The behavior of concurrent and parallel programs can be specified in a functional style. We introduced a relational model for synthesizing abstract parallel imperative programs earlier. In this paper we investigate the applicability of the specification and verification tools of the model for proving temporal properties of concrete programs written in a pure functional language, in Concurrent Clean. Destructive updates preserving referential transparency are possible by using so called unique types. Clean programs perform I/O by accessing their unique environment. We present a methodology for proving safety and liveness properties of concurrent, interleaved Clean Object I/O processes and show examples for verification of simple Clean programs.

We introduce the basic concepts of a relational model of parallel programming. We define the concepts of a problem, an abstract program and a solution. Our approach is functional, problems are given an own semantical meaning. The abstract program is regarded as a relation generated by a set of nondeterministic conditional assignments similar to the concept of abstract program in UNITY. We introduce the behaviour relation of a parallel program which is easy to compare to the relation which is the interpretation of a problem. This paper covers only a brief summary of the model. For further information see [7]. The main goal of this paper is to introduce some basic composition methods for parallel programs and problems. We define the union, extension and sequence of problems. Similarly we formalize the concept of union, superposition and sequence of parallel programs. We analyze how one can solve a compound problem using the appropriate program construct. Categories and Subject Descripto...

The behavior of concurrent and parallel programs can be speci ed in a functional style. We introduced a relational model for synthesizing abstract parallel imperative programs this way earlier. In this paper we investigate the applicability of the speci cation and veri cation tools of the model for proving temporal properties of concrete programs written in a pure functional language, in Concurrent Clean. Destructive updates preserving referential transparency are possible in this language by using the so called unique types. For example Clean programs perform I/O by accessing their unique environment. Furthermore, dynamic types of Clean make it possible to load some pieces of the program during run-time. We present a methodology for proving safety and liveness properties of concurrent, interleaved Clean Object I/O processes that also use dynamic types and show simple examples for veri cation of correctness of such Clean programs.