The Barendregt Cube with Definitions and Generalised Reduction

Abstract

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Parameters in Pure Type Systems

“…(z+z)), then a natural way of doing so is to use type systems with a definition mechanism. For example, in the definition systems of [8,32] Of course, this declaration can imitate the behaviour of the function double perfectly well. But it has the following disadvantages:…”

“…Pascal does not have a mechanism to construct types of the form A -; B. Note that this disadvantage is not faced by the account of [8).…”

“…-Due to the way in which double is defined in [8,32]' it is (again) a separate subterm in a PTS. But double itself is not a separate expression in Pascal; one can't write x := double in a program body.…”

“…This viewpoint suggests that allowing the iI-formation rule (SI,82,8,) also allows the parameter construction rule (81182)' Formally, one can work with systems in which we do allow the llformation rule, but do not allow the parameter construction rule. We prove, however, that if the II -construction rule (81,82,82) is allowed, a parameter construction involving rule (81,82) can be imitated by A-abstractions (Theorem 100).…”

On One-Pass CPS Transformations

“…In his PhD thesis [44,46], Sabry considered β lift , a generalized reduction that is most easily described using evaluation contexts [6]:…”