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Computational types from a logical perspective
 Journal of Functional Programming
, 1998
"... Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus ..."
Abstract

Cited by 54 (6 self)
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Moggi’s computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many different notions of computation have the categorical structure of a strong monad on a cartesian closed category. In this paper we show that the computational lambda calculus also arises naturally as the term calculus corresponding (by the CurryHoward correspondence) to a novel intuitionistic modal propositional logic. We give natural deduction, sequent calculus and Hilbertstyle presentations of this logic and prove strong normalisation and confluence results. 1
Leftmost outsidein narrowing calculi
 Journal of Functional Programming
, 1997
"... We present narrowing calculi that are computation models of functionallogic programming languages. The narrowing calculi are based on the notion of the leftmost outsidein reduction of Huet and Lévy. We note the correspondence between the narrowing and reduction derivations, and define the leftmost ..."
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Cited by 14 (3 self)
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We present narrowing calculi that are computation models of functionallogic programming languages. The narrowing calculi are based on the notion of the leftmost outsidein reduction of Huet and Lévy. We note the correspondence between the narrowing and reduction derivations, and define the leftmost outsidein narrowing derivation. We then give a narrowing calculus OINC that generates the leftmost outsidein narrowing derivations. It consists of several inference rules that perform the leftmost outsidein narrowing. We prove the completeness of OINC using an ordering defined over a narrowing derivation space. In order to use the calculus OINC as a model of computation of functionallogic programming we extend OINC to incorporate strict equality. The extension results in a new narrowing calculus sOINC. We show also that sOINC enjoys the same completeness property as OINC. Key Words narrowing, functionallogic programming, standard reduction derivation, leftmostoutsidein narrowing derivation, narrowing calculus, completeness 1