type theory
Noun
Meaning
type theory (usually uncountable, plural type theories)
(mathematics, computer science) A branch of mathematical logic and theoretical computer science concerned with types.
Coordinate term: set theory
Synonyms
Examples
Although the axiom schema of replacement is a standard axiom in set theory today, it is often omitted from systems of type theory and foundation systems in topos theory.
As a result, research into this class of formal systems began to address both logical and computational aspects; this area of research came to be known as modern type theory.
A stratified formula is one that type theory would allow, were the ontology to include types.
Active * Homotopy type theory is being researched.
Axiom of infinity Ramified types and the axiom of reducibility In simple type theory objects are elements of various disjoint "types".
Dependent type theory in full generality is very powerful: it is able to express almost any conceivable property of programs directly in the types of the program.