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3 Fundamenta Informaticae

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Infinitary Axiomatization of the Equational Theory of Context-Free Languages

Grathwohl N. B. B., Henglein F., Kozen D.

Fundamenta Informaticae

2017

Vol. 150, nr 3/4

241--257

We give a natural complete infinitary axiomatization of the equational theory of the context-free languages, answering a question of Leiß (1992).

CoCaml: Functional Programming with Regular Coinductive Types

Jeannin J.-B., Kozen D., Silva A.

Fundamenta Informaticae

2017

Vol. 150, nr 3/4

347--377

Functional languages offer a high level of abstraction, which results in programs that are elegant and easy to understand. Central to the development of functional programming are inductive and coinductive types and associated programming constructs, such as pattern-matching. Whereas inductive types have a long tradition and are well supported in most languages, coinductive types are subject of more recent research and are less mainstream. We present CoCaml, a functional programming language extending OCaml, which allows us to define recursive functions on regular coinductive datatypes. These functions are defined like usual recursive functions, but parameterized by an equation solver. We present a full implementation of all the constructs and solvers and show how these can be used in a variety of examples, including operations on infinite lists, infinitary γ-terms, and p-adic numbers.

Church–Rosser Made Easy

Kozen D.

Fundamenta Informaticae

2010

Vol. 103, nr 1-4

129-136

The Church–Rosser theorem states that the λ-calculus is confluent under β-reductions. The standard proof of this result is due to Tait and Martin-Löf. In this note, we present an alternative proof based on the notion of acceptable orderings. The technique is easily modified to give confluence of the βη-calculus.