Abstract
The framework Pure Type System (\(\mathcal{PTS}\)) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist some acute problems that make it difficult for \(\mathcal{PTS}\) to accommodate many common realistic programming features such as general recursion, recursive types, effects (e.g., exceptions, references, input/output), etc. In this paper, we propose a new framework Applied Type System (\(\mathcal{ATS}\)) to allow for designing and formalizing type systems that can readily support common realistic programming features. The key salient feature of \(\mathcal{ATS}\) lies in a complete separation between statics, in which types are formed and reasoned about, and dynamics, in which programs are constructed and evaluated. With this separation, it is no longer possible for a program to occur in a type as is otherwise allowed in \(\mathcal{PTS}\). We present not only a formal development of \(\mathcal{ATS}\) but also mention some examples in support of using \(\mathcal{ATS}\) as a framework to form type systems for practical programming.
Partially supported by NSF grants no. CCR-0224244 and no. CCR-0229480
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Xi, H. (2004). Applied Type System. In: Berardi, S., Coppo, M., Damiani, F. (eds) Types for Proofs and Programs. TYPES 2003. Lecture Notes in Computer Science, vol 3085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24849-1_25
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DOI: https://doi.org/10.1007/978-3-540-24849-1_25
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