1. Outline I. Specification and Definition II. Typed Predicate Logic III. Specification in TPL IV. Theories off Types V. Polymorphic Specifications VI.

TOWARDS A PHILOSOPHY OF COMPUTER SCIENCE

THE LOGIC OF SPECIFICATION1What kind of thing is the definition of a computer/1OutlineSpecification and DefinitionTyped Predicate LogicSpecification in TPLTheories off TypesPolymorphic SpecificationsThe Type of SpecificationsRecursive Specifications CorrectnessComputable SpecificationsAxiomatic Definitions

22SPECIFICATION and DEFINITION

3 Stipulative Definitions A stipulative definition is a type of definition in which a new (or even an existing term) is given a specific meaning in a given context. They introduce new things i.e., relations, objects, functions, properties,...For example, grue was stipulated to be a property of an object that makes it appear green if observed before some future time t, and blue if observed afterward.They involve no commitment that the assigned meaning agrees with any prior use. A stipulative definition cannot be correct or incorrect.

4Mathematical ExamplesG(x) 3x+2x+7x+9

P[x, y] z.y=x+z

a x.xNx