Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Information and Computation - Semantics of Data Types
Strictness analysis via abstract interpretation for recursively defined types
Information and Computation
Handbook of logic in computer science (vol. 2): background: computational structures
Handbook of logic in computer science (vol. 2): background: computational structures
Handbook of logic in computer science (vol. 2)
The Barendregt cube with definitions and generalised reduction
Information and Computation
The Definition of Standard ML
Pure Type Systems with Definitions
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
Parameters in Pure Type Systems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
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The Barendregt Cube (introduced in [3]) is a framework in which eight important typed λ-calculi are described in a uniform way. Moreover, many type systems (like Automath [18], LF [11], ML [17], and system F [10]) can be related to one of these eight systems. Furthermore, via the propositions-as-types principle, many logical systems can be described in the Barendregt Cube as well (see for instance [9]). However, there are important systems (including AUTOMATH, LF and ML) that cannot be adequately placed in the Barendregt Cube or in the larger framework of Pure Type Systems. In this paper we add a parameter mechanism to the systems of the Barendregt Cube. In doing so, we obtain a refinement of the Cube. In this refined Barendregt Cube, systems like AUTOMATH, LF, and ML can be described more naturally and accurately than in the original Cube.