We present a natural semantics that models the untyped, normal order A-calculus plus McCarthy's amb in the context of call-by-need parameter passing. This results in a singular semantics for amb.Previous work on singular choice has concentrated on erratic choice, a less interesting nondeterministic choice operator, and only in relation to callby-value parameter passing, or call-by-name restricted to deterministic terms.The natural semantics contains rules for both convergent and divergent behaviour, allowing it to distinguish programs that differ only in their divergent behaviour. As a result, it is more discriminating than current domain-theoretic models. This, and the fact that it models singular amb, makes the natural semantics suitable for reasoning about lazy, functional languages containing McCarthy's amb.

Abstract. Binding time analysis is an important part of off-line partial evaluation, annotating expressions as being safely evaluable from known data or possibly depending on unknown data. Polymorphism gives a much simpler definition than the known polyvariant schemes allowing us to reason formally about the system and prove it correct. This paper is based on work in [14].

Abstract. The combination of parameter polymorphism, subtyping extended to qualified and polymorphic types, and polymorphic recursion is useful in standard type inference and gives expressive type-based program analyses, but raises difficult algorithmic problems. In a program analysis context we show how Mycroft's iterative method of computing principal types for a type system with polymorphic recursion can be generalized and adapted to work in a setting with subtyping. This does not only yield a proof of existence of principal types (most general properties), but also an algorithm for computing them. The punch-line of the development is that a very simple modification of the basic algorithm reduces its computational complexity from exponential time to polynomial time relative to the size of the given, explicitly typed program.This solves the open problem of finding an inference algorithm for polymorphic binding-time analysis [7].

We present a type-based flow analysis for simply typed lambda calculus with booleans, data-structures and recursion. The analysis is exact in the following sense: if the analysis predicts a redex, there exists a reduction sequence (using standard reduction plus context propagation rules) such that this redex will be reduced. The precision is accomplished using intersection typing. It follows that the analysis is non-elementary recursive -more surprisingly, the analysis is decidable. We argue that the specification of such an analysis provides a good starting point for developing new flow analyses and an important benchmark against which other flow analyses can be compared. Furthermore, we believe that the techniques employed for stating and proving exactness are of independent interest: they provide methods for reasoning about the precision of program analyses.A preliminary version of this paper has previously been published (Mossin 1997b). The present paper extends, elaborates and corrects this previously published abstract. † This construct is chosen instead of separate operators for picking the first and second component of the pair, as these operators discard data. This would imply that the non-standard reduction of Section 7 and the completeness results of Section 9 would be less elegant (though no less true).Flow analysis seeks a safe approximation to the possible consumptions during any reduction of a term. That is, given e, a flow analysis will compute Φ such that whenever e −→ * e , we have R(e −→ * e ) ⊆ Φ.

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