. In this paper we present a general framework for type-based analyses of functional programs. Our framework is a generalisation of our earlier work on strictness analysis and was inspired by Burn's logical framework. The framework is parameterised by a set of types to represent properties and interpretations for constants in the language. To construct a new analysis, the user needs only to supply a model for the types (which properties they denote) and sound rules for the constants. We identify the local properties that must be proven to guarantee the correctness of a specific analysis and algorithm. We illustrate the approach by recasting Hunt and Sand's binding time analysis in our framework. Furthermore we report on experimental results suggesting that our generic inference algorithm can provide the basis for an efficient program analyser. 1 Introduction The first explicit use of types in program analysis was by Kuo and Mishra [14]. They presented a type system for inferring stric...

We give a semantics to a polymorphic effect analysis that tracks possibly-thrown exceptions and possible non-termination for a higher-order language. The semantics is defined using partial equivalence relations over a standard monadic, domain-theoretic model of the original language and establishes the correctness of both the analysis itself and of the contextual program transformations that it enables.

Binding-time 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.

Interpretation Franck V'edrine Laboratoire Informatique de l' ' Ecole Normale Sup'erieure 45 rue d'Ulm, 75230 Paris Cedex 05 FRANCE email: vedrine@dmi.ens.fr Abstract. Given a description of inputs and parameters in a program, a Binding-Time Analysis determines parts of a program which can be evaluated at compile-time. A Strictness Analysis determines parts of a program, whose early evaluation does not change the value of the result. In this paper, we present an analysis which subsumes both analyses for a first-order functional language. The analysis is formulated in terms of Abstract Interpretation based upon approximation of a fixpoint collecting semantics using Galois connections. 1 Introduction Binding-Time Analysis (B.T.A) is useful for partial evaluation. It finds out which parts of a program can be evaluated at compile-time with respect to well known arguments, or more generally, when a dynamic expression can be unfrozen. Combined with Strictness Analysis, it enables to class...

domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Specification of analyses . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.4 Semantic correctness . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.5 Solving systems of equations . . . . . . . . . . . . . . . . . . . . . 13 1.3 This document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Program analysis with conjunctive types 17 2.1 Strictness types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.1 Lindenbaum algebras . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 The strictness logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Relationship to abstract interpretation . . . . . . . . . . . . . . . . . . . . 22 2.4 A variation: binding-time analysis . . . . . . . . . . . . . . . . . . . . . . 22 3 Disjunctions and data structures: Properties 25 3.1 Axiomatisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.1 Normal Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Abstract domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.1 Base Types, Products, Sums and Functions . . . . . . . . . . . . . 31 3.2.2 Recursive Data Structures . . . . . . . . . . . . . . . . . . . . . . 32 3.2.3 Strictness Properties of Lists . . . . . . . . . . . . . . . . . . . . . 35 4 Disjunctions and data structures: Logic 37 4.1 Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1.1 Strictness Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1.2 Proving properties for lists . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Bibliographical not...

The projection-based strictness analysis of Wadler and Hughes is elegant and theoretically satisfying except in one respect: the need for lifting. The domains and functions over which the analysis is performed need to be transformed, leading to a less direct correspondence between analysis and program than might be hoped for. In this paper we shall see that the projection analysis may be reformulated in terms of partial projections, so removing this infelicity. There are additional benefits of the formulation: the two forms of information captured by the projection are distinguished, and the operational significance of the range of the projection fits exactly with the theory of unboxed types. 1 Introduction The method of projection-based backwards strictness analysis for first-order, lazy functional languages was first presented by Wadler and Hughes (1987) in 1987, and has undergone significant development since then. The method is elegant and theoretically satisfying except in one r...

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.

First-order projection-based binding-time analysis has proven genuinely useful in partial evaluation [Lau91a, Lau91c]. There have been three notable generalisations of projection-based analysis to higher order. The first lacked a formal basis [Mog89]; the second used structures strictly more general that projections, namely partial equivalence relations (PERs) [HS91]; the third involved a complex construction that gave rise to impractically large abstract domains [Dav93]. This paper presents a technique free of these shortcomings: it is simple, entirely projection-based, satisfies a formal correctness condition, and gives rise to reasonably small abstract domains. Though the technique is cast in terms of projections, there is also an interpretation in terms of PERs. The principal limitation of the technique is the restriction to monomorphic typing. 1 Introduction and Background We take as given that binding-time analysis is essential for good partial evaluation, and we do not address...

In program optimisation an analysis determines some information about a portion of a program, which is then used to justify certain transformations on the code. The correctness of the optimisation can be argued monolithically by considering the behaviour of the optimiser and a particular analysis in conjunction. Alternatively, correctness can be established by finding an interface, a semantic property, between the analysis and the transformation. The semantic property provides modularity by giving a specification for a systematic construction of the analysis, and the program transformations are justified via the semantic properties. This paper considers the problem of partial evaluation. The safety of a partial evaluator ("it does not go wrong") has previously been argued in the monolithic style by considering the behaviour of a particular binding-time analysis and program specialiser in conjunction. In this paper we pursue the alternative approach of justifying the binding-time prop...

This article investigates formal properties of a family of semantically sound flow-sensitive type systems for tracking information flow in simple While programs. The family is indexed by the choice of flow lattice.