src/CTT/Arith.thy
author webertj
Sun, 14 Nov 2004 01:40:27 +0100
changeset 15283 f21466450330
parent 12110 f8b4b11cd79d
child 17441 5b5feca0344a
permissions -rw-r--r--
DOCTYPE declaration added

(*  Title:      CTT/arith
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1991  University of Cambridge

Arithmetic operators and their definitions

Proves about elementary arithmetic: addition, multiplication, etc.
Tests definitions and simplifier.
*)

Arith = CTT +

consts "#+","-","|-|"   :: "[i,i]=>i"   (infixr 65)
       "#*",div,mod     :: "[i,i]=>i"   (infixr 70)

syntax (xsymbols)
  "op #*"      :: [i, i] => i   (infixr "#\\<times>" 70)

syntax (HTML output)
  "op #*"      :: [i, i] => i   (infixr "#\\<times>" 70)

rules
  add_def     "a#+b == rec(a, b, %u v. succ(v))"  
  diff_def    "a-b == rec(b, a, %u v. rec(v, 0, %x y. x))"  
  absdiff_def "a|-|b == (a-b) #+ (b-a)"  
  mult_def    "a#*b == rec(a, 0, %u v. b #+ v)"  
  mod_def     "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y. succ(v)))"
  div_def     "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y. v))"
end