Higher-order, linear, concurrent constraint programming

We present a very simple and powerful framework for indeterminate, asynchronous, higher-order computation based on the formula-as-agent and proof-ascomputation interpretation of (higher-order) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constraint programming paradigm [Sar89] in two fundamental ways: (1) by allowing for the consumption of information by agents it permits a direct modelling of (indeterminate) state change in a logical framework, and (2) by admitting simply-typed -terms as dataobjects, it permits the construction, transmission and application of (abstractions of) programs at run-time. Much more dramatically, however, the framework can be seen as presenting higher-order (and if desired, constraint-enriched) versions of a variety of other asynchronous concurrent systems, including the asynchronous (‘‘input guarded”) fragment of the (first-order) -calculus, Hewitt’s actors formalism, (abstract forms of) Gelernter’s Linda, asynchronous assignment-based languages, and Petri nets. It can also be seen as smoothly layering around the functional programming style provided by the -calculus a minimal amount of extra logical machinery needed to obtain concurrency, synchronization and indeterminism declaratively. Additionally, there are remarkably simple and direct translations of the untyped -calculus into the higher-order linear cc (HLcc) programming paradigm. We give (1) a simple operational semantics for HLcc, (2) establish several connections between proof-theory and operational semantics, (3) develop the notion of bisimulation for HLcc, along the lines of [Tho89], (4) establish that logical An abstract of this paper has been submitted for publication. Please send comments to the authors.