## Propositional Functions and Families of Types (1989)

Venue: | In Workshop on Programming Logic |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Smith89propositionalfunctions,

author = {Jan M. Smith},

title = {Propositional Functions and Families of Types},

booktitle = {In Workshop on Programming Logic},

year = {1989},

pages = {140--159}

}

### OpenURL

### Abstract

Introduction In order to capture some of the programmers errors, several computer languages, like Pascal and ML, are equipped with a type system. Using the Curry-Howard interpretation of propositions as types [3, 8], or as we shall say here, propositions as sets, a type system can be made strong enough to be used to specify the task a program is supposed to do. This is one of the basis for Martin-Lof's suggestion in [11] to use his formulation of type theory for programming; his ideas are exploited in [14] and there are several computer implementations of type theory [4, 16]. Similar ideas are also behind Coquand and Huet's calculus of constructions [2]. The idea of propositions as sets is closely related to the intuitionistic explanations of the logical constants given by Heyting [7]. In Martin-Lof's type theory, the interpretation of propositions as sets is fundamental since the notions of proposition and set are identical. So a logical constant is definitionally equal to th

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