A semantic framework for the COLD-family of languages

Abstract

This document introduces a framework which can be used as a general scheme for describing the semantics of languages from the COLD-family. The approach can be classified in the category of 'transformational semantics', where three linguistic levels are distinguished. The first level, called MPL, is a many-sorted version of Scott's E-logic restricted to strict predicates and functions and extended with a minimal fixpoint operator for predicates. The second level, called COLD-logic, can be viewed as a COLD-oriented specialisation of MPL. Among other things, it contains the standard sort 'State' and standard predicates for the initial state, reachability of states, modification of states and existence of objects. The third level defines a language, called COLD-flat, which can be viewed as an extended subset of COLD-S. The main issues that have been omitted are parameterised classes, import/export facilities and recursive definitions, while predicates have been added to the language. The semantics of each linguistic level (except the first) is defined by a formal translation to the next lower level. An example of such a translation from COLD-flat to COLD-logic is presented in the appendix.