A Fully Abstract Semantics for Concurrent Graph Reduction
نویسنده
چکیده
This paper presents a fully abstract semantics for a variant of the untyped λ-calculus with recursive declarations. We first present a summary of existing work on full abstraction for the untyped λ-calculus, concentrating on ABRAMSKY and ONG’s work on the lazy λ-calculus. ABRAMSKY and ONG’s work is based on leftmost outermost reduction without sharing. This is notably inefficient, and many implementations model sharing by reducing syntax graphs rather than syntax trees. Here we present a concurrent graph reduction algorithm for the λ-calculus with recursive declarations, in a style similar to BERRY and BOUDOL’s Chemical Abstract Machine. We adapt ABRAMSKY and ONG’s techniques, and present a program logic and denotational semantics for the λ-calculus with recursive declarations, and show that the three semantics are equivalent.
منابع مشابه
A Fully Abstract Semantics for Value-passing CCS for Trees
This paper provides a fully abstract semantics for valuepassing CCS for trees (VCCTS). The operational semantics is given both in terms of a reduction semantics and in terms of a labelled transition semantics. The labelled transition semantics is non-sequential, allowing more than one action occurring simultaneously. We develop the theory of behavioral equivalence by introducing both weak barbe...
متن کاملA Chemical Abstract Machine for Graph Reduction
Graph reduction is an implementation technique for the lazy λ-calculus. It has been used to implement many non-strict functional languages, such as lazy ML, Gofer and Miranda. Parallel graph reduction allows for concurrent evaluation. In this paper, we present parallel graph reduction as a Chemical Abstract Machine, and show that the resulting testing semantics is adequate wrt testing equivalen...
متن کاملFully-abstract concurrent games for pi
We define a semantics for Milner’s pi-calculus, with three main novelties. First, it provides a fully-abstract model for fair testing equivalence, whereas previous semantics covered variants of bisimilarity and the may and must testing equivalences. Second, it is based on reduction semantics, whereas previous semantics were based on labelled transition systems. Finally, it has a strong game sem...
متن کاملFully-abstract concurrent games for π
We define a semantics for Milner’s pi-calculus, with three main novelties. First, it provides a fully-abstract model for fair testing equivalence, whereas previous semantics covered variants of bisimilarity and the may and must testing equivalences. Second, it is based on reduction semantics, whereas previous semantics were based on labelled transition systems. Finally, it has a strong game sem...
متن کاملA Fully Abstract May Testing Semantics for Concurrent Objects
This paper provides a fully abstract semantics for a variant of the concurrent object calculus. We define may testing for concurrent object components and then characterise it using a trace semantics inspired by UML interaction diagrams. The main result of this paper is to show that the trace semantics is fully abstract for may testing. This is the first such result for a concurrent object lang...
متن کامل