src/CTT/Arith.thy
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
child 1474 3f7d67927fe2
permissions -rw-r--r--
Initial revision
     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