In a short section on the semantics of programs within his discussion of program correctness, Primiero seems to endorse the received view on the Scott-Strachey approach to denotational semantics as directly related to correctness. While this is true to some extent, I argue that the mathematical entities associated with programs play a lesser role in reasoning on program correctness, while the mathematical foundations of denotational semantics, namely the theory of domains, have contributed significantly to the conceptual understanding of programming and (...) of computation in general. (shrink)

Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching (...) upon the relations of continuity with non-determinism. (shrink)

We present a type inference system for pure λ-calculus which includes, in addition to arrow types, also universal and existential type quantifiers, intersection and union types, and type recursion. The interest of this system lies in the fact that it offers a possibility to study in a unified framework a wide range of type constructors. We investigate the main syntactical properties of the system, including an analysis of the preservation of types under parallel reduction strategies, leading to a form of (...) the subject-reduction property. We describe a model for this system where types are special subsets of a D∞ model for λ-calculus, without imposing any formal contractiveness constraint on types of the kind considered for a closely related system by MacQueen, Plotkin and Sethi. (shrink)

We expose some basic elements of a style of programming supported by functional languages like Haskell by relating them to a coherent set of notions and techniques from Curry’s work in combinatory logic and formal systems, and their algebraic and categorical interpretations. Our account takes the form of a commentary to a simple fragment of Haskell code attempting to isolate the conceptual sources of the linguistic abstractions involved.