Abstract
λS extends the λ-calculus with recursive bindings, barriers, and updatable memory cells with synchronized operations. The calculus can express both deterministic and nondeterministic computations. It is designed to be useful for reasoning about compiler optimizations and thus allows reductions anywhere, even inside λ's. Despite the presence of side effects, the calculus retains fine-grained, implicit parallelism and non-strict functions: there is no global, sequentializing store. Barriers, for sequencing, capture a robust notion of termination. Although λS was developed as a foundation for the parallel functional languages pH and Id, we believe that barriers give it wider applicability — to sequential, explicitly parallel and concurrent languages. In this paper we describe the λS-calculus and its properties, based on a notion of observable information in a term. We also describe reduction strategies to compute maximal observable information even in the presence of unbounded nondeterminism.
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