Coq is an interactive proof assistant for the development of mathematical theories and
formally certified software. It is based on a theory called the calculus of inductive …

Pattern matching has proved an extremely powerful and durable notion in functional
programming. This paper contributes a new programming notation for type theory which …

A fertile field of research in theoretical computer science investigates the representation of
general recursive functions in intensional type theories. Among the most successful …

One of the leading textbooks for formal methods is Software Foundations (SF), written by
Benjamin Pierce in collaboration with others, and based on Coq. After five years using SF in …

In this paper, I show that general recursive definitions can be represented in the free monad
which supports the 'effect'of making a recursive call, without saying how these calls should …

Constructive type theory is an expressive programming language in which both algorithms
and proofs can be represented. A limitation of constructive type theory as a programming …

The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his
work on categorical set theory to discuss the relationship between wellfounded induction …

In this paper I present a partial formalisation of a normaliser for type theory in Agda [Ulf
Norell. Agda 2, 2007. http://www. cs. chalmers. se/~ ulfn/]; extending previous work on big …

An indexed inductive definition (IID) is a simultaneous inductive definition of an indexed
family of sets. An inductive–recursive definition (IRD) is a simultaneous inductive definition …

The aim of this thesis is to provide an infrastructure for general recursive function definitions
in a proof assistant based on higher-order logic (HOL) that has no native support for …