2017 32nd Annual ACM/IEEE Symposium on Logic inâ€¦

2017

We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalizing the groupoid model of type theory. As an application, weâ€¦ (More)

A constructive version of Newton-Puiseux theorem for computing the Puiseux expansion of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers areâ€¦ (More)

In this paper, we show that Markovâ€™s principle is not derivable in dependent type theory with natural numbers and one universe. One way to prove this would be to remark that Markovâ€™s principle doesâ€¦ (More)

In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, andâ€¦ (More)

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advancedâ€¦ (More)

In this thesis we present two applications of sheaf semantics. The first is to give constructive proof of Newtonâ€“Puiseux theorem. The second is to show the independence of Markovâ€™s principle fromâ€¦ (More)

In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, andâ€¦ (More)