About the completeness of type systems

Kahrs, Stefan About the completeness of type systems. In: UNSPECIFIED. (Full text available)

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Abstract

The original purpose of type systems for programming languages was to prevent certain forms of run-time errors, like using a number as a function. Some type systems go as far as guaranteeing the absence of run-time errors, e.g. the type system of Standard ML. One can call such a type system ``sound''. This raises the question of the dual notion of completeness, i.e. is everything typable that does not have run-time errors? Or, to put it in another way: does the type system restrict the expressive power of the underlying implementation in an undesirable way? To make this rather vague idea precise we define an abstract notion of ``type system'', together with general notions of soundness and completeness. We examine several type systems for these properties, for instance λ^τ and PCF are both complete, but for very different reasons.

Item Type:	Conference or workshop item (UNSPECIFIED)
Uncontrolled keywords:	completeness, type systems, definability
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions:	Faculties > Sciences > School of Computing > Theoretical Computing Group
Depositing User:	Mark Wheadon
Date Deposited:	27 Aug 2009 19:29 UTC
Last Modified:	15 May 2014 15:30 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/21352 (The current URI for this page, for reference purposes)