|
1247
|
1 |
(* Title: GroupDefs.thy
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Markus Wenzel, TU Muenchen
|
|
|
4 |
*)
|
|
|
5 |
|
|
|
6 |
GroupDefs = MonoidGroupInsts + Prod + Fun +
|
|
|
7 |
|
|
|
8 |
|
|
|
9 |
(* bool *)
|
|
|
10 |
|
|
|
11 |
instance
|
|
2907
|
12 |
bool :: {times, inverse, one}
|
|
1247
|
13 |
|
|
|
14 |
defs
|
|
|
15 |
times_bool_def "x * y == (x ~= y)"
|
|
2907
|
16 |
inverse_bool_def "inverse x == (x::bool)"
|
|
1247
|
17 |
one_bool_def "1 == False"
|
|
|
18 |
|
|
|
19 |
|
|
|
20 |
(* cartesian products *)
|
|
|
21 |
|
|
|
22 |
instance
|
|
2907
|
23 |
"*" :: (term, term) {times, inverse, one}
|
|
1247
|
24 |
|
|
|
25 |
defs
|
|
|
26 |
times_prod_def "p * q == (fst p * fst q, snd p * snd q)"
|
|
2907
|
27 |
inverse_prod_def "inverse p == (inverse (fst p), inverse (snd p))"
|
|
1247
|
28 |
one_prod_def "1 == (1, 1)"
|
|
|
29 |
|
|
|
30 |
|
|
|
31 |
(* function spaces *)
|
|
|
32 |
|
|
|
33 |
instance
|
|
2907
|
34 |
fun :: (term, term) {times, inverse, one}
|
|
1247
|
35 |
|
|
|
36 |
defs
|
|
|
37 |
times_fun_def "f * g == (%x. f x * g x)"
|
|
2907
|
38 |
inverse_fun_def "inverse f == (%x. inverse (f x))"
|
|
1247
|
39 |
one_fun_def "1 == (%x. 1)"
|
|
|
40 |
|
|
|
41 |
end
|