; Department of Computer Science, University of Edinburgh, U.K.; 0
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. We give syntax and a PER-model semantics for a typed -calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtyping systems. Singleton types have applications in the use of type systems for specification and program extraction: given a program P we can form the very tight specification fPg which is met uniquely by P . Singletons integrate abbreviational definitions into a type system: the hypothesis x : fMg asserts x = M . The addition of singleton types is a nonconservative extension of familiar subtyping theories. In our system, more terms are typable and previously typable terms have more (non-dependent) types. 1 Introducing Singletons and Subtyping Type systems for current programming languages provide only coarse distinctions amongst data values: Real, Bool, String, etc. Constructive type theories ...
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In Eighth International Workshop on Computer Science Logic