An operational interpretation of coinductive types
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and generalization of the notion of productivity in term rewr...
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| Veröffentlicht in: | Logical methods in computer science Jg. 16, Issue 1 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Logical Methods in Computer Science e.V
01.01.2020
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| Schlagworte: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and generalization of the notion of productivity in term rewriting to a setting with higher-order functions and with data specified by nested higher-order inductive and coinductive definitions. Intuitively, we interpret lazy data structures in a higher-order functional language by potentially infinite terms corresponding to their complete unfoldings. We prove an approximation theorem which essentially states that if a term reduces to an arbitrarily large finite approximation of an infinite object in the interpretation of a coinductive type, then it infinitarily (i.e. in the "limit") reduces to an infinite object in the interpretation of this type. We introduce a sufficient syntactic correctness criterion, in the form of a type system, for finite terms decorated with type information. Using the approximation theorem, we show that each well-typed term has a well-defined interpretation in our semantics. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.23638/LMCS-16(1:11)2020 |