 |
infix 9 ` ; infix 9 `% ; infix 9 `%%; infixr 9 oo; |
|
19 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
20 |
(* ----- general proof facilities ------------------------------------------- *) |
1274 | 21 |
|
14820 | 22 |
fun inferT sg pre_tm = |
15531 | 23 |
#1 (Sign.infer_types (Sign.pp sg) sg (K NONE) (K NONE) [] true ([pre_tm],propT)); |
1274 | 24 |
|
17985 | 25 |
fun pg'' thy defs t tacs = |
26 |
let val t' = inferT thy t in |
|
27 |
standard (Goal.prove thy [] (Logic.strip_imp_prems t') (Logic.strip_imp_concl t') |
|
28 |
(fn prems => rewrite_goals_tac defs THEN EVERY (tacs (map (rewrite_rule defs) prems)))) |
|
29 |
end; |
|
30 |
||
1274 | 31 |
fun pg' thy defs t tacsf=pg'' thy defs t (fn [] => tacsf |
2033 | 32 |
| prems=> (cut_facts_tac prems 1)::tacsf); |
1274 | 33 |
|
2033 | 34 |
fun case_UU_tac rews i v = case_tac (v^"=UU") i THEN |
35 |
asm_simp_tac (HOLCF_ss addsimps rews) i; |
|
1274 | 36 |
|
37 |
val chain_tac = REPEAT_DETERM o resolve_tac |
|
5291 | 38 |
[chain_iterate, ch2ch_Rep_CFunR, ch2ch_Rep_CFunL]; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
39 |
|
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
40 |
(* ----- general proofs ----------------------------------------------------- *) |
1274 | 41 |
|
1644 | 42 |
val all2E = prove_goal HOL.thy "[| !x y . P x y; P x y ==> R |] ==> R" |
43 |
(fn prems =>[ |
|
2033 | 44 |
resolve_tac prems 1, |
45 |
cut_facts_tac prems 1, |
|
46 |
fast_tac HOL_cs 1]); |
|
1274 | 47 |
|
18057 | 48 |
val dist_eqI = prove_goal (the_context ()) "!!x::'a::po. ~ x << y ==> x ~= y" |
10230 | 49 |
(fn prems => [ |
50 |
(blast_tac (claset() addDs [antisym_less_inverse]) 1)]); |
|
4755 | 51 |
(* |
52 |
infixr 0 y; |
|
53 |
val b = 0; |
|
54 |
fun _ y t = by t; |
|
55 |
fun g defs t = let val sg = sign_of thy; |
|
56 |
val ct = Thm.cterm_of sg (inferT sg t); |
|
57 |
in goalw_cterm defs ct end; |
|
58 |
*) |
|
1274 | 59 |
|
60 |
in |
|
61 |
||
4043 | 62 |
fun theorems (((dname,_),cons) : eq, eqs : eq list) thy = |
1274 | 63 |
let |
64 |
||
4030 | 65 |
val dummy = writeln ("Proving isomorphism properties of domain "^dname^" ..."); |
1274 | 66 |
val pg = pg' thy; |
67 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
68 |
(* ----- getting the axioms and definitions --------------------------------- *) |
1274 | 69 |
|
16486 | 70 |
local fun ga s dn = get_thm thy (Name (dn ^ "." ^ s)) in |
4043 | 71 |
val ax_abs_iso = ga "abs_iso" dname; |
72 |
val ax_rep_iso = ga "rep_iso" dname; |
|
73 |
val ax_when_def = ga "when_def" dname; |
|
74 |
val axs_con_def = map (fn (con,_) => ga (extern_name con^"_def") dname) cons; |
|
75 |
val axs_dis_def = map (fn (con,_) => ga ( dis_name con^"_def") dname) cons; |
|
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
76 |
val axs_mat_def = map (fn (con,_) => ga ( mat_name con^"_def") dname) cons; |
16394
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
77 |
val axs_sel_def = List.concat(map (fn (_,args) => List.mapPartial (fn arg => |
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
78 |
Option.map (fn sel => ga (sel^"_def") dname) (sel_of arg)) args) |
4043 | 79 |
cons); |
80 |
val ax_copy_def = ga "copy_def" dname; |
|
1274 | 81 |
end; (* local *) |
82 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
83 |
(* ----- theorems concerning the isomorphism -------------------------------- *) |
1274 | 84 |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
85 |
val dc_abs = %%:(dname^"_abs"); |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
86 |
val dc_rep = %%:(dname^"_rep"); |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
87 |
val dc_copy = %%:(dname^"_copy"); |
1274 | 88 |
val x_name = "x"; |
89 |
||
15742 | 90 |
val iso_locale = iso_intro OF [ax_abs_iso, ax_rep_iso]; |
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
91 |
val abs_strict = ax_rep_iso RS (allI RS retraction_strict); |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
92 |
val rep_strict = ax_abs_iso RS (allI RS retraction_strict); |
15742 | 93 |
val abs_defin' = iso_locale RS iso_abs_defin'; |
94 |
val rep_defin' = iso_locale RS iso_rep_defin'; |
|
12037 | 95 |
val iso_rews = map standard [ax_abs_iso,ax_rep_iso,abs_strict,rep_strict]; |
1274 | 96 |
|
15742 | 97 |
(* ----- generating beta reduction rules from definitions-------------------- *) |
98 |
||
99 |
local |
|
100 |
fun arglist (Const _ $ Abs (s,_,t)) = let |
|
101 |
val (vars,body) = arglist t |
|
102 |
in (s :: vars, body) end |
|
103 |
| arglist t = ([],t); |
|
104 |
fun bind_fun vars t = Library.foldr mk_All (vars,t); |
|
105 |
fun bound_vars 0 = [] | bound_vars i = (Bound (i-1) :: bound_vars (i-1)); |
|
106 |
in |
|
107 |
fun appl_of_def def = let |
|
16403 | 108 |
val (_ $ con $ lam) = concl_of def; |
109 |
val (vars, rhs) = arglist lam; |
|
110 |
val lhs = mk_cRep_CFun (con, bound_vars (length vars)); |
|
111 |
val appl = bind_fun vars (lhs == rhs); |
|
112 |
val cs = ContProc.cont_thms lam; |
|
113 |
val betas = map (fn c => mk_meta_eq (c RS beta_cfun)) cs; |
|
15742 | 114 |
in pg (def::betas) appl [rtac reflexive_thm 1] end; |
115 |
end; |
|
116 |
||
117 |
val when_appl = appl_of_def ax_when_def; |
|
118 |
val con_appls = map appl_of_def axs_con_def; |
|
119 |
||
120 |
local |
|
16778 | 121 |
fun arg2typ n arg = let val t = TVar (("'a",n),pcpoS) |
15742 | 122 |
in (n+1, if is_lazy arg then mk_uT t else t) end; |
123 |
fun args2typ n [] = (n,oneT) |
|
124 |
| args2typ n [arg] = arg2typ n arg |
|
125 |
| args2typ n (arg::args) = let val (n1,t1) = arg2typ n arg; |
|
126 |
val (n2,t2) = args2typ n1 args |
|
127 |
in (n2, mk_sprodT (t1, t2)) end; |
|
128 |
fun cons2typ n [] = (n,oneT) |
|
129 |
| cons2typ n [con] = args2typ n (snd con) |
|
130 |
| cons2typ n (con::cons) = let val (n1,t1) = args2typ n (snd con); |
|
131 |
val (n2,t2) = cons2typ n1 cons |
|
132 |
in (n2, mk_ssumT (t1, t2)) end; |
|
133 |
in |
|
134 |
fun cons2ctyp cons = ctyp_of (sign_of thy) (snd (cons2typ 1 cons)); |
|
135 |
end; |
|
136 |
||
1274 | 137 |
local |
15742 | 138 |
val iso_swap = iso_locale RS iso_iso_swap; |
1274 | 139 |
fun one_con (con,args) = let val vns = map vname args in |
17811 | 140 |
Library.foldr mk_ex (vns, foldr1 mk_conj ((%:x_name === con_app2 con %: vns):: |
15742 | 141 |
map (defined o %:) (nonlazy args))) end; |
17811 | 142 |
val exh = foldr1 mk_disj ((%:x_name===UU)::map one_con cons); |
15742 | 143 |
val my_ctyp = cons2ctyp cons; |
144 |
val thm1 = instantiate' [SOME my_ctyp] [] exh_start; |
|
145 |
val thm2 = rewrite_rule (map mk_meta_eq ex_defined_iffs) thm1; |
|
146 |
val thm3 = rewrite_rule [mk_meta_eq conj_assoc] thm2; |
|
1274 | 147 |
in |
15742 | 148 |
val exhaust = pg con_appls (mk_trp exh)[ |
149 |
(* first 3 rules replace "x = UU \/ P" with "rep$x = UU \/ P" *) |
|
150 |
rtac disjE 1, |
|
151 |
etac (rep_defin' RS disjI1) 2, |
|
152 |
etac disjI2 2, |
|
153 |
rewrite_goals_tac [mk_meta_eq iso_swap], |
|
154 |
rtac thm3 1]; |
|
155 |
val casedist = standard (rewrite_rule exh_casedists (exhaust RS exh_casedist0)); |
|
1274 | 156 |
end; |
157 |
||
158 |
local |
|
15570 | 159 |
fun bind_fun t = Library.foldr mk_All (when_funs cons,t); |
1829 | 160 |
fun bound_fun i _ = Bound (length cons - i); |
15570 | 161 |
val when_app = Library.foldl (op `) (%%:(dname^"_when"), mapn bound_fun 1 cons); |
1274 | 162 |
in |
15742 | 163 |
val when_strict = pg [when_appl, mk_meta_eq rep_strict] |
164 |
(bind_fun(mk_trp(strict when_app))) |
|
165 |
[resolve_tac [sscase1,ssplit1,strictify1] 1]; |
|
166 |
val when_apps = let fun one_when n (con,args) = pg (when_appl :: con_appls) |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
167 |
(bind_fun (lift_defined %: (nonlazy args, |
2033 | 168 |
mk_trp(when_app`(con_app con args) === |
5291 | 169 |
mk_cRep_CFun(bound_fun n 0,map %# args)))))[ |
15742 | 170 |
asm_simp_tac (HOLCF_ss addsimps [ax_abs_iso]) 1]; |
2033 | 171 |
in mapn one_when 1 cons end; |
1274 | 172 |
end; |
173 |
val when_rews = when_strict::when_apps; |
|
174 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
175 |
(* ----- theorems concerning the constructors, discriminators and selectors - *) |
1274 | 176 |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
177 |
val dis_rews = let |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
178 |
val dis_stricts = map (fn (con,_) => pg axs_dis_def (mk_trp( |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
179 |
strict(%%:(dis_name con)))) [ |
15742 | 180 |
rtac when_strict 1]) cons; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
181 |
val dis_apps = let fun one_dis c (con,args)= pg axs_dis_def |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
182 |
(lift_defined %: (nonlazy args, |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
183 |
(mk_trp((%%:(dis_name c))`(con_app con args) === |
16778 | 184 |
%%:(if con=c then TT_N else FF_N))))) [ |
2033 | 185 |
asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
15570 | 186 |
in List.concat(map (fn (c,_) => map (one_dis c) cons) cons) end; |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
187 |
val dis_defins = map (fn (con,args) => pg [] (defined(%:x_name) ==> |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
188 |
defined(%%:(dis_name con)`%x_name)) [ |
4043 | 189 |
rtac casedist 1, |
2033 | 190 |
contr_tac 1, |
8149
941afb897532
added tacticals DETERM_UNTIL and DETERM_UNTIL_SOLVED
oheimb
parents:
7906
diff
changeset
|
191 |
DETERM_UNTIL_SOLVED (CHANGED(asm_simp_tac |
2033 | 192 |
(HOLCF_ss addsimps dis_apps) 1))]) cons; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
193 |
in dis_stricts @ dis_defins @ dis_apps end; |
1274 | 194 |
|
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
195 |
val mat_rews = let |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
196 |
val mat_stricts = map (fn (con,_) => pg axs_mat_def (mk_trp( |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
197 |
strict(%%:(mat_name con)))) [ |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
198 |
rtac when_strict 1]) cons; |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
199 |
val mat_apps = let fun one_mat c (con,args)= pg axs_mat_def |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
200 |
(lift_defined %: (nonlazy args, |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
201 |
(mk_trp((%%:(mat_name c))`(con_app con args) === |
16778 | 202 |
(if con=c |
203 |
then %%:returnN`(mk_ctuple (map %# args)) |
|
204 |
else %%:failN))))) |
|
205 |
[asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
206 |
in List.concat(map (fn (c,_) => map (one_mat c) cons) cons) end; |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
207 |
in mat_stricts @ mat_apps end; |
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
208 |
|
15570 | 209 |
val con_stricts = List.concat(map (fn (con,args) => map (fn vn => |
15742 | 210 |
pg con_appls |
2033 | 211 |
(mk_trp(con_app2 con (fn arg => if vname arg = vn |
212 |
then UU else %# arg) args === UU))[ |
|
213 |
asm_simp_tac (HOLCF_ss addsimps [abs_strict]) 1] |
|
214 |
) (nonlazy args)) cons); |
|
1274 | 215 |
val con_defins = map (fn (con,args) => pg [] |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
216 |
(lift_defined %: (nonlazy args, |
2033 | 217 |
mk_trp(defined(con_app con args)))) ([ |
2445
51993fea433f
removed Holcfb.thy and Holcfb.ML, moving classical3 to HOL.ML as classical2
oheimb
parents:
2276
diff
changeset
|
218 |
rtac rev_contrapos 1, |
2033 | 219 |
eres_inst_tac [("f",dis_name con)] cfun_arg_cong 1, |
220 |
asm_simp_tac (HOLCF_ss addsimps dis_rews) 1] )) cons; |
|
1274 | 221 |
val con_rews = con_stricts @ con_defins; |
222 |
||
17840
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
223 |
val con_compacts = |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
224 |
let |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
225 |
val rules = [compact_sinl, compact_sinr, compact_spair, compact_up, compact_ONE]; |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
226 |
fun one_compact (con,args) = pg con_appls |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
227 |
(lift (fn x => %%:compactN $ %:(vname x)) (args, mk_trp(%%:compactN $ (con_app con args)))) |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
228 |
[rtac (iso_locale RS iso_compact_abs) 1, REPEAT (resolve_tac rules 1 ORELSE atac 1)]; |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
229 |
in map one_compact cons end; |
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
230 |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
231 |
val sel_stricts = let fun one_sel sel = pg axs_sel_def (mk_trp(strict(%%:sel))) [ |
2033 | 232 |
simp_tac (HOLCF_ss addsimps when_rews) 1]; |
16394
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
233 |
in List.concat(map (fn (_,args) => List.mapPartial (fn arg => Option.map one_sel (sel_of arg)) args) cons) end; |
1274 | 234 |
val sel_apps = let fun one_sel c n sel = map (fn (con,args) => |
2033 | 235 |
let val nlas = nonlazy args; |
236 |
val vns = map vname args; |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
237 |
in pg axs_sel_def (lift_defined %: |
15570 | 238 |
(List.filter (fn v => con=c andalso (v<>List.nth(vns,n))) nlas, |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
239 |
mk_trp((%%:sel)`(con_app con args) === |
15570 | 240 |
(if con=c then %:(List.nth(vns,n)) else UU)))) |
2033 | 241 |
( (if con=c then [] |
242 |
else map(case_UU_tac(when_rews@con_stricts)1) nlas) |
|
15570 | 243 |
@(if con=c andalso ((List.nth(vns,n)) mem nlas) |
2033 | 244 |
then[case_UU_tac (when_rews @ con_stricts) 1 |
15570 | 245 |
(List.nth(vns,n))] else []) |
2033 | 246 |
@ [asm_simp_tac(HOLCF_ss addsimps when_rews)1])end) cons; |
15570 | 247 |
in List.concat(map (fn (c,args) => |
16842 | 248 |
List.concat(List.mapPartial I (mapn (fn n => fn arg => Option.map (one_sel c n) (sel_of arg)) 0 args))) cons) end; |
16394
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
249 |
val sel_defins = if length cons=1 then List.mapPartial (fn arg => Option.map (fn sel => pg [](defined(%:x_name)==> |
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
250 |
defined(%%:sel`%x_name)) [ |
4043 | 251 |
rtac casedist 1, |
2033 | 252 |
contr_tac 1, |
8149
941afb897532
added tacticals DETERM_UNTIL and DETERM_UNTIL_SOLVED
oheimb
parents:
7906
diff
changeset
|
253 |
DETERM_UNTIL_SOLVED (CHANGED(asm_simp_tac |
16394
495dbcd4f4c9
in domain declarations, selector names are now optional
huffman
parents:
16385
diff
changeset
|
254 |
(HOLCF_ss addsimps sel_apps) 1))])(sel_of arg)) |
2033 | 255 |
(filter_out is_lazy (snd(hd cons))) else []; |
1274 | 256 |
val sel_rews = sel_stricts @ sel_defins @ sel_apps; |
257 |
||
258 |
val distincts_le = let |
|
259 |
fun dist (con1, args1) (con2, args2) = pg [] |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
260 |
(lift_defined %: ((nonlazy args1), |
2033 | 261 |
(mk_trp (con_app con1 args1 ~<< con_app con2 args2))))([ |
2445
51993fea433f
removed Holcfb.thy and Holcfb.ML, moving classical3 to HOL.ML as classical2
oheimb
parents:
2276
diff
changeset
|
262 |
rtac rev_contrapos 1, |
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
263 |
eres_inst_tac[("f",dis_name con1)] monofun_cfun_arg 1] |
2033 | 264 |
@map(case_UU_tac (con_stricts @ dis_rews)1)(nonlazy args2) |
265 |
@[asm_simp_tac (HOLCF_ss addsimps dis_rews) 1]); |
|
1274 | 266 |
fun distinct (con1,args1) (con2,args2) = |
2267 | 267 |
let val arg1 = (con1, args1) |
268 |
val arg2 = (con2, |
|
269 |
ListPair.map (fn (arg,vn) => upd_vname (K vn) arg) |
|
270 |
(args2, variantlist(map vname args2,map vname args1))) |
|
2033 | 271 |
in [dist arg1 arg2, dist arg2 arg1] end; |
1274 | 272 |
fun distincts [] = [] |
273 |
| distincts (c::cs) = (map (distinct c) cs) :: distincts cs; |
|
274 |
in distincts cons end; |
|
15570 | 275 |
val dist_les = List.concat (List.concat distincts_le); |
4043 | 276 |
val dist_eqs = let |
1274 | 277 |
fun distinct (_,args1) ((_,args2),leqs) = let |
2033 | 278 |
val (le1,le2) = (hd leqs, hd(tl leqs)); |
279 |
val (eq1,eq2) = (le1 RS dist_eqI, le2 RS dist_eqI) in |
|
280 |
if nonlazy args1 = [] then [eq1, eq1 RS not_sym] else |
|
281 |
if nonlazy args2 = [] then [eq2, eq2 RS not_sym] else |
|
282 |
[eq1, eq2] end; |
|
1274 | 283 |
fun distincts [] = [] |
4062 | 284 |
| distincts ((c,leqs)::cs) = List.concat |
2267 | 285 |
(ListPair.map (distinct c) ((map #1 cs),leqs)) @ |
286 |
distincts cs; |
|
12037 | 287 |
in map standard (distincts (cons~~distincts_le)) end; |
1274 | 288 |
|
289 |
local |
|
16321
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
290 |
fun pgterm rel con args = |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
291 |
let |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
292 |
fun append s = upd_vname(fn v => v^s); |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
293 |
val (largs,rargs) = (args, map (append "'") args); |
17811 | 294 |
val concl = mk_trp (foldr1 mk_conj (ListPair.map rel (map %# largs, map %# rargs))); |
16321
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
295 |
val prem = mk_trp (rel(con_app con largs,con_app con rargs)); |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
296 |
val prop = prem ===> lift_defined %: (nonlazy largs, concl); |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
297 |
in pg con_appls prop end; |
15570 | 298 |
val cons' = List.filter (fn (_,args) => args<>[]) cons; |
1274 | 299 |
in |
16321
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
300 |
val inverts = |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
301 |
let |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
302 |
val abs_less = ax_abs_iso RS (allI RS injection_less) RS iffD1; |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
303 |
val tacs = [ |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
304 |
dtac abs_less 1, |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
305 |
REPEAT (dresolve_tac [sinl_less RS iffD1, sinr_less RS iffD1] 1), |
16385 | 306 |
asm_full_simp_tac (HOLCF_ss addsimps [spair_less]) 1]; |
16321
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
307 |
in map (fn (con,args) => pgterm (op <<) con args tacs) cons' end; |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
308 |
val injects = |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
309 |
let |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
310 |
val abs_eq = ax_abs_iso RS (allI RS injection_eq) RS iffD1; |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
311 |
val tacs = [ |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
312 |
dtac abs_eq 1, |
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
313 |
REPEAT (dresolve_tac [sinl_inject, sinr_inject] 1), |
16385 | 314 |
asm_full_simp_tac (HOLCF_ss addsimps [spair_eq]) 1]; |
16321
ef32a42f4079
faster proofs of inverts and injects lemmas, with fewer strictness hypotheses
huffman
parents:
16224
diff
changeset
|
315 |
in map (fn (con,args) => pgterm (op ===) con args tacs) cons' end; |
1274 | 316 |
end; |
317 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
318 |
(* ----- theorems concerning one induction step ----------------------------- *) |
1274 | 319 |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
320 |
val copy_strict = pg[ax_copy_def](mk_trp(strict(dc_copy`%"f"))) [ |
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
321 |
asm_simp_tac(HOLCF_ss addsimps [abs_strict, when_strict]) 1]; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
322 |
val copy_apps = map (fn (con,args) => pg [ax_copy_def] |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
323 |
(lift_defined %: (nonlazy_rec args, |
2033 | 324 |
mk_trp(dc_copy`%"f"`(con_app con args) === |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
325 |
(con_app2 con (app_rec_arg (cproj (%:"f") eqs)) args)))) |
2033 | 326 |
(map (case_UU_tac (abs_strict::when_strict::con_stricts) |
327 |
1 o vname) |
|
15570 | 328 |
(List.filter (fn a => not (is_rec a orelse is_lazy a)) args) |
2033 | 329 |
@[asm_simp_tac (HOLCF_ss addsimps when_apps) 1, |
15742 | 330 |
simp_tac (HOLCF_ss addsimps con_appls) 1]))cons; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
331 |
val copy_stricts = map (fn (con,args) => pg [] (mk_trp(dc_copy`UU` |
2033 | 332 |
(con_app con args) ===UU)) |
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
333 |
(let val rews = copy_strict::copy_apps@con_rews |
2033 | 334 |
in map (case_UU_tac rews 1) (nonlazy args) @ [ |
335 |
asm_simp_tac (HOLCF_ss addsimps rews) 1] end)) |
|
15570 | 336 |
(List.filter (fn (_,args)=>exists is_nonlazy_rec args) cons); |
1274 | 337 |
val copy_rews = copy_strict::copy_apps @ copy_stricts; |
4043 | 338 |
in thy |> Theory.add_path (Sign.base_name dname) |
8438 | 339 |
|> (#1 o (PureThy.add_thmss (map Thm.no_attributes [ |
4043 | 340 |
("iso_rews" , iso_rews ), |
341 |
("exhaust" , [exhaust] ), |
|
342 |
("casedist" , [casedist]), |
|
343 |
("when_rews", when_rews ), |
|
17840
11bcd77cfa22
domain package generates compactness lemmas for new constructors
huffman
parents:
17811
diff
changeset
|
344 |
("compacts", con_compacts), |
4043 | 345 |
("con_rews", con_rews), |
346 |
("sel_rews", sel_rews), |
|
347 |
("dis_rews", dis_rews), |
|
348 |
("dist_les", dist_les), |
|
349 |
("dist_eqs", dist_eqs), |
|
350 |
("inverts" , inverts ), |
|
351 |
("injects" , injects ), |
|
8438 | 352 |
("copy_rews", copy_rews)]))) |
16462 | 353 |
|> (#1 o PureThy.add_thmss [(("match_rews", mat_rews), [Simplifier.simp_add_global])]) |
12037 | 354 |
|> Theory.parent_path |> rpair (iso_rews @ when_rews @ con_rews @ sel_rews @ dis_rews @ |
355 |
dist_les @ dist_eqs @ copy_rews) |
|
1274 | 356 |
end; (* let *) |
357 |
||
4043 | 358 |
fun comp_theorems (comp_dnam, eqs: eq list) thy = |
1274 | 359 |
let |
4008 | 360 |
val dnames = map (fst o fst) eqs; |
361 |
val conss = map snd eqs; |
|
362 |
val comp_dname = Sign.full_name (sign_of thy) comp_dnam; |
|
363 |
||
12037 | 364 |
val d = writeln("Proving induction properties of domain "^comp_dname^" ..."); |
1274 | 365 |
val pg = pg' thy; |
366 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
367 |
(* ----- getting the composite axiom and definitions ------------------------ *) |
1274 | 368 |
|
16486 | 369 |
local fun ga s dn = get_thm thy (Name (dn ^ "." ^ s)) in |
4043 | 370 |
val axs_reach = map (ga "reach" ) dnames; |
371 |
val axs_take_def = map (ga "take_def" ) dnames; |
|
372 |
val axs_finite_def = map (ga "finite_def") dnames; |
|
373 |
val ax_copy2_def = ga "copy_def" comp_dnam; |
|
374 |
val ax_bisim_def = ga "bisim_def" comp_dnam; |
|
375 |
end; (* local *) |
|
376 |
||
16486 | 377 |
local fun gt s dn = get_thm thy (Name (dn ^ "." ^ s)); |
378 |
fun gts s dn = get_thms thy (Name (dn ^ "." ^ s)) in |
|
4043 | 379 |
val cases = map (gt "casedist" ) dnames; |
15570 | 380 |
val con_rews = List.concat (map (gts "con_rews" ) dnames); |
381 |
val copy_rews = List.concat (map (gts "copy_rews") dnames); |
|
1274 | 382 |
end; (* local *) |
383 |
||
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
384 |
fun dc_take dn = %%:(dn^"_take"); |
1274 | 385 |
val x_name = idx_name dnames "x"; |
386 |
val P_name = idx_name dnames "P"; |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
387 |
val n_eqs = length eqs; |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
388 |
|
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
389 |
(* ----- theorems concerning finite approximation and finite induction ------ *) |
1274 | 390 |
|
391 |
local |
|
16224
57094b83774e
Domain package generates match functions for new datatypes, for use with the fixrec package
huffman
parents:
15742
diff
changeset
|
392 |
val iterate_Cprod_ss = simpset_of Fix.thy; |
1274 | 393 |
val copy_con_rews = copy_rews @ con_rews; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
394 |
val copy_take_defs =(if n_eqs = 1 then [] else [ax_copy2_def]) @ axs_take_def; |
17811 | 395 |
val take_stricts=pg copy_take_defs(mk_trp(foldr1 mk_conj(map(fn((dn,args),_)=> |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
396 |
strict(dc_take dn $ %:"n")) eqs))) ([ |
13454 | 397 |
induct_tac "n" 1, |
4030 | 398 |
simp_tac iterate_Cprod_ss 1, |
2033 | 399 |
asm_simp_tac (iterate_Cprod_ss addsimps copy_rews)1]); |
1274 | 400 |
val take_stricts' = rewrite_rule copy_take_defs take_stricts; |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
401 |
val take_0s = mapn(fn n=> fn dn => pg axs_take_def(mk_trp((dc_take dn $ %%:"0") |
2033 | 402 |
`%x_name n === UU))[ |
403 |
simp_tac iterate_Cprod_ss 1]) 1 dnames; |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
404 |
val c_UU_tac = case_UU_tac (take_stricts'::copy_con_rews) 1; |
17811 | 405 |
val take_apps = pg copy_take_defs (mk_trp(foldr1 mk_conj |
15570 | 406 |
(List.concat(map (fn ((dn,_),cons) => map (fn (con,args) => Library.foldr mk_all |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
407 |
(map vname args,(dc_take dn $ (%%:"Suc" $ %:"n"))`(con_app con args) === |
15570 | 408 |
con_app2 con (app_rec_arg (fn n=>dc_take (List.nth(dnames,n))$ %:"n")) |
2033 | 409 |
args)) cons) eqs)))) ([ |
410 |
simp_tac iterate_Cprod_ss 1, |
|
13454 | 411 |
induct_tac "n" 1, |
2033 | 412 |
simp_tac(iterate_Cprod_ss addsimps copy_con_rews) 1, |
413 |
asm_full_simp_tac (HOLCF_ss addsimps |
|
15570 | 414 |
(List.filter (has_fewer_prems 1) copy_rews)) 1, |
2033 | 415 |
TRY(safe_tac HOL_cs)] @ |
15570 | 416 |
(List.concat(map (fn ((dn,_),cons) => map (fn (con,args) => |
2033 | 417 |
if nonlazy_rec args = [] then all_tac else |
418 |
EVERY(map c_UU_tac (nonlazy_rec args)) THEN |
|
419 |
asm_full_simp_tac (HOLCF_ss addsimps copy_rews)1 |
|
420 |
) cons) eqs))); |
|
1274 | 421 |
in |
12037 | 422 |
val take_rews = map standard (atomize take_stricts @ take_0s @ atomize take_apps); |
1274 | 423 |
end; (* local *) |
424 |
||
425 |
local |
|
15570 | 426 |
fun one_con p (con,args) = Library.foldr mk_All (map vname args, |
2033 | 427 |
lift_defined (bound_arg (map vname args)) (nonlazy args, |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
428 |
lift (fn arg => %:(P_name (1+rec_of arg)) $ bound_arg args arg) |
15570 | 429 |
(List.filter is_rec args,mk_trp(%:p $ con_app2 con (bound_arg args) args)))); |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
430 |
fun one_eq ((p,cons),concl) = (mk_trp(%:p $ UU) ===> |
15570 | 431 |
Library.foldr (op ===>) (map (one_con p) cons,concl)); |
432 |
fun ind_term concf = Library.foldr one_eq (mapn (fn n => fn x => (P_name n, x))1conss, |
|
17811 | 433 |
mk_trp(foldr1 mk_conj (mapn concf 1 dnames))); |
1274 | 434 |
val take_ss = HOL_ss addsimps take_rews; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
435 |
fun quant_tac i = EVERY(mapn(fn n=> fn _=> res_inst_tac[("x",x_name n)]spec i) |
2033 | 436 |
1 dnames); |
15570 | 437 |
fun ind_prems_tac prems = EVERY(List.concat (map (fn cons => ( |
2033 | 438 |
resolve_tac prems 1 :: |
15570 | 439 |
List.concat (map (fn (_,args) => |
2033 | 440 |
resolve_tac prems 1 :: |
441 |
map (K(atac 1)) (nonlazy args) @ |
|
15570 | 442 |
map (K(atac 1)) (List.filter is_rec args)) |
2033 | 443 |
cons))) conss)); |
1274 | 444 |
local |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
445 |
(* check whether every/exists constructor of the n-th part of the equation: |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
446 |
it has a possibly indirectly recursive argument that isn't/is possibly |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
447 |
indirectly lazy *) |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
448 |
fun rec_to quant nfn rfn ns lazy_rec (n,cons) = quant (exists (fn arg => |
2033 | 449 |
is_rec arg andalso not(rec_of arg mem ns) andalso |
450 |
((rec_of arg = n andalso nfn(lazy_rec orelse is_lazy arg)) orelse |
|
451 |
rec_of arg <> n andalso rec_to quant nfn rfn (rec_of arg::ns) |
|
15570 | 452 |
(lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg)))) |
2033 | 453 |
) o snd) cons; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
454 |
fun all_rec_to ns = rec_to forall not all_rec_to ns; |
4030 | 455 |
fun warn (n,cons) = if all_rec_to [] false (n,cons) then (warning |
15570 | 456 |
("domain "^List.nth(dnames,n)^" is empty!"); true) else false; |
16842 | 457 |
fun lazy_rec_to ns = rec_to exists I lazy_rec_to ns; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
458 |
|
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
459 |
in val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs; |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
460 |
val is_emptys = map warn n__eqs; |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
461 |
val is_finite = forall (not o lazy_rec_to [] false) n__eqs; |
1274 | 462 |
end; |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
463 |
in (* local *) |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
464 |
val finite_ind = pg'' thy [] (ind_term (fn n => fn dn => %:(P_name n)$ |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
465 |
(dc_take dn $ %:"n" `%(x_name n)))) (fn prems => [ |
2033 | 466 |
quant_tac 1, |
2445
51993fea433f
removed Holcfb.thy and Holcfb.ML, moving classical3 to HOL.ML as classical2
oheimb
parents:
2276
diff
changeset
|
467 |
simp_tac HOL_ss 1, |
13454 | 468 |
induct_tac "n" 1, |
2033 | 469 |
simp_tac (take_ss addsimps prems) 1, |
470 |
TRY(safe_tac HOL_cs)] |
|
15570 | 471 |
@ List.concat(map (fn (cons,cases) => [ |
2033 | 472 |
res_inst_tac [("x","x")] cases 1, |
473 |
asm_simp_tac (take_ss addsimps prems) 1] |
|
15570 | 474 |
@ List.concat(map (fn (con,args) => |
2033 | 475 |
asm_simp_tac take_ss 1 :: |
476 |
map (fn arg => |
|
477 |
case_UU_tac (prems@con_rews) 1 ( |
|
15570 | 478 |
List.nth(dnames,rec_of arg)^"_take n$"^vname arg)) |
479 |
(List.filter is_nonlazy_rec args) @ [ |
|
2033 | 480 |
resolve_tac prems 1] @ |
481 |
map (K (atac 1)) (nonlazy args) @ |
|
15570 | 482 |
map (K (etac spec 1)) (List.filter is_rec args)) |
2033 | 483 |
cons)) |
4043 | 484 |
(conss~~cases))); |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
485 |
|
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
486 |
val take_lemmas =mapn(fn n=> fn(dn,ax_reach)=> pg'' thy axs_take_def(mk_All("n", |
2033 | 487 |
mk_trp(dc_take dn $ Bound 0 `%(x_name n) === |
488 |
dc_take dn $ Bound 0 `%(x_name n^"'"))) |
|
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
489 |
===> mk_trp(%:(x_name n) === %:(x_name n^"'"))) (fn prems => [ |
2033 | 490 |
res_inst_tac[("t",x_name n )](ax_reach RS subst) 1, |
491 |
res_inst_tac[("t",x_name n^"'")](ax_reach RS subst) 1, |
|
492 |
stac fix_def2 1, |
|
493 |
REPEAT(CHANGED(rtac(contlub_cfun_arg RS ssubst)1 |
|
494 |
THEN chain_tac 1)), |
|
495 |
stac contlub_cfun_fun 1, |
|
496 |
stac contlub_cfun_fun 2, |
|
497 |
rtac lub_equal 3, |
|
498 |
chain_tac 1, |
|
499 |
rtac allI 1, |
|
500 |
resolve_tac prems 1])) 1 (dnames~~axs_reach); |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
501 |
|
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
502 |
(* ----- theorems concerning finiteness and induction ----------------------- *) |
1274 | 503 |
|
504 |
val (finites,ind) = if is_finite then |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
505 |
let |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
506 |
fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %:"x" === %:"x"); |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
507 |
val finite_lemmas1a = map (fn dn => pg [] (mk_trp(defined (%:"x")) ===> |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
508 |
mk_trp(mk_disj(mk_all("n",dc_take dn $ Bound 0 ` %:"x" === UU), |
2033 | 509 |
take_enough dn)) ===> mk_trp(take_enough dn)) [ |
510 |
etac disjE 1, |
|
511 |
etac notE 1, |
|
512 |
resolve_tac take_lemmas 1, |
|
513 |
asm_simp_tac take_ss 1, |
|
514 |
atac 1]) dnames; |
|
17811 | 515 |
val finite_lemma1b = pg [] (mk_trp (mk_all("n",foldr1 mk_conj (mapn |
2033 | 516 |
(fn n => fn ((dn,args),_) => mk_constrainall(x_name n,Type(dn,args), |
517 |
mk_disj(dc_take dn $ Bound 1 ` Bound 0 === UU, |
|
518 |
dc_take dn $ Bound 1 ` Bound 0 === Bound 0))) 1 eqs)))) ([ |
|
519 |
rtac allI 1, |
|
13454 | 520 |
induct_tac "n" 1, |
2033 | 521 |
simp_tac take_ss 1, |
522 |
TRY(safe_tac(empty_cs addSEs[conjE] addSIs[conjI]))] @ |
|
15570 | 523 |
List.concat(mapn (fn n => fn (cons,cases) => [ |
2033 | 524 |
simp_tac take_ss 1, |
525 |
rtac allI 1, |
|
526 |
res_inst_tac [("x",x_name n)] cases 1, |
|
527 |
asm_simp_tac take_ss 1] @ |
|
15570 | 528 |
List.concat(map (fn (con,args) => |
2033 | 529 |
asm_simp_tac take_ss 1 :: |
15570 | 530 |
List.concat(map (fn vn => [ |
2033 | 531 |
eres_inst_tac [("x",vn)] all_dupE 1, |
532 |
etac disjE 1, |
|
533 |
asm_simp_tac (HOL_ss addsimps con_rews) 1, |
|
534 |
asm_simp_tac take_ss 1]) |
|
535 |
(nonlazy_rec args))) |
|
536 |
cons)) |
|
4043 | 537 |
1 (conss~~cases))); |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
538 |
val finites = map (fn (dn,l1b) => pg axs_finite_def (mk_trp( |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
539 |
%%:(dn^"_finite") $ %:"x"))[ |
2033 | 540 |
case_UU_tac take_rews 1 "x", |
541 |
eresolve_tac finite_lemmas1a 1, |
|
542 |
step_tac HOL_cs 1, |
|
543 |
step_tac HOL_cs 1, |
|
544 |
cut_facts_tac [l1b] 1, |
|
545 |
fast_tac HOL_cs 1]) (dnames~~atomize finite_lemma1b); |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
546 |
in |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
547 |
(finites, |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
548 |
pg'' thy[](ind_term (fn n => fn dn => %:(P_name n) $ %:(x_name n)))(fn prems => |
2033 | 549 |
TRY(safe_tac HOL_cs) :: |
15570 | 550 |
List.concat (map (fn (finite,fin_ind) => [ |
2033 | 551 |
rtac(rewrite_rule axs_finite_def finite RS exE)1, |
552 |
etac subst 1, |
|
553 |
rtac fin_ind 1, |
|
554 |
ind_prems_tac prems]) |
|
555 |
(finites~~(atomize finite_ind)) )) |
|
1274 | 556 |
) end (* let *) else |
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
557 |
(mapn (fn n => fn dn => read_instantiate_sg (sign_of thy) |
2033 | 558 |
[("P",dn^"_finite "^x_name n)] excluded_middle) 1 dnames, |
16778 | 559 |
pg'' thy [] (Library.foldr (op ===>) (mapn (fn n => K(mk_trp(%%:admN $ %:(P_name n)))) |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
560 |
1 dnames, ind_term (fn n => fn dn => %:(P_name n) $ %:(x_name n)))) |
2033 | 561 |
(fn prems => map (fn ax_reach => rtac (ax_reach RS subst) 1) |
562 |
axs_reach @ [ |
|
563 |
quant_tac 1, |
|
564 |
rtac (adm_impl_admw RS wfix_ind) 1, |
|
4030 | 565 |
REPEAT_DETERM(rtac adm_all2 1), |
566 |
REPEAT_DETERM(TRY(rtac adm_conj 1) THEN |
|
567 |
rtac adm_subst 1 THEN |
|
2033 | 568 |
cont_tacR 1 THEN resolve_tac prems 1), |
569 |
strip_tac 1, |
|
570 |
rtac (rewrite_rule axs_take_def finite_ind) 1, |
|
571 |
ind_prems_tac prems]) |
|
4755 | 572 |
handle ERROR => (warning "Cannot prove infinite induction rule"; refl)) |
1274 | 573 |
end; (* local *) |
574 |
||
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
575 |
(* ----- theorem concerning coinduction ------------------------------------- *) |
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
576 |
|
1274 | 577 |
local |
578 |
val xs = mapn (fn n => K (x_name n)) 1 dnames; |
|
1637
b8a8ae2e5de1
Updated: 01-Mar-96 when functional strictified, copy_def based on when_def
oheimb
parents:
1512
diff
changeset
|
579 |
fun bnd_arg n i = Bound(2*(n_eqs - n)-i-1); |
1274 | 580 |
val take_ss = HOL_ss addsimps take_rews; |
4755 | 581 |
val sproj = prj (fn s => K("fst("^s^")")) (fn s => K("snd("^s^")")); |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
582 |
val coind_lemma=pg[ax_bisim_def](mk_trp(mk_imp(%%:(comp_dname^"_bisim") $ %:"R", |
15570 | 583 |
Library.foldr (fn (x,t)=> mk_all(x,mk_all(x^"'",t))) (xs, |
584 |
Library.foldr mk_imp (mapn (fn n => K(proj (%:"R") eqs n $ |
|
2033 | 585 |
bnd_arg n 0 $ bnd_arg n 1)) 0 dnames, |
17811 | 586 |
foldr1 mk_conj (mapn (fn n => fn dn => |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
587 |
(dc_take dn $ %:"n" `bnd_arg n 0 === |
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
588 |
(dc_take dn $ %:"n" `bnd_arg n 1)))0 dnames)))))) |
2033 | 589 |
([ rtac impI 1, |
13454 | 590 |
induct_tac "n" 1, |
2033 | 591 |
simp_tac take_ss 1, |
592 |
safe_tac HOL_cs] @ |
|
15570 | 593 |
List.concat(mapn (fn n => fn x => [ |
2033 | 594 |
rotate_tac (n+1) 1, |
595 |
etac all2E 1, |
|
4755 | 596 |
eres_inst_tac [("P1", sproj "R" eqs n^ |
2033 | 597 |
" "^x^" "^x^"'")](mp RS disjE) 1, |
598 |
TRY(safe_tac HOL_cs), |
|
599 |
REPEAT(CHANGED(asm_simp_tac take_ss 1))]) |
|
600 |
0 xs)); |
|
1274 | 601 |
in |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
602 |
val coind = pg [] (mk_trp(%%:(comp_dname^"_bisim") $ %:"R") ===> |
15570 | 603 |
Library.foldr (op ===>) (mapn (fn n => fn x => |
11531
d038246a62f2
Renamed functions % and %% to avoid clash with syntax for proof terms.
berghofe
parents:
10835
diff
changeset
|
604 |
mk_trp(proj (%:"R") eqs n $ %:x $ %:(x^"'"))) 0 xs, |
17811 | 605 |
mk_trp(foldr1 mk_conj (map (fn x => %:x === %:(x^"'")) xs)))) ([ |
2033 | 606 |
TRY(safe_tac HOL_cs)] @ |
15570 | 607 |
List.concat(map (fn take_lemma => [ |
2033 | 608 |
rtac take_lemma 1, |
609 |
cut_facts_tac [coind_lemma] 1, |
|
610 |
fast_tac HOL_cs 1]) |
|
611 |
take_lemmas)); |
|
1274 | 612 |
end; (* local *) |
613 |
||
4043 | 614 |
in thy |> Theory.add_path comp_dnam |
8438 | 615 |
|> (#1 o (PureThy.add_thmss (map Thm.no_attributes [ |
4043 | 616 |
("take_rews" , take_rews ), |
617 |
("take_lemmas", take_lemmas), |
|
618 |
("finites" , finites ), |
|
619 |
("finite_ind", [finite_ind]), |
|
620 |
("ind" , [ind ]), |
|
8438 | 621 |
("coind" , [coind ])]))) |
12037 | 622 |
|> Theory.parent_path |> rpair take_rews |
1274 | 623 |
end; (* let *) |
624 |
end; (* local *) |
|
625 |
end; (* struct *) |