1 (* Title: CTT/arith |
1 (* Title: CTT/arith |
2 ID: $Id$ |
2 ID: $Id$ |
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
4 Copyright 1991 University of Cambridge |
4 Copyright 1991 University of Cambridge |
5 |
5 |
6 Arithmetic operators and their definitions |
6 Arithmetic operators and their definitions |
7 |
7 |
8 Proves about elementary arithmetic: addition, multiplication, etc. |
8 Proves about elementary arithmetic: addition, multiplication, etc. |
9 Tests definitions and simplifier. |
9 Tests definitions and simplifier. |
10 *) |
10 *) |
11 |
11 |
12 Arith = CTT + |
12 Arith = CTT + |
13 |
13 |
14 consts "#+","-","|-|" :: "[i,i]=>i" (infixr 65) |
14 consts "#+","-","|-|" :: "[i,i]=>i" (infixr 65) |
15 "#*",div,mod :: "[i,i]=>i" (infixr 70) |
15 "#*",div,mod :: "[i,i]=>i" (infixr 70) |
16 |
16 |
17 rules |
17 rules |
18 add_def "a#+b == rec(a, b, %u v.succ(v))" |
18 add_def "a#+b == rec(a, b, %u v.succ(v))" |
19 diff_def "a-b == rec(b, a, %u v.rec(v, 0, %x y.x))" |
19 diff_def "a-b == rec(b, a, %u v.rec(v, 0, %x y.x))" |
20 absdiff_def "a|-|b == (a-b) #+ (b-a)" |
20 absdiff_def "a|-|b == (a-b) #+ (b-a)" |