This paper presents generic derivations of induction for impredicatively typed lambda-encoded datatypes, in the Cedille type theory. Cedille is a pure type theory extending the Curry-style Calculusâ€¦ (More)

It is common to model inductive datatypes as least fixed points of functors. We show that within the Cedille type theory we can relax functoriality constraints and generically derive an inductionâ€¦ (More)

Dependently typed languages are well known for having a problem with code reuse. Traditional non-indexed algebraic datatypes (e.g. lists) appear alongside a plethora of indexed variations (e.g.â€¦ (More)

We report a work on certified parsing for context-free grammars. In our development we implement the Cockeâ€“Youngerâ€“Kasami parsing algorithm and prove it correct using the Agda dependently typedâ€¦ (More)

Every context-free grammar can be transformed into an equivalent one in the Chomsky normal form by a sequence of four transformations. In this work on formalization of language theory, we proveâ€¦ (More)

Definitions of many mathematical structures used in computer science are parametrized by finite sets. To work with such structures in proof assistants, we need to be able to explain what a finite setâ€¦ (More)

In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programmingâ€¦ (More)

Many applications have to maintain evolving data sources as well as views on these sources. If sources change, the corresponding views have to be adapted. Complete recomputation of views is typicallyâ€¦ (More)

We report on a certified parser generator for regular languages using the Agda programming language. Specifically, we programmed a transformation of regular expressions into a Boolean-matrix basedâ€¦ (More)