## Deliverables: A Categorical Approach to Program Development in Type Theory (1992)

Citations: | 24 - 1 self |

### BibTeX

@MISC{McKinna92deliverables:a,

author = {James Hugh McKinna},

title = {Deliverables: A Categorical Approach to Program Development in Type Theory},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC). This system contains a powerful programming language of higher-order primitive recursion and higher-order intuitionistic logic. It is supported by Pollack's versatile LEGO implementation, which I use extensively to develop the mathematical constructions studied here. I systematically investigate Burstall's notion of deliverable, that is, a program paired with a proof of correctness. This approach separates the concerns of programming and logic, since I want a simple program extraction mechanism. The \Sigma-types of the calculus enable us to achieve this. There are many similarities with the subset interpretation of Martin-Lof type theory. I show that deliverables have a rich categorical structure, so that correctness proofs may be decomposed in a principled way. The categorical combinators which I define in the system package up much logical bo...