Results 1  10
of
99
Notions of Computation and Monads
, 1991
"... The i.calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with Iterms. However, if one goes further and uses bnconversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with ..."
Abstract

Cited by 884 (16 self)
 Add to MetaCart
The i.calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with Iterms. However, if one goes further and uses bnconversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from calues to values) that may jeopardise the applicability of theoretical results, In this paper we introduce calculi. based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
Computational Interpretations of Linear Logic
 Theoretical Computer Science
, 1993
"... We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluati ..."
Abstract

Cited by 323 (3 self)
 Add to MetaCart
(Show Context)
We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cutelimination.
The Logic of Bunched Implications
 BULLETIN OF SYMBOLIC LOGIC
, 1999
"... We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication; it can be viewed as a merging of intuition ..."
Abstract

Cited by 220 (42 self)
 Add to MetaCart
We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers # new and # new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predic...
Anytime, anywhere: modal logics for mobile ambients
 In POPL ’00: Proceedings of the 27th ACM SIGPLANSIGACT symposium on Principles of programming languages
, 2000
"... The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a m ..."
Abstract

Cited by 187 (13 self)
 Add to MetaCart
(Show Context)
The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1
A Linearly Typed Assembly Language
 In Workshop on Types in Compilation
"... Today's typesafe lowlevel languages rely on garbage collection to recycle heapallocated objects safely. We present LTAL, a safe, lowlevel, yet simple language that "stands on its own": it guarantees safe execution within a fixed memory space, without relying on external runtime s ..."
Abstract

Cited by 160 (39 self)
 Add to MetaCart
(Show Context)
Today's typesafe lowlevel languages rely on garbage collection to recycle heapallocated objects safely. We present LTAL, a safe, lowlevel, yet simple language that "stands on its own": it guarantees safe execution within a fixed memory space, without relying on external runtime support. We demonstrate the expressiveness of LTAL by giving a typepreserving compiler for the functional core of ML. But this independence comes at a steep price: LTAL's type system imposes a draconian discipline of linearity that ensures that memory can be reused safely, but prohibits any useful kind of sharing. We present the results of experiments with a prototype LTAL system that show just how high the price of linearity can be.
Linear Types Can Change the World!
 PROGRAMMING CONCEPTS AND METHODS
, 1990
"... The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no refere ..."
Abstract

Cited by 148 (9 self)
 Add to MetaCart
(Show Context)
The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no reference counting or garbage collection, and safely admit destructive array update. Linear types extend Schmidt's notion of single threading; provide an alternative to Hudak and Bloss' update analysis; and offer a practical complement to Lafont and Holmström's elegant linear languages.
Alias Types for Recursive Data Structures
, 2000
"... Linear type systems permit programmers to deallocate or explicitly recycle memory, but they are severly restricted by the fact that they admit no aliasing. This paper describes a pseudolinear type system that allows a degree of aliasing and memory reuse as well as the ability to define complex recu ..."
Abstract

Cited by 147 (14 self)
 Add to MetaCart
(Show Context)
Linear type systems permit programmers to deallocate or explicitly recycle memory, but they are severly restricted by the fact that they admit no aliasing. This paper describes a pseudolinear type system that allows a degree of aliasing and memory reuse as well as the ability to define complex recursive data structures. Our type system can encode conventional linear data structures such as linear lists and trees as well as more sophisticated data structures including cyclic and doublylinked lists and trees. In the latter cases, our type system is expressive enough to represent pointer aliasing and yet safely permit destructive operations such as object deallocation. We demonstrate the flexibility of our type system by encoding two common compiler optimizations: destinationpassing style and DeutschSchorrWaite or "linkreversal" traversal algorithms.
How to Declare an Imperative
, 1995
"... How can we integrate interaction into a purely declarative language? This tutorial describes a solution to this problem based on a monad. The solution has been implemented in the functional language Haskell and the declarative language Escher. Comparisons are given to other approaches to interaction ..."
Abstract

Cited by 111 (3 self)
 Add to MetaCart
How can we integrate interaction into a purely declarative language? This tutorial describes a solution to this problem based on a monad. The solution has been implemented in the functional language Haskell and the declarative language Escher. Comparisons are given to other approaches to interaction based on synchronous streams, continuations, linear logic, and side effects.
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
Abstract

Cited by 111 (19 self)
 Add to MetaCart
Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
A Type System for Bounded Space and Functional inPlace Update
, 2000
"... We show how linear typing can be used to obtain functional programs which modify heapallocated data structures in place. We present this both as a "design pattern" for writing Ccode in a functional style and as a compilation process from linearly typed firstorder functional programs int ..."
Abstract

Cited by 103 (16 self)
 Add to MetaCart
(Show Context)
We show how linear typing can be used to obtain functional programs which modify heapallocated data structures in place. We present this both as a "design pattern" for writing Ccode in a functional style and as a compilation process from linearly typed firstorder functional programs into malloc()free C code. The main technical result is the correctness of this compilation. The crucial innovation over previous linear typing schemes consists of the introduction of a resource type # which controls the number of constructor symbols such as cons in recursive definitions and ensures linear space while restricting expressive power surprisingly little. While the space e#ciency brought about by the new typing scheme and the compilation into C can also be realised by with stateoftheart optimising compilers for functional languages such as Ocaml [16], the present method provides guaranteed bounds on heap space which will be of use for applications such as languages for embedd...