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Type and effect systems
 ACM Computing Surveys
, 1999
"... Abstract. The design and implementation of a correct system can benefit from employing static techniques for ensuring that the dynamic behaviour satisfies the specification. Many programming languages incorporate types for ensuring that certain operations are only applied to data of the appropriate ..."
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Abstract. The design and implementation of a correct system can benefit from employing static techniques for ensuring that the dynamic behaviour satisfies the specification. Many programming languages incorporate types for ensuring that certain operations are only applied to data of the appropriate form. A natural extension of type checking techniques is to enrich the types with annotations and effects that further describe intensional aspects of the dynamic behaviour.
Abstract Interpretation of Functional Languages: From Theory to Practice
, 1991
"... Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with ..."
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Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with a formal semantic basis. It is known how abstract interpretation for the simply typed lambda calculus can be formalised by using binary logical relations. This has the advantage of making correctness and other semantic concerns straightforward to reason about. Its main disadvantage is that it enforces the identification of properties as sets. This thesis shows how the known formalism can be generalised by the use of ternary logical relations, and in particular how this allows abstract values to deno...
Deriving algorithms from type inference systems: Application to strictness analysis
, 1994
"... The role of nonstandard type inference in static program analysis has been much studied recently. Early work emphasised the efficiency of type inference algorithms and paid little attention to the correctness of the inference system. Recently more powerful inference systems have been investigated b ..."
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The role of nonstandard type inference in static program analysis has been much studied recently. Early work emphasised the efficiency of type inference algorithms and paid little attention to the correctness of the inference system. Recently more powerful inference systems have been investigated but the connection with efficient inference algorithms has been obscured. The contribution of this paper is twofold: first we show how to transform a program logic into an algorithm and, second, we introduce the notion of lazy types and show how to derive an efficient algorithm for strictness analysis. 1 Introduction Two major formal frameworks have been proposed for static analysis of functional languages: abstract interpretation and type inference. A lot of work has been done to characterise formally the correctness and the power of abstract interpretation. However the development of algorithms has not kept pace with the theoretical developments. This is now a major barrier that is preven...
Inference of Polymorphic and Conditional Strictness Properties
 IN CONF. REC. POPL ’98: 25TH ACM SYMP. PRINC. OF PROG. LANGS
, 1998
"... We define an inference system for modular strictness analysis of functional programs by extending a conjunctive strictness logic with polymorphic and conditional properties. This extended set of properties is used to define a syntaxdirected, polymorphic strictness analysis based on polymorphic recu ..."
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We define an inference system for modular strictness analysis of functional programs by extending a conjunctive strictness logic with polymorphic and conditional properties. This extended set of properties is used to define a syntaxdirected, polymorphic strictness analysis based on polymorphic recursion whose soundness is established via a translation from the polymorphic system into the conjunctive system. From the polymorphic analysis, an inference algorithm based on constraint resolution is derived and shown complete for variant of the polymorphic analysis. The algorithm deduces at the same time a property and a set of hypotheses on the free variables of an expression which makes it suitable for analysis of program with module structure.
Minimal thunkification
 Proceedings of the Third International Workshop on Static Analysis WSA'93, volume 724 of Lecture Notes in Computer Science
, 1993
"... Abstract. By “thunkifying ” the arguments to function applications and “dethunkifying ” variables one can translate a λexpression e into a λexpression e ′ , such that callbyvalue evaluation of e ′ gives the same result as callbyname evaluation of e. By using the result of a strictness analysis ..."
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Abstract. By “thunkifying ” the arguments to function applications and “dethunkifying ” variables one can translate a λexpression e into a λexpression e ′ , such that callbyvalue evaluation of e ′ gives the same result as callbyname evaluation of e. By using the result of a strictness analysis, some of these thunkifications can be avoided. In this paper we present a type system for strictness analysis; present a translation algorithm which exploits the strictness proof tree; and give a combined proof of the correctness of the analysis/translation. 1
Strictness logic and polymorphic invariance
 In Proc. Logical Found. Comp. Sci
, 1992
"... We describe a logic for reasoning about higherorder strictness properties of typed lambda terms. The logic arises from axiomatising the inclusion order on certain closed subsets of domains. The axiomatisation of the lattice of strictness properties is shown to be sound and complete, and we then giv ..."
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We describe a logic for reasoning about higherorder strictness properties of typed lambda terms. The logic arises from axiomatising the inclusion order on certain closed subsets of domains. The axiomatisation of the lattice of strictness properties is shown to be sound and complete, and we then give a program logic for assigning properties to terms. This places work on strictness analysis via type inference on a firm theoretical foundation. We then use proof theoretic techniques to show how the derivable strictness properties of different instances of polymorphically typed terms are related. 1
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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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.
Strictness and Totality Analysis
 In Static Analysis, LNCS 864
, 1994
"... We definea novel inference system for strictness and totality analysis for the simplytyped lazy lambdacalculus with constants and fixpoints. Strictness information identifies those terms that definitely denote bottom (i.e. do not evaluate to WHNF) whereas totality information identifies those terms ..."
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We definea novel inference system for strictness and totality analysis for the simplytyped lazy lambdacalculus with constants and fixpoints. Strictness information identifies those terms that definitely denote bottom (i.e. do not evaluate to WHNF) whereas totality information identifies those terms that definitely do not denote bottom (i.e. do evaluate to WHNF). The analysis is presented as an annotated type system allowing conjunctions only at "toplevel". We give examples of its use and prove the correctness with respect to a naturalstyle operational semantics. 1 Introduction Strictness analysis has proved useful in the implementation of lazy functional languages as Miranda, Lazy ML and Haskell: when a function is strict it is safe to evaluate its argument before performing the function call. Totality analysis is equally useful but has not be adopted so widely: if the argument to a function is known to terminate then it is safe to evaluate it before performing the function call [1...
Elimination of Negation in a Logical Framework
, 2000
"... Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with ..."
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Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higherorder HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
Bindingtime Analysis: Abstract Interpretation versus Type Inference
 IN PROC. ICCL'94, FIFTH IEEE INTERNATIONAL CONFERENCE ON COMPUTER LANGUAGES
, 1994
"... Bindingtime analysis is important in partial evaluators. Its task is to determine which parts of a program can be evaluated if some of the expected input is known. Two approaches to do this are abstract interpretation and type inference. We compare two specific such analyses to see which one deter ..."
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Cited by 10 (3 self)
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Bindingtime analysis is important in partial evaluators. Its task is to determine which parts of a program can be evaluated if some of the expected input is known. Two approaches to do this are abstract interpretation and type inference. We compare two specific such analyses to see which one determines most program parts to be eliminable. The first is a an abstract interpretation approach based on closure analysis and the second is the type inference approach of Gomard and Jones. Both apply to the pure calculus. We prove that the abstract interpretation approach is more powerful than that of Gomard and Jones: the former determines the same and possibly more program parts to be eliminable as the latter.