author | wenzelm |
Fri, 18 Aug 2017 20:47:47 +0200 | |
changeset 66453 | cc19f7ca2ed6 |
parent 62726 | 5b2a7caa855b |
permissions | -rw-r--r-- |
62696 | 1 |
(* Title: HOL/Corec_Examples/Tests/Misc_Poly.thy |
2 |
Author: Aymeric Bouzy, Ecole polytechnique |
|
3 |
Author: Jasmin Blanchette, Inria, LORIA, MPII |
|
4 |
Copyright 2015, 2016 |
|
5 |
||
6 |
Miscellaneous polymorphic examples. |
|
7 |
*) |
|
8 |
||
62726 | 9 |
section \<open>Miscellaneous Polymorphic Examples\<close> |
62696 | 10 |
|
11 |
theory Misc_Poly |
|
66453
cc19f7ca2ed6
session-qualified theory imports: isabelle imports -U -i -d '~~/src/Benchmarks' -a;
wenzelm
parents:
62726
diff
changeset
|
12 |
imports "HOL-Library.BNF_Corec" |
62696 | 13 |
begin |
14 |
||
15 |
codatatype ('a, 'b) T0 = |
|
16 |
C1 (lab: "'a * 'b") (tl11: "('a, 'b) T0") (tl12: "('a, 'b) T0") |
|
17 |
| C2 (lab: "'a * 'b") (tl2: "('a, 'b) T0") |
|
18 |
| C3 (tl3: "('a, 'b) T0 list") |
|
19 |
||
20 |
codatatype stream = S (hd: nat) (tl: stream) |
|
21 |
||
22 |
corec test0 where |
|
23 |
"test0 x y = (case (x, y) of |
|
24 |
(S a1 s1, S a2 s2) \<Rightarrow> S (a1 + a2) (test0 s1 s2))" |
|
25 |
||
26 |
friend_of_corec test0 where |
|
27 |
"test0 x y = (case (x, y) of |
|
28 |
(S a1 s1, S a2 s2) \<Rightarrow> S (a1 + a2) (test0 s1 s2))" |
|
29 |
sorry |
|
30 |
||
31 |
corec test01 where |
|
32 |
"test01 x y = C2 (fst (lab x), snd (lab y)) (test01 (tl2 x) (tl2 y))" |
|
33 |
||
34 |
friend_of_corec test01 :: "('a, 'b) T0 \<Rightarrow> ('a, 'b) T0 \<Rightarrow> ('a, 'b) T0" where |
|
35 |
"test01 x y = C2 (fst (lab x), snd (lab y)) (test01 (tl2 x) (tl2 y))" |
|
36 |
sorry |
|
37 |
||
38 |
corec test02 where |
|
39 |
"test02 x y = C2 (fst (lab x), snd (lab y)) (test01 (test02 x (tl2 y)) (test02 (tl2 x) y))" |
|
40 |
||
41 |
friend_of_corec test02 :: "('a, 'b) T0 \<Rightarrow> ('a, 'b) T0 \<Rightarrow> ('a, 'b) T0" where |
|
42 |
"test02 x y = C2 (fst (lab x), snd (lab y)) (test01 (test02 x (tl2 y)) (test02 (tl2 x) y))" |
|
43 |
sorry |
|
44 |
||
45 |
corec test03 where |
|
46 |
"test03 x = C2 (lab x) (C2 (lab x) (test02 x x))" |
|
47 |
||
48 |
friend_of_corec test03 where |
|
49 |
"test03 x = C2 (lab x) (C2 (lab x) (test02 (test03 (tl2 x)) (test03 (tl2 x))))" |
|
50 |
sorry |
|
51 |
||
52 |
corec test04 where |
|
53 |
"test04 x = (case x of C1 a t1 t2 \<Rightarrow> C1 a (test04 t1) (test04 t2) | C2 a t \<Rightarrow> C2 a (test04 t) | C3 l \<Rightarrow> C3 l)" |
|
54 |
||
55 |
friend_of_corec test04 where |
|
56 |
"test04 x = (case x of C1 a t1 t2 \<Rightarrow> C1 a (test04 t1) (test04 t2) | C2 a t \<Rightarrow> C2 a (test04 t) | C3 l \<Rightarrow> C3 l)" |
|
57 |
sorry |
|
58 |
||
59 |
corec test05 where |
|
60 |
"test05 x y = (case (x, y) of |
|
61 |
(C1 a t11 t12, C1 b t21 t22) \<Rightarrow> C1 (fst a, snd b) (test05 t11 t21) (test05 t12 t22) |
|
62 |
| (C1 a t11 _, C2 b t2) \<Rightarrow> C2 (fst a, snd b) (test05 t11 t2) |
|
63 |
| (C2 a t1, C1 b _ t22) \<Rightarrow> C2 (fst a, snd b) (test05 t1 t22) |
|
64 |
| (C2 a t1, C2 b t2) \<Rightarrow> C2 (fst a, snd b) (test05 t1 t2) |
|
65 |
| (_, _) \<Rightarrow> C3 [])" |
|
66 |
||
67 |
friend_of_corec test05 :: "('a, 'b) T0 \<Rightarrow> ('a, 'b) T0 \<Rightarrow> ('a, 'b) T0" where |
|
68 |
"test05 x y = (case (x, y) of |
|
69 |
(C1 a t11 t12, C1 b t21 t22) \<Rightarrow> C1 (fst a, snd b) (test05 t11 t21) (test05 t12 t22) |
|
70 |
| (C1 a t11 _, C2 b t2) \<Rightarrow> C2 (fst a, snd b) (test05 t11 t2) |
|
71 |
| (C2 a t1, C1 b _ t22) \<Rightarrow> C2 (fst a, snd b) (test05 t1 t22) |
|
72 |
| (C2 a t1, C2 b t2) \<Rightarrow> C2 (fst a, snd b) (test05 t1 t2) |
|
73 |
| (_, _) \<Rightarrow> C3 [])" |
|
74 |
sorry |
|
75 |
||
76 |
corec test06 where |
|
77 |
"test06 x = |
|
78 |
(if \<not> is_C1 x then |
|
79 |
let tail = tl2 x in |
|
80 |
C1 (lab x) (test06 tail) tail |
|
81 |
else |
|
82 |
C2 (lab x) (test06 (tl12 x)))" |
|
83 |
||
84 |
friend_of_corec test06 where |
|
85 |
"test06 x = |
|
86 |
(if \<not> is_C1 x then |
|
87 |
let tail = tl2 x in |
|
88 |
C1 (lab x) (test06 tail) tail |
|
89 |
else |
|
90 |
C2 (lab x) (test06 (tl12 x)))" |
|
91 |
sorry |
|
92 |
||
93 |
corec test07 where |
|
94 |
"test07 xs = C3 (map (\<lambda>x. test07 (tl3 x)) xs)" |
|
95 |
||
96 |
friend_of_corec test07 :: "('a, 'b) T0 list \<Rightarrow> ('a, 'b) T0" where |
|
97 |
"test07 xs = C3 (map (\<lambda>x. test07 (tl3 x)) xs)" |
|
98 |
sorry |
|
99 |
||
100 |
corec test08 where |
|
101 |
"test08 xs = (case xs of |
|
102 |
[] \<Rightarrow> C3 [] |
|
103 |
| T # r \<Rightarrow> C1 (lab T) (test08 r) T)" |
|
104 |
||
105 |
friend_of_corec test08 where |
|
106 |
"test08 xs = (case xs of |
|
107 |
[] \<Rightarrow> C3 [] |
|
108 |
| T # r \<Rightarrow> C1 (lab T) (test08 r) T)" |
|
109 |
sorry |
|
110 |
||
111 |
corec test09 where |
|
112 |
"test09 xs = (case xs of |
|
113 |
[] \<Rightarrow> C3 [] |
|
114 |
| (C1 n T1 T2) # r \<Rightarrow> C1 n (test09 (T1 # r)) (test09 (T2 # r)) |
|
115 |
| _ # r \<Rightarrow> C3 [test09 r])" |
|
116 |
||
117 |
friend_of_corec test09 where |
|
118 |
"test09 xs = (case xs of |
|
119 |
[] \<Rightarrow> C3 [] |
|
120 |
| (C1 n T1 T2) # r \<Rightarrow> C1 n (test09 (T1 # r)) (test09 (T2 # r)) |
|
121 |
| _ # r \<Rightarrow> C3 [test09 r])" |
|
122 |
sorry |
|
123 |
||
124 |
codatatype 'h tree = |
|
125 |
Node (node: 'h) (branches: "'h tree list") |
|
126 |
||
127 |
consts integerize_list :: "'a list \<Rightarrow> int" |
|
128 |
||
129 |
corec f10 where |
|
130 |
"f10 x y = Node |
|
131 |
(integerize_list (branches x) + integerize_list (branches y)) |
|
132 |
(map (\<lambda>(x, y). f10 x y) (zip (branches x) (branches y)))" |
|
133 |
||
134 |
friend_of_corec f10 :: "int tree \<Rightarrow> int tree \<Rightarrow> int tree" where |
|
135 |
"f10 x y = Node |
|
136 |
(integerize_list (branches x) + integerize_list (branches y)) |
|
137 |
(map (\<lambda>(x, y). f10 x y) (zip (branches x) (branches y)))" |
|
138 |
sorry |
|
139 |
||
140 |
codatatype llist = |
|
141 |
Nil | LCons llist |
|
142 |
||
143 |
consts friend :: "llist \<Rightarrow> llist" |
|
144 |
||
145 |
friend_of_corec friend where |
|
146 |
"friend x = Nil" |
|
147 |
sorry |
|
148 |
||
149 |
corec f11 where |
|
150 |
"f11 x = (case friend x of Nil \<Rightarrow> Nil | LCons y \<Rightarrow> LCons (f11 y))" |
|
151 |
||
152 |
corec f12 where |
|
153 |
"f12 t = Node (node t) (map f12 (branches t))" |
|
154 |
||
155 |
friend_of_corec f12 where |
|
156 |
"f12 t = Node (node t) (map f12 (branches t))" |
|
157 |
sorry |
|
158 |
||
159 |
corec f13 where |
|
160 |
"f13 n ts = Node n (map (%t. f13 (node t) (branches t)) ts)" |
|
161 |
||
162 |
friend_of_corec f13 where |
|
163 |
"f13 n ts = Node n (map (%t. f13 (node t) (branches t)) ts)" |
|
164 |
sorry |
|
165 |
||
166 |
corec f14 where |
|
167 |
"f14 t_opt = Node undefined |
|
168 |
(case map_option branches t_opt of |
|
169 |
None \<Rightarrow> [] |
|
170 |
| Some ts \<Rightarrow> map (f14 o Some) ts)" |
|
171 |
||
172 |
friend_of_corec f14 :: "'a tree option \<Rightarrow> 'a tree" where |
|
173 |
"f14 t_opt = Node undefined |
|
174 |
(case map_option branches t_opt of |
|
175 |
None \<Rightarrow> [] |
|
176 |
| Some ts \<Rightarrow> map (f14 o Some) ts)" |
|
177 |
sorry |
|
178 |
||
179 |
corec f15 where |
|
180 |
"f15 ts_opt = Node undefined |
|
181 |
(case map_option (map branches) ts_opt of |
|
182 |
None \<Rightarrow> [] |
|
183 |
| Some tss \<Rightarrow> map (f15 o Some) tss)" |
|
184 |
||
185 |
friend_of_corec f15 :: "'a tree list option \<Rightarrow> 'a tree" where |
|
186 |
"f15 ts_opt = Node undefined |
|
187 |
(case map_option (map branches) ts_opt of |
|
188 |
None \<Rightarrow> [] |
|
189 |
| Some tss \<Rightarrow> map (f15 o Some) tss)" |
|
190 |
sorry |
|
191 |
||
192 |
corec f16 where |
|
193 |
"f16 ts_opt = Node undefined |
|
194 |
(case ts_opt of |
|
195 |
None \<Rightarrow> [] |
|
196 |
| Some ts \<Rightarrow> map (f16 o Some o branches) ts)" |
|
197 |
||
198 |
friend_of_corec f16 :: "'a tree list option \<Rightarrow> 'a tree" where |
|
199 |
"f16 ts_opt = Node undefined |
|
200 |
(case ts_opt of |
|
201 |
None \<Rightarrow> [] |
|
202 |
| Some ts \<Rightarrow> map (f16 o Some o branches) ts)" |
|
203 |
sorry |
|
204 |
||
205 |
corec f18 :: "'a tree \<Rightarrow> 'a tree" where |
|
206 |
"f18 t = Node (node t) (map (f18 o f12) (branches t))" |
|
207 |
||
208 |
friend_of_corec f18 :: "'z tree \<Rightarrow> 'z tree" where |
|
209 |
"f18 t = Node (node t) (map (f18 o f12) (branches t))" |
|
210 |
sorry |
|
211 |
||
212 |
corec f19 where |
|
213 |
"f19 t = Node (node t) (map (%f. f [t]) (map f13 [undefined]))" |
|
214 |
||
215 |
friend_of_corec f19 where |
|
216 |
"f19 t = Node (node t) (map (%f. f [t]) (map f13 [undefined]))" |
|
217 |
sorry |
|
218 |
||
219 |
datatype ('a, 'b, 'c) h = H1 (h_a: 'a) (h_tail: "('a, 'b, 'c) h") | H2 (h_b: 'b) (h_c: 'c) (h_tail: "('a, 'b, 'c) h") | H3 |
|
220 |
||
221 |
term "map_h (map_option f12) (%n. n) f12" |
|
222 |
||
223 |
corec f20 where |
|
224 |
"f20 x y = Node (node y) (case (map_h (map_option f12) (%n. n) f12 x) of |
|
225 |
H1 None r \<Rightarrow> (f20 r y) # (branches y) |
|
226 |
| H1 (Some t) r \<Rightarrow> (f20 r t) # (branches y) |
|
227 |
| H2 n t r \<Rightarrow> (f20 r (Node n [])) # (branches y) |
|
228 |
| H3 \<Rightarrow> branches y)" |
|
229 |
||
230 |
friend_of_corec f20 :: "('a tree option, 'a, 'a tree) h \<Rightarrow> 'a tree \<Rightarrow> 'a tree" where |
|
231 |
"f20 x y = Node (node y) (case (map_h (map_option f12) (%n. n) f12 x) of |
|
232 |
H1 None r \<Rightarrow> (f20 r y) # (branches y) |
|
233 |
| H1 (Some t) r \<Rightarrow> (f20 r t) # (branches y) |
|
234 |
| H2 n t r \<Rightarrow> (f20 r (Node n [])) # (branches y) |
|
235 |
| H3 \<Rightarrow> branches y)" |
|
236 |
sorry |
|
237 |
||
238 |
corec f21 where |
|
239 |
"f21 x xh = |
|
240 |
Node (node x) (case xh of |
|
241 |
H1 (Some a) yh \<Rightarrow> (f21 x (map_h (map_option (f20 yh)) id id yh)) # (branches a) |
|
242 |
| H1 None yh \<Rightarrow> [f21 x yh] |
|
243 |
| H2 b c yh \<Rightarrow> (f21 c (map_h id (%n. n + b) id yh)) # (branches x) |
|
244 |
| H3 \<Rightarrow> branches x)" |
|
245 |
||
246 |
friend_of_corec f21 where |
|
247 |
"f21 x xh = |
|
248 |
Node (node x) (case xh of |
|
249 |
H1 (Some a) yh \<Rightarrow> (f21 x (map_h (map_option (f20 yh)) (%t. t) (%t. t) yh)) # (branches a) |
|
250 |
| H1 None yh \<Rightarrow> [f21 x yh] |
|
251 |
| H2 b c yh \<Rightarrow> (f21 c (map_h (%t. t) (%n. n + b) (%t. t) yh)) # (branches x) |
|
252 |
| H3 \<Rightarrow> branches x)" |
|
253 |
sorry |
|
254 |
||
255 |
corec f22 :: "('a \<Rightarrow> 'h tree) \<Rightarrow> 'a list \<Rightarrow> 'h tree" where |
|
256 |
"f22 f x = Node undefined (map f x)" |
|
257 |
||
258 |
friend_of_corec f22 :: "('h \<Rightarrow> 'h tree) \<Rightarrow> 'h list \<Rightarrow> 'h tree" where |
|
259 |
"f22 f x = Node undefined (map f x)" |
|
260 |
sorry |
|
261 |
||
262 |
corec f23 where |
|
62698 | 263 |
"f23 xh = Node undefined |
62696 | 264 |
(if is_H1 xh then |
265 |
(f23 (h_tail xh)) # (branches (h_a xh)) |
|
266 |
else if is_H1 xh then |
|
267 |
(f23 (h_tail xh)) # (h_c xh) # (branches (h_b xh)) |
|
268 |
else |
|
269 |
[])" |
|
270 |
||
271 |
friend_of_corec f23 where |
|
62698 | 272 |
"f23 xh = Node undefined |
62696 | 273 |
(if is_H1 xh then |
274 |
(f23 (h_tail xh)) # (branches (h_a xh)) |
|
275 |
else if is_H1 xh then |
|
276 |
(f23 (h_tail xh)) # (h_c xh) # (branches (h_b xh)) |
|
277 |
else |
|
278 |
[])" |
|
279 |
sorry |
|
280 |
||
281 |
corec f24 where |
|
62698 | 282 |
"f24 xh = |
62696 | 283 |
(if is_H1 xh then |
284 |
Node 0 ((f24 (h_tail xh)) # (h_a xh 0)) |
|
285 |
else if is_H2 xh then |
|
286 |
Node (h_b xh) ((f24 (h_tail xh)) # (h_c xh 0)) |
|
287 |
else |
|
288 |
Node 0 [])" |
|
289 |
||
290 |
friend_of_corec f24 :: "(('b :: {zero}) \<Rightarrow> 'b tree list, 'b, 'b \<Rightarrow> 'b tree list) h \<Rightarrow> 'b tree" where |
|
62698 | 291 |
"f24 xh = |
62696 | 292 |
(if is_H1 xh then |
293 |
Node 0 ((f24 (h_tail xh)) # (h_a xh 0)) |
|
294 |
else if is_H2 xh then |
|
295 |
Node (h_b xh) ((f24 (h_tail xh)) # (h_c xh 0)) |
|
296 |
else |
|
297 |
Node 0 [])" |
|
298 |
sorry |
|
299 |
||
300 |
codatatype ('a, 'b, 'c) s = |
|
301 |
S (s1: 'a) (s2: 'b) (s3: 'c) (s4: "('a, 'b, 'c) s") |
|
302 |
||
303 |
corec (friend) ga :: "('a, 'b, nat) s \<Rightarrow> _" where |
|
304 |
"ga s = S (s1 s) (s2 s) (s3 s) (s4 s)" |
|
305 |
||
306 |
corec (friend) gb :: "('a, nat, 'b) s \<Rightarrow> _" where |
|
307 |
"gb s = S (s1 s) (s2 s) (s3 s) (s4 s)" |
|
308 |
||
309 |
consts foo :: "('b \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'a" |
|
310 |
||
311 |
corecursive (friend) gc :: "(nat, 'a, 'b) s \<Rightarrow> _" where |
|
312 |
"gc s = S (s1 s) (s2 s) (s3 s) (foo (undefined :: 'a \<Rightarrow> 'a) s)" |
|
313 |
sorry |
|
314 |
||
315 |
end |