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Summary: Algorithmic equality in Heyting Arithmetic modulo
Lisa Allali
May 2, 2007
Lisa Allali Algorithmic equality in Heyting Arithmetic modulo
Introduction
Proving 1+1=2
Axiomatic Heyting Arithmetic
Leibniz's axiom scheme + deduction
Heyting Arithmetic modulo - previous version
Leibniz's rewrite rule + few steps of deduction remaining
The new Heyting Arithmetic modulo
1 + 1 = 2 , no deduction
Lisa Allali Algorithmic equality in Heyting Arithmetic modulo
Deduction modulo
Deduction modulo = reasoning + computation
Natural deduction rules
A congruence
Some rules in deduction modulo :
Ax if A and A B
B
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