## Foundations and Applications of Higher-Dimensional Directed Type Theory

### BibTeX

@MISC{n.n._foundationsand,

author = {n.n.},

title = {Foundations and Applications of Higher-Dimensional Directed Type Theory},

year = {}

}

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### Abstract

Intuitionistic type theory [43] is an expressive formalism that unifies mathematics and computation. A central concept is the propositions-as-types principle, according to which propositions are interpreted as types, and proofs of a proposition are interpreted as programs of the associated type. Mathematical propositions are thereby to be understood as specifications, or problem descriptions, that are solved by providing a program that meets the specification. Conversely, a program can, by the same token, be understood as a proof of its type viewed as a proposition. Over the last quarter-century type theory has emerged as the central organizing principle of programming language research, through the identification of the informal concept of language features with type structure. Numerous benefits accrue from the identification of proofs and programs in type theory. First, it provides the foundation for integrating types and verification, the two most successful formal methods used to ensure the correctness of software. Second, it provides a language for the mechanization of mathematics in which proof checking is equivalent to type checking, and proof search is equivalent to writing a program to meet a specification.