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(* Title: CTT/arith
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1991 University of Cambridge
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Arithmetic operators and their definitions
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Proves about elementary arithmetic: addition, multiplication, etc.
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Tests definitions and simplifier.
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*)
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Arith = CTT +
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consts "#+","-","|-|" :: "[i,i]=>i" (infixr 65)
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"#*",div,mod :: "[i,i]=>i" (infixr 70)
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rules
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add_def "a#+b == rec(a, b, %u v.succ(v))"
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diff_def "a-b == rec(b, a, %u v.rec(v, 0, %x y.x))"
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absdiff_def "a|-|b == (a-b) #+ (b-a)"
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mult_def "a#*b == rec(a, 0, %u v. b #+ v)"
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mod_def "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y.succ(v)))"
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div_def "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y.v))"
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end
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