Results 11  20
of
56
Relational parametricity and control
 Logical Methods in Computer Science
"... www.lmcsonline.org ..."
Duality between CallbyName Recursion and CallbyValue Iteration
 In Proc. Computer Science Logic, Springer Lecture Notes in Comput. Sci
, 2001
"... We investigate the duality between callbyname recursion and callbyvalue iteration on the calculi. The duality between callbyname and callbyvalue was first studied by Filinski, and Selinger has studied the categorytheoretic duality on the models of the callbyname calculus and the callby ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
We investigate the duality between callbyname recursion and callbyvalue iteration on the calculi. The duality between callbyname and callbyvalue was first studied by Filinski, and Selinger has studied the categorytheoretic duality on the models of the callbyname calculus and the callbyvalue one. We extend the callbyname calculus and the callbyvalue one with a fixedpoint operator and an iteration operator, respectively. We show that the dual translations constructed by Selinger can be expanded into our extended calculi, and we also discuss their implications to practical applications.
A Computational Interpretation of the λμcalculus
, 1998
"... This paper proposes a simple computational interpretation of Parigot's calculus. The calculus is an extension of the typed calculus which corresponds via the CurryHoward correspondence to classical logic. Whereas other work has given computational interpretations by translating the calculus int ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
This paper proposes a simple computational interpretation of Parigot's calculus. The calculus is an extension of the typed calculus which corresponds via the CurryHoward correspondence to classical logic. Whereas other work has given computational interpretations by translating the calculus into other calculi, I wish to propose here that the calculus itself has a simple computational interpretation: it is a typed  calculus which is able to save and restore the runtime environment. This interpretation is best given as a singlestep semantics which, in particular, leads to a relatively simple, but powerful, operational theory.
2005, ‘A ProofTheoretic Foundation of Abortive Continuations (Extended version
"... Abstract. We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce’s law without enforcing Ex Falso Quodlibet. We show that a “natural ” implementation of this logic is Parigot’s classical natural deduction. We then move on to the comp ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
Abstract. We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce’s law without enforcing Ex Falso Quodlibet. We show that a “natural ” implementation of this logic is Parigot’s classical natural deduction. We then move on to the computational side and emphasize that Parigot’s λµ corresponds to minimal classical logic. A continuation constant must be added to λµ to get full classical logic. The extended calculus is isomorphic to a syntactical restriction of Felleisen’s theory of control that offers a more expressive reduction semantics. This isomorphic calculus is in correspondence with a refined version of Prawitz’s natural deduction.
Combining algebraic effects with continuations
, 2007
"... We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor ext ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories.
Explicit Substitution Internal Languages for Autonomous and *Autonomous Categories
 In Proc. Category Theory and Computer Science (CTCS'99), Electron
, 1999
"... We introduce a family of explicit substitution type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that the simplytyped calculus with surjective pairing is the internal language for cartesian closed categories. We show tha ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We introduce a family of explicit substitution type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that the simplytyped calculus with surjective pairing is the internal language for cartesian closed categories. We show that the eight equality and three commutation congruence axioms of the autonomous type theory characterise autonomous categories exactly. The associated rewrite systems are all strongly normalising; modulo a simple notion of congruence, they are also confluent. As a corollary, we solve a Coherence Problem a la Lambek [12]: the equality of maps in any autonomous category freely generated from a discrete graph is decidable. 1 Introduction In this paper we introduce a family of type theories which can be regarded as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that the standard simplytyped calculus with surjective pairing is...
Exceptions, Continuations and MacroExpressiveness
 LNCS 2305
, 2002
"... This paper studies the dierences between exceptions and continuations via the problem of expressing exceptions using rstclass continuations in a functionalimperative language. The main result is that exceptions cannot be macroexpressed using rstclass continuations and references (contrary to ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
This paper studies the dierences between exceptions and continuations via the problem of expressing exceptions using rstclass continuations in a functionalimperative language. The main result is that exceptions cannot be macroexpressed using rstclass continuations and references (contrary to \folklore"). This is shown using two kinds of counterexample. The rst consists of two terms which are equivalent with respect to contexts containing continuations and references, but which can be distinguished using exceptions. It is shown, however, that there are no such terms which do not contain callcc. However, there is a 1 sentence of rstorder logic which is satised when interpreted in the domain of programs containing continuations and references but not satised in the domain of programs with exceptions and references.
Completeness and Partial Soundness Results for Intersection & Union Typing for λµ ˜µ
 Annals of Pure and Applied Logic
"... This paper studies intersection and union type assignment for the calculus λµ ˜µ [17], a proofterm syntax for Gentzen’s classical sequent calculus, with the aim of defining a typebased semantics, via setting up a system that is closed under conversion. We will start by investigating what the minima ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
This paper studies intersection and union type assignment for the calculus λµ ˜µ [17], a proofterm syntax for Gentzen’s classical sequent calculus, with the aim of defining a typebased semantics, via setting up a system that is closed under conversion. We will start by investigating what the minimal requirements are for a system for λµ ˜µ to be closed under subject expansion; this coincides with System M ∩ ∪ , the notion defined in [19]; however, we show that this system is not closed under subject reduction, so our goal cannot be achieved. We will then show that System M ∩ ∪ is also not closed under subjectexpansion, but can recover from this by presenting System M C as an extension of M ∩ ∪ (by adding typing rules) and showing that it satisfies subject expansion; it still lacks subject reduction. We show how to restrict M ∩ ∪ so that it satisfies subjectreduction as well by limiting the applicability to type assignment rules, but only when limiting reduction to (confluent) callbyname or callbyvalue reduction M ∩ ∪ ; in restricting the system, we sacrifice subject expansion. These results combined show that a sound and complete intersection and union type assignment system cannot be defined for λµ ˜µ with respect to full reduction.
Type Theories for Autonomous and *Autonomous Categories: I. Type Theories and Rewrite Systems  II. Internal Languages and Coherence Theorems
, 1998
"... We introduce a family of type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that simplytyped calculus (augmented by appropriate constructs for products and the terminal object) is the internal language for cartesian clos ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We introduce a family of type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that simplytyped calculus (augmented by appropriate constructs for products and the terminal object) is the internal language for cartesian closed categories. The rules are presented in the style of Gentzen's Sequent Calculus. A key feature is the systematic treatment of naturality conditions by explicitly representing the categorical composition, or cut in the type theory, by explicit substitution, and the introduction of new letconstructs, one for each of the three type constructors ?;\Omega and (, and a Parigotstyle ¯abstraction to give expression to the involutive negation. The commutation congruences of these theories are precisely those imposed by the naturality conditions. In particular the type theory for autonomous categories may be regarded as a term assignment system for the multiplicative (\Omega ; (;?;?)fragmen...