Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). In this paper a binding time analysis for the simply typed lambda calculus is presented. The analysis takes the form of an abstract interpretation and uses a novel formalisation of the problem of binding time analysis, based on the use of partial equivalence relations. A simple proof of correctness is achieved by the use of logical relations. 1 Introduction Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). A binding time analysis performed prior to the partial evaluation process can have several practical benefits (see [...

Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over non-standard 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...

This paper presents a precise connection between a non-commutative version of intuitionistic linear logic (INLL) and concurrent constraint programming (cc). The contribution of this paper is twofold: ffl on the one hand, we refine existing logical characterizations of operational aspects of concurrent constraint programming, by providing a logical interpretation of finer observable properties of cc programs, namely successes and suspensions. ffl on the other ha...

plete, 23 has binary products, 20 has equalizers, 20 has pullbacks, 20 indiscrete, 13 left exact, 23 lex, 23 locally small, 4 path, 3 quotient, 3 regular, 29 slice, 4 small, 13 ccc, 63 closure operation on poset, 54 cocone for a functor, 25 codomain, 1 coequalizer, 25 coequalizer diagram, 25 coherent logic, 33 colimiting cocone, 25 comonad, 53 comparison functor, 57 complement in a lattice, 15 composition, 1 comultiplication of comonad, 53 cone for a functor, 17 congruence relation, 3 coproduct, 25 coproduct inclusions, 25 coprojections, 25 counit of adjunction, 45 counit of comonad, 53 diagram commutes, 4 diagram of type C, 17 domain, 1 duality principle, 6 embedding, 10 epi, 6 epimorphism, 6 equality judgement in -calculus, 67 equalizer, 18 equalizer diagram, 18 equivalence of categories, 15 equivalent categories, 15 equivalent formulas, 39 evaluation in ccc, 64 exponents in ccc, 64 frame, 39 free group, 3 free monoid, 46 functor, 2 contravariant, 5 co

Engberg and Winskel's Petri net semantics of linear logic is re-considered, from the point of view of the logic BI of bunched implications. We first show how BI can be used to overcome a number of difficulties pointed out by Engberg and Winskel, and we argue that it provides a more natural logic for the net semantics. We then briefly consider a more expressive logic based on an extension of BI with classical and modal features.

) Sebastian Hunt Department Of Computing Imperial College London SW7 2BZ Abstract We show how Wadler and Hughes's use of Scott projections to describe properties of functions ("Projections for Strictness Analysis", FPCA 1987) can be generalised by the use of partial equivalence relations. We describe an analysis (in the form of an abstract interpretation) for identifying such properties for functions defined in the simply typed -calculus. Our analysis has a very simple proof of correctness, based on the use of logical relations. We go on to consider how to derive `best' correct interpretations for constants. 1 Introduction In [WH87], Phil Wadler and John Hughes suggested a method of describing properties of functions using projections, and developed an analysis for identifying such properties for functions defined in a first-order functional language. (A projection is a continuous map on a cpo ff : D ! D, such that ff v id D and ff ffi ff = ff.) For an example of [WH87]'...

has equalizers, 20 has pullbacks, 20 indiscrete, 13 left exact, 23 lex, 23 locally small, 4 path, 3 quotient, 3 regular, 29 slice, 4 small, 13 ccc, 63 closure operation on poset, 54 cocone for a functor, 25 codomain, 1 coequalizer, 25 coequalizer diagram, 25 coherent logic, 33 colimiting cocone, 25 comonad, 53 comparison functor, 57 complement in a lattice, 15 composition, 1 comultiplication of comonad, 53 cone for a functor, 17 congruence relation, 3 coproduct, 25 coproduct inclusions, 25 coprojections, 25 counit of adjunction, 45 counit of comonad, 53 diagram commutes, 4 diagram of type C, 17 domain, 1 duality principle, 6 embedding, 10 epi, 6 epimorphism, 6 equality judgement in -calculus, 67 equalizer, 18 equalizer diagram, 18 equivalence of categories, 15 equivalent categories, 15 equivalent formulas, 39 evaluation in ccc, 64 exponents in ccc, 64 frame, 39 free group, 3 free monoid, 46 functor, 2 contravariant, 5 covariant, 5