Towards a Mathematical Science of Computation

J. McCarthy
Computer Science Department
Stanford University
Stanford, CA 95305
jmc@cs.stanford.edu
http://www-formal.stanford.edu/jmc/

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Abstract:

• Introduction
• What Are The Entities With Which Computer Science Deals?
• What Kinds of Facts About Problems, Procedures, data Spaces, Programs, And Computers Would We Like to Derive?
• What Are The Axioms And Rules of Inference of A Mathematical Science of Computation?
• What Important Results Have Been Obtained Relevant to A Mathematical Science of Computation?
• How Can A Mathematical Science of Computation Help in The Solution of Practical Problems?
• Using Conditional Expressions to Define Functions Recursively
• Proving Statements About Recursive Functions
• Recursive Functions, Flow Charts, And Algolic Programs
• Recursion Induction on Algolic Programs
• The Description of Programming Languages
• Abstract Syntax of Programming Languages
• Semantics
• The Limitations of Machines And Men as Problem-Solvers
• References
• About this document ...