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17
A formulaeastypes interpretation of subtractive logic
 Journal of Logic and Computation
, 2004
"... We present a formulaeastypes interpretation of Subtractive Logic (i.e. biintuitionistic logic). This presentation is twofold: we first define a very natural restriction of the λµcalculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural ..."
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Cited by 23 (1 self)
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We present a formulaeastypes interpretation of Subtractive Logic (i.e. biintuitionistic logic). This presentation is twofold: we first define a very natural restriction of the λµcalculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a computational standpoint, the resulting calculus provides a type system for firstclass coroutines (a restricted form of firstclass continuations). Keywords: CurryHoward isomorphism, Subtractive Logic, control operators, coroutines. 1
Computation with classical sequents
 MATHEMATICAL STRUCTURES OF COMPUTER SCIENCE
, 2008
"... X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X ..."
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Cited by 16 (16 self)
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X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X an expressive platform on which algebraic objects and many different (applicative) programming paradigms can be mapped. In this paper we will present the syntax and reduction rules for X and in order to demonstrate the expressive power of X, we will show how elaborate calculi can be embedded, like the λcalculus, Bloo and Rose’s calculus of explicit substitutions λx, Parigot’s λµ and Curien and Herbelin’s λµ ˜µ.
From X to π; representing the classical sequent calculus
"... Abstract. We study the πcalculus, enriched with pairing and nonblocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cutelimination) and assignable types are preserved. ..."
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Cited by 12 (12 self)
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Abstract. We study the πcalculus, enriched with pairing and nonblocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cutelimination) and assignable types are preserved. Since X enjoys the CurryHoward isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK have a representation in π.
Callbyvalue is dual to callbyname, reloaded
 In Rewriting Technics and Application, RTA’05, volume 3467 of LNCS
, 2005
"... Abstract. We consider the relation of the dual calculus of Wadler (2003) to the λµcalculus of Parigot (1992). We give translations from the λµcalculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, ..."
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Cited by 11 (0 self)
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Abstract. We consider the relation of the dual calculus of Wadler (2003) to the λµcalculus of Parigot (1992). We give translations from the λµcalculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, translating from λµ to dual and then ‘reloading ’ from dual back into λµ yields a term equal to the original term. Composing the translations with duality on the dual calculus yields an involutive notion of duality on the λµcalculus. A previous notion of duality on the λµcalculus has been suggested by Selinger (2001), but it is not involutive. Note This paper uses color to clarify the relation of types and terms, and of source and target calculi. If the URL below is not in blue please download the color version from
Relational parametricity and control
 Logical Methods in Computer Science
"... www.lmcsonline.org ..."
Semantics of linear continuationpassing in callbyname
 In Proc. Functional and Logic Programming, Springer Lecture Notes in Comput. Sci
, 2004
"... Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disj ..."
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Cited by 6 (4 self)
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Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed callbyname programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disjunctions ” from models of intuitionistic linear logic with sums. On the syntactic side, we give a simply typed callbyname λµcalculus in which the use of names (continuation variables) is restricted to be linear. Its semantic interpretation into a category of linear continuations then amounts to the callbyname continuationpassing style (CPS) transformation into a linear lambda calculus with sum types. We show that our calculus is sound for this CPS semantics, hence for models given by the categories of linear continuations.
Classical Callbyneed and duality
"... Abstract. We study callbyneed from the point of view of the duality between callbyname and callbyvalue. We develop sequentcalculus style versions of callbyneed both in the minimal and classical case. As a result, we obtain a natural extension of callbyneed with control operators. This lea ..."
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Cited by 4 (4 self)
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Abstract. We study callbyneed from the point of view of the duality between callbyname and callbyvalue. We develop sequentcalculus style versions of callbyneed both in the minimal and classical case. As a result, we obtain a natural extension of callbyneed with control operators. This leads us to introduce a callbyneed λµcalculus. Finally, by using the dualities principles of λµ˜µcalculus, we show the existence of a new callbyneed calculus, which is distinct from callbyname, callbyvalue and usual callbyneed theories. 1
Poetic effects
 Lingua
, 1992
"... Abstract. This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λcalculus, we use here λµcalculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λµcalculus, one corresponding to classic ..."
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Cited by 1 (1 self)
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Abstract. This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λcalculus, we use here λµcalculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λµcalculus, one corresponding to classical natural deduction, and the other to classical sequent calculus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.
Investigations into the duality of computation
"... The work presented here is an extension of a previous work realised jointly with PierreLouis Curien [CH00]. The current work focuses on the pure calculus of variables and binders that operates at the core of the duality between callbyname and callbyvalue evaluations. A CurryHowardde Bruijn co ..."
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Cited by 1 (0 self)
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The work presented here is an extension of a previous work realised jointly with PierreLouis Curien [CH00]. The current work focuses on the pure calculus of variables and binders that operates at the core of the duality between callbyname and callbyvalue evaluations. A CurryHowardde Bruijn correspondence is given that shed light on some aspects of Gentzen’s sequent calculus. This includes a sequentfree presentation of it.