Well-going programs can be typed

Authors:
Stefan Kahrs
Affiliations:
University of Kent at Canterbury, Computing Laboratory, Canterbury, United Kingdom
Venue:
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Year:
2003

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Abstract

Our idiomatically objectionable title is a pun on Milner's "well-typed programs do not go wrong" -- because we provide a completeness result for type-checking rather than a soundness result. We show that the well-behaved functions of untyped PCF are already expressible in typed PCF: any equivalence class of the partial logical equivalence generated from the flat natural numbers in the model given by PCF's operational semantics is inhabited by a well-typed term.