src/CTT/arith.thy
 changeset 0 a5a9c433f639
equal inserted replaced
-1:000000000000 0:a5a9c433f639
`       `
`     1 (*  Title: 	CTT/arith`
`       `
`     2     ID:         \$Id\$`
`       `
`     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory`
`       `
`     4     Copyright   1991  University of Cambridge`
`       `
`     5 `
`       `
`     6 Arithmetic operators and their definitions`
`       `
`     7 `
`       `
`     8 Proves about elementary arithmetic: addition, multiplication, etc.`
`       `
`     9 Tests definitions and simplifier.`
`       `
`    10 *)`
`       `
`    11 `
`       `
`    12 Arith = CTT +`
`       `
`    13 `
`       `
`    14 consts "#+","-","|-|"	:: "[i,i]=>i"	(infixr 65)`
`       `
`    15        "#*",div,mod     :: "[i,i]=>i"	(infixr 70)`
`       `
`    16 `
`       `
`    17 rules`
`       `
`    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))"  `
`       `
`    20   absdiff_def "a|-|b == (a-b) #+ (b-a)"  `
`       `
`    21   mult_def    "a#*b == rec(a, 0, %u v. b #+ v)"  `
`       `
`    22   mod_def     "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y.succ(v)))"`
`       `
`    23   div_def     "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y.v))"`
`       `
`    24 end`