An Implementation of Set Theory with Pointed Graphs in Dedukti
Abstract
DEDUKTI is a type-checker for the λ Π-calculus modulo theory, a logical framework that allows the extension of conversion with user-defined rewrite rules. In this paper, we present the implementation of a version of Dowek-Miquel's intuitionistic set theory in DEDUKTI. To do so, we adapt this theory-based on the concept of pointed graphs-from Deduction modulo theory to λ Π-calculus modulo theory, and we formally write the proofs in DEDUKTI. In particular, this implementation requires the definition of a deep embedding of a certain class of formulas, as well as its interpretation in the theory.
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