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Setoids in Type Theory
, 2000
"... Formalising mathematics in dependent type theory often requires to use setoids, i.e. types with an explicit equality relation, as a representation of sets. This paper surveys some possible denitions of setoids and assesses their suitability as a basis for developing mathematics. In particular, we ..."
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Cited by 30 (4 self)
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Formalising mathematics in dependent type theory often requires to use setoids, i.e. types with an explicit equality relation, as a representation of sets. This paper surveys some possible denitions of setoids and assesses their suitability as a basis for developing mathematics. In particular, we argue that a commonly advocated approach to partial setoids is unsuitable, and more generally that total setoids seem better suited for formalising mathematics. 1
A TwoLevel Approach towards Lean ProofChecking
, 1996
"... We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle t ..."
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Cited by 16 (4 self)
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We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle types. The potential of our twolevel approach is illustrated by some examples developed in Lego.