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Term Assignment for Intuitionistic Linear Logic
, 1992
"... In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky) and has two important properties which they lac ..."
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Cited by 60 (10 self)
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In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is welltyped). We define a simple (but more general than previous proposals) categorical model for Intuitionistic Linear Logic and show how this can be used to derive the term assignment system. We also consider term reduction arising from cutelimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these, as well as with the equations which follow from our categorical model.
Once Upon a Polymorphic Type
, 1998
"... We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and app ..."
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Cited by 41 (6 self)
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We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approximate, or defined over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type polymorphism, an essential feature of typed functional programming languages. Secondly, we include general Haskellstyle userdefined algebraic data types. Thirdly, we explain and solve the `poisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchburystyle operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation, and we are currently integrating the system into the Glasgow Haskell Compiler.
Simple Usage Polymorphism
 TIC 2000
, 2000
"... We present a novel inference algorithm for a type system featuring subtyping and usage (annotation) polymorphism. This algorithm infers simplypolymorphic types rather than the constrainedpolymorphic types usual in such a setting; it achieves this by means of constraint approximation. The algorithm ..."
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Cited by 11 (0 self)
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We present a novel inference algorithm for a type system featuring subtyping and usage (annotation) polymorphism. This algorithm infers simplypolymorphic types rather than the constrainedpolymorphic types usual in such a setting; it achieves this by means of constraint approximation. The algorithm is motivated by practical considerations and experience of a previous system, and has been implemented in a production compiler with positive results. We believe the algorithm may well have applications in settings other than usagetype inference.
Garbage Collection Based on a Linear Type System
, 2000
"... We propose a typedirected garbage collection (GC) scheme for a programming language with static memory management based on a linear type system. Linear type systems, which can guarantee certain values (called linear values) to be used only once during program execution, are useful for memory man ..."
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Cited by 11 (2 self)
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We propose a typedirected garbage collection (GC) scheme for a programming language with static memory management based on a linear type system. Linear type systems, which can guarantee certain values (called linear values) to be used only once during program execution, are useful for memory management: memory space for linear values can be reclaimed immediately after they are used. However, conventional pointertracing GC does not work under such a memory management scheme: if the memory space for used linear values is still reachable through pointers, dangling pointers are created. This problem is solved by exploiting static type information during garbage collection in a way similar to tagfree GC. Type information in our linear type system represents not only the shapes of heap objects but also how many times the heap objects are accessed in the rest of computation. Using such type information at GCtime, our GC can avoid tracing dangling pointers; in addition, our GC can...
Type Theory and Projections for Static Analysis
, 1995
"... A system of annotated types is proposed as a means of describing and inferring static information, such as strictness and constancy, about functional programs. An abstract semantics is given in terms of projections. A close connection between annotated type assignment and projection analysis is demo ..."
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Cited by 1 (1 self)
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A system of annotated types is proposed as a means of describing and inferring static information, such as strictness and constancy, about functional programs. An abstract semantics is given in terms of projections. A close connection between annotated type assignment and projection analysis is demonstrated.
Analysing Resource Use in the λCalculus By Type Inference
, 1994
"... If we view functions as processes, then their resources are their arguments, supplied through application, and used by the function to produce a result. In this paper, we define resource use for functions, based on the syntactic notion of needed redexes from [BKKS86]. We introduce a variant of neede ..."
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If we view functions as processes, then their resources are their arguments, supplied through application, and used by the function to produce a result. In this paper, we define resource use for functions, based on the syntactic notion of needed redexes from [BKKS86]. We introduce a variant of neededhess, tailneededness, and define packets of needed descendants of redexes in order to mea sure the degree of neededhess. These results are generalised to produce a semantic characterisation of the resource use properties of functions, using a termmodel. By means of the CurryHoward isomorphism, we apply these ideas to proof trees of propositions in Intuitionistic Logic to demonstrate that propositions, i.e. types, can be used to express the usage properties of functions. A resourceaware type system capable of inferring such types for Aterms is presented.
www.cl.cam.ac.uk/users/kw217/
"... research.microsoft.com/Users/simonpj/ We present a novel inference algorithm for a type system featuring subtyping and usage (annotation) polymorphism. This algorithm infers simplypolymorphic types rather than the constrainedpolymorphic types usual in such a setting; it achieves this by means of c ..."
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research.microsoft.com/Users/simonpj/ We present a novel inference algorithm for a type system featuring subtyping and usage (annotation) polymorphism. This algorithm infers simplypolymorphic types rather than the constrainedpolymorphic types usual in such a setting; it achieves this by means of constraint approximation. The algorithm is motivated by practical considerations and experience of a previous system, and has been implemented in a production compiler with positive results. We believe the algorithm may well have applications in settings other than usagetype inference. 1
Multiple Modalities
, 1998
"... Linear logic removes the structural rules of Weakening and Contraction and adds an S4like modality (written !). Only formulae of the form !OE can be weakened or contracted. An interesting question is whether these two capabilities can be separated, using two different modalities. This question was ..."
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Linear logic removes the structural rules of Weakening and Contraction and adds an S4like modality (written !). Only formulae of the form !OE can be weakened or contracted. An interesting question is whether these two capabilities can be separated, using two different modalities. This question was studied semantically in a comprehensive paper by Jacobs. This paper considers the question prooftheoretically, giving sequent calculus, natural deduction and axiomatic formulations. c fl G M B December 17, i 1 Introduction Girard's linear logic [16] removes the two structural rules of Weakening and Contraction, i.e. 1 \Gamma \Gamma / Weakening \Gamma; OE \Gamma / \Gamma; OE; OE \Gamma / Contraction \Gamma; OE \Gamma / This has the profound effect of dividing the connectives into two variants, additive and multiplicative. (For the most part of this paper, only the (multiplicative) implication connective is considered.) Unfortunately, a logic without these two structural rules is ve...
Type Theory and Projections for HigherOrder Static Analysis
"... A system of annotated types is proposed as a means of describing and inferring static information, such as strictness and constancy, about functional programs. An abstract semantics is given in terms of projections. The paper then proceeds to demonstrate a close connection between annotated type ass ..."
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A system of annotated types is proposed as a means of describing and inferring static information, such as strictness and constancy, about functional programs. An abstract semantics is given in terms of projections. The paper then proceeds to demonstrate a close connection between annotated type assignment and projection analysis.