src/CTT/Arith.thy
author paulson
Mon Dec 07 18:26:25 1998 +0100 (1998-12-07)
changeset 6019 0e55c2fb2ebb
parent 3837 d7f033c74b38
child 10467 e6e7205e9e91
permissions -rw-r--r--
tidying
     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