src/ZF/arith.thy
 author paulson Fri, 16 Feb 1996 18:00:47 +0100 changeset 1512 ce37c64244c0 parent 124 858ab9a9b047 permissions -rw-r--r--
Elimination of fully-functorial style. Type tactic changed to a type abbrevation (from a datatype). Constructor tactic and function apply deleted.
```
(*  Title: 	ZF/arith.thy
ID:         \$Id\$
Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory

Arithmetic operators and their definitions
*)

Arith = Epsilon + "simpdata" +
consts
rec  :: "[i, i, [i,i]=>i]=>i"
"#*" :: "[i,i]=>i"      		(infixl 70)
div  :: "[i,i]=>i"      		(infixl 70)
mod  :: "[i,i]=>i"      		(infixl 70)
"#+" :: "[i,i]=>i"      		(infixl 65)
"#-" :: "[i,i]=>i"      		(infixl 65)

rules
rec_def  "rec(k,a,b) ==  transrec(k, %n f. nat_case(a, %m. b(m, f`m), n))"

add_def  "m#+n == rec(m, n, %u v.succ(v))"
diff_def "m#-n == rec(n, m, %u v. rec(v, 0, %x y.x))"
mult_def "m#*n == rec(m, 0, %u v. n #+ v)"
mod_def  "m mod n == transrec(m, %j f. if(j<n, j, f`(j#-n)))"
div_def  "m div n == transrec(m, %j f. if(j<n, 0, succ(f`(j#-n))))"
end
```