## Paper: Partial Objects In Constructive Type Theory (at LICS 1987)

**Robert L. Constable Scott F. Smith**

### Abstract

Constructive type theories generally treat only total functions; partial functions present serious difficulties. In this paper, a theory of partial objects is given which puts partial functions in a general context. Semantic foundations for the theory are given in terms of a theory of inductive relations. The domain of convergence of a partial function is exactly characterized by a predicate within the theory, allowing for abstract reasoning about termination. Induction principles are given for reasoning about these functions, and comparisons are made to the domain theoretic account of LCF. Finally, an undecidability result is presented to suggest connections to a subset of recursive function theory.

### BibTeX

@InProceedings{ConstableSmith-PartialObjectsInCon, author = {Robert L. Constable and Scott F. Smith}, title = {Partial Objects In Constructive Type Theory}, booktitle = {Proceedings of the Second Annual IEEE Symposium on Logic in Computer Science (LICS 1987)}, year = {1987}, month = {June}, pages = {183--193}, location = {Ithaca, NY, USA}, publisher = {IEEE Computer Society Press} }