Abstract
We contribute to the syntactic study of F ≤, a variant of second order λ-calculus F which appears as a paradigmatic kernel language for polymorphism and subtyping. The type system of F ≤ has a maximum type Top and bounded quantification. We endow this language with the familiar β-rules (for terms and types), to which we add extensionality rules: the η-rules (for terms and types), and a rule (top) which equates all terms of type Top. These rules are suggested by the axiomatization of cartesian closed categories. We show that this theory βηtop≤ is decidable, by exhibiting an effectively weakly normalizing and confluent rewriting system for it. Our proof of confluence relies on the confluence of a corresponding system on F 1 (the extension of F with a terminal type), and follows a general pattern that we investigate for itself in a separate paper.
This work was carried on with the partial support of E.E.C., Esprit Basic Research Action 3003 CLICS.
This work was carried on with the partial support of E.E.C., Esprit Basic Research Action 3070 FIDE and of Italian C.N.R., P.F.I. “Sistemi informatici e calcolo parallelo”.
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Curien, PL., Ghelli, G. (1991). Subtyping + extensionality: Confluence of βηtop reduction in F≤ . In: Ito, T., Meyer, A.R. (eds) Theoretical Aspects of Computer Software. TACS 1991. Lecture Notes in Computer Science, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54415-1_72
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DOI: https://doi.org/10.1007/3-540-54415-1_72
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