## Inductive, Projective, and Retractive Types (1993)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Howard93inductive,projective,,

author = {Brian T. Howard},

title = {Inductive, Projective, and Retractive Types},

institution = {},

year = {1993}

}

### OpenURL

### Abstract

We give an analysis of classes of recursive types by presenting two extensions of the simply-typed lambda calculus. The first language only allows recursive types with built-in principles of well-founded induction, while the second allows more general recursive types which permit non-terminating computations. We discuss the expressive power of the languages, examine the properties of reduction-based operational semantics for them, and give examples of their use in expressing iteration over large ordinals and in simulating both call-by-name and call-by-value versions of the untyped lambda calculus. The motivations for this work come from category theoretic models. 1 Introduction An examination of the common uses of recursion in defining types reveals that there are two distinct classes of operations being performed. The first class of recursive type contains what are generally known as the "inductive" types, as well as their duals, the "coinductive" or "projective" types. The distingui...