Expression continuity and the formal differentiation of algorithms
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Application of lattice algebra to loop optimization
POPL '75 Proceedings of the 2nd ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The theory of parsing, translation, and compiling
The theory of parsing, translation, and compiling
High level operations in automatic programming
Proceedings of the ACM SIGPLAN symposium on Very high level languages
Induction variables in very high level languages
POPL '76 Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages
Recent developments in SAIL, an algol-based language for artificial intelligence.
Recent developments in SAIL, an algol-based language for artificial intelligence.
Programming languages and their compilers: Preliminary notes
Programming languages and their compilers: Preliminary notes
Mechanical translation of set theoretic problem specifications into efficient RAM code-A case study
Journal of Symbolic Computation
A categorized bibliography on incremental computation
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Some Observations Concerning Formal Differentiation of Set Theoretic Expressions
ACM Transactions on Programming Languages and Systems (TOPLAS)
Finite Differencing of Computable Expressions
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficiency by Incrementalization: An Introduction
Higher-Order and Symbolic Computation
Synthesizing abstract data type specifications
ACM-SE 20 Proceedings of the 20th annual Southeast regional conference
ACM Transactions on Programming Languages and Systems (TOPLAS)
Transformational programming: applications to algorithms and systems
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computational Divided Differencing and Divided-Difference Arithmetics
Higher-Order and Symbolic Computation
Optimizing aggregate array computations in loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Core role-based access control: efficient implementations by transformations
Proceedings of the 2006 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Formal integration: A program transformation technique
Computer Languages
| Hi-index | 0.01 |
In this paper we study the profitability of applying the "reduction in strength" technique to programs in set-theoretic languages, focusing on the high level constructs involving set-formers. We define recursively two classes of expressions we shall call inductively computable set-formers and inductively computable predicates which can be evaluated with an order of magnitude improvement of the asymptotic running time as compared to the straightforward evaluation. The quantity developed for this comparison can be used to derive further results when additional information is known. For programs written in very high level languages, which often consist mostly of "nested" iterative constructs, this technique amounts to altering the "algorithm" used to compute the program by replacing it with an asymptotically faster algorithm.