# Nonwellfounded sets and programming language semantics

## Abstract

For a large class of transition systems that are defined by specifications in the SOS style, it is shown how these induce a compositional semantics. The main difference with earlier work on this subject is the use of a nonstandard set theory that is based on Aczel's anti-foundation-axiom. Solving recursive domain equations in this theory leads to solutions that contain nonwellfounded elements. These are particularly useful for justifying recursive definitions, both of semantic operators and semantic models. The use of nonwellfounded sets further allows for the construction of compositional models for a larger class of transition systems than in the setting of complete metric spaces, which was used before.

## 1980 Mathematics Subject Classification

68B10 68C01## 1986 Computing Reviews Categories

D.3.1 F.3.2 F.3.3## Key words and phrases

Structured operational semantics labelled transition system transition system specification bisimulation interpretation compositionality nonwellfounded sets anti-foundation-axiom## Preview

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