Book ChapterDOI
Towards a Mathematical Science of Computation
TLDR
The prospects for a mathematical science of computation is discussed and it is shown that from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler's laws.Abstract:
In this paper I shall discuss the prospects for a mathematical science of computation. In a mathematical science, it is possible to deduce from the basic assumptions, the important properties of the entities treated by the science. Thus, from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler’s laws.read more
Citations
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Book ChapterDOI
Some philosophical problems from the standpoint of artificial intelligence
TL;DR: In this paper, the authors consider the problem of reasoning about whether a strategy will achieve a goal in a deterministic world and present a method to construct a sentence of first-order logic which will be true in all models of certain axioms if and only if a certain strategy can achieve a certain goal.
Book ChapterDOI
Assigning Meanings to Programs
TL;DR: This paper attempts to provide an adequate basis for formal definitions of the meanings of programs in appropriately defined programming languages, in such a way that a rigorous standard is established for proofs about computer programs, including proofs of correctness, equivalence, and termination.
Journal ArticleDOI
Simplify: a theorem prover for program checking
TL;DR: The article describes two techniques, error context reporting and error localization, for helping the user to determine the reason that a false conjecture is false, and includes detailed performance figures on conjectures derived from realistic program-checking problems.
Journal ArticleDOI
Initial Algebra Semantics and Continuous Algebras
TL;DR: An overview of initial algebra semantics is provided and the major technical feature is an initial continuous algebra which permits unified algebraic treatment of iterative and recursive semantic features in the same framework as more basic operations.
Proceedings ArticleDOI
Definitional interpreters for higher-order programming languages
TL;DR: The definition of a simple applicative programming language by means of an interpreter written in a similar language is considered, and the treatment of imperative features such as jumps and assignment is discussed.
References
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Book ChapterDOI
A Basis for a Mathematical Theory of Computation
TL;DR: The chapter explores what practical results can be expected from a suitable mathematical theory and presents several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms.
A Basis for a Mathematical Theory of Computation
TL;DR: In this paper, the mathematical theory of computation is discussed and several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms are also presented.