Equational logic as a programming language
Equational logic as a programming language
Communications of the ACM
The parallel execution of DO loops
Communications of the ACM
Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
Dependence graphs and compiler optimizations
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Time and Parallel Processor Bounds for Fortran-Like Loops
IEEE Transactions on Computers
Compilation of Nonprocedural Specifications into Computer Programs
IEEE Transactions on Software Engineering
Algorithm specification in a very high level language
ACM '87 Proceedings of the 1987 Fall Joint Computer Conference on Exploring technology: today and tomorrow
The symbolic hyperplane transformation for recursively defined arrays
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
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This paper describes a new method of automatic generation of concurrent programs which construct arrays defined by sets of recursive equations. We assume that the time of computation of an array element is a linear combination of its indices, and we use integer programming to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system.