Equations is a plugin for the Coq proof assistant which provides a notation for defining
programs by dependent pattern-matching and structural or well-founded recursion. It …

Markov's principle (MP) is an axiom in some varieties of constructive mathematics, stating
that Σ01 propositions (ie existential quantification over a decidable predicate on N) are …

We give a formalised and machine-checked account of computability theory in the Calculus
of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof …

Dependently typed programming languages and proof assistants such as Agda and Coq
rely on computation to automatically simplify expressions during type checking. To …

We study various formulations of the completeness of first-order logic phrased in
constructive type theory and mechanised in the Coq proof assistant. Specifically, we …

There is a critical tension between substitution, dependent elimination and effects in type
theory. In this paper, we crystallize this tension in the form of a no-go theorem that …

We propose the first framework for defining relational program logics for arbitrary monadic
effects. The framework is embedded within a relational dependent type theory and is highly …

The internal Church thesis (CT) is a logical principle stating that one can associate to any
function f: N→ N a concrete code, in some Turing-complete language, that computes f. While …