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OUTL1NE

OF A

MATHEMAT1CAL THEORY

OF

COMPUTATION

by

Dana Scott

Princeton Univers i ty

Technical Monograph PRG-2

November 1970

Oxford University Computing Laboratory.

Programming Research Group.

4S Banbury Road.

Oxford.

L~t;C'i¡¤~I.,~ry

?

1970 by Dana Scott

Department of Philosophy,

1879 Hall,

Princeton University,

Princeton, New Jersey, 08540.

This paper is a revised and slightly expanded version

of a paper under the same title in the Proceedings of the Fourth

Annual Princeton Conference on Information Sciences and Systems

(1970) .

ABSTRACT

This paper introduces a theory of computation which

is mathematical rather than operational in its approach.

The theory is based on the idea that data types can be partial?

ly ordered by a relation similar to that of approximation,

and as a resul t

can be considered as complete lattices.

properties of these lattices and the functions on them are

discussed in an informal manner and shown to be very suit?

able for developing a mathematical theory of the semantics

of programming languages.

A preliminary result of this

approach is the construction of the first "mathematical"

model for the A-calculus.

The

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