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CPS Translations and Applications: The Cube and Beyond
 Higher Order and Symbolic Computation
, 1996
"... Continuation passing style (CPS) translations of typed calculi have numerous applications. However, the range of these applications has been conned by the fact that CPS translations are known for nondependent type systems only, thus excluding wellknown systems like the calculus of constructions ( ..."
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Continuation passing style (CPS) translations of typed calculi have numerous applications. However, the range of these applications has been conned by the fact that CPS translations are known for nondependent type systems only, thus excluding wellknown systems like the calculus of constructions (CC) and the logical frameworks (LF). This paper presents techniques for CPS translating systems with dependent types, with an emphasis on pure typetheoretical applications.
The Relevance of ProofIrrelevance: A MetaTheoretical Study of Generalised Calculi of Constructions
"... . We propose a general technique, inspired from proofirrelevance, to prove strong normalisation and consistency for extensions of the Calculus of Constructions. 1 Introduction The Calculus of Constructions (CC) [12] is a powerful typed calculus which may be used both as a programming language an ..."
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. We propose a general technique, inspired from proofirrelevance, to prove strong normalisation and consistency for extensions of the Calculus of Constructions. 1 Introduction The Calculus of Constructions (CC) [12] is a powerful typed calculus which may be used both as a programming language and as a logical framework. However, CC is minimal in the sense that the generalised function space \Pi x : A: B is its only type constructor. The minimality of CC imposes strict limits to its applicability and has given rise to a spate of proposals to include new term/type constructors: algebraic types [3, 7], fixpoints [1], control operators [6] and inductive types [21] to mention only the examples considered in this papersome proposals are actually concerned with the more general setting of Pure Type Systems [4]. While most of these calculi, which we call Generalised Calculi of Constructions (GCCs), are known to enjoy metatheoretical properties similar to CC itself, there are no genera...