1 (* Title: CTT/Arith.thy
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Copyright 1991 University of Cambridge
7 header {* Arithmetic operators and their definitions *}
14 Proves about elementary arithmetic: addition, multiplication, etc.
15 Tests definitions and simplifier.
19 "#+" :: "[i,i]=>i" (infixr 65)
20 "-" :: "[i,i]=>i" (infixr 65)
21 "|-|" :: "[i,i]=>i" (infixr 65)
22 "#*" :: "[i,i]=>i" (infixr 70)
23 div :: "[i,i]=>i" (infixr 70)
24 mod :: "[i,i]=>i" (infixr 70)
27 "op #*" :: "[i, i] => i" (infixr "#\<times>" 70)
30 "op #*" :: "[i, i] => i" (infixr "#\<times>" 70)
33 add_def: "a#+b == rec(a, b, %u v. succ(v))"
34 diff_def: "a-b == rec(b, a, %u v. rec(v, 0, %x y. x))"
35 absdiff_def: "a|-|b == (a-b) #+ (b-a)"
36 mult_def: "a#*b == rec(a, 0, %u v. b #+ v)"
37 mod_def: "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y. succ(v)))"
38 div_def: "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y. v))"
40 ML {* use_legacy_bindings (the_context ()) *}