# Pure type systems with judgemental equality Artikel i vetenskaplig tidskrift, 2006

In a typing system, there are two approaches that may be taken to the notion of equality. One can use some external relation of convertibility defined on the terms of the grammar, such as $\beta$-convertibility or $\beta \eta$-convertibility; or one can introduce a judgement form for equality into the rules of the typing system itself. For quite some time, it has been an open problem whether the two systems produced by these two choices are equivalent. This problem is essentially the problem of proving that the Subject Reduction property holds in the system with judgemental equality. In this paper, we shall prove that the equivalence holds for all functional Pure Type Systems (PTSs). The proof essentially consists of proving the Church-Rosser Theorem for a typed version of parallel one-step reduction. This method should generalise easily to many typing systems which satisfy the Uniqueness of Types property.

type theory

pure type systems

## Författare

Chalmers, Data- och informationsteknik, Datavetenskap

#### Journal of Functional Programming

0956-7968 (ISSN) 1469-7653 (eISSN)

Vol. 16 2 219-246

#### Ämneskategorier

Algebra och logik

Datavetenskap (datalogi)

#### Styrkeområden

Informations- och kommunikationsteknik

#### Fundament

Grundläggande vetenskaper

#### DOI

10.1017/S0956796805005770

2018-08-23