Computer Science > Logic in Computer Science
[Submitted on 28 Nov 2019 (v1), last revised 7 May 2021 (this version, v5)]
Title:A Formal System for the Universal Quantification of Schematic Variables
View PDFAbstract:We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$ accompanied by other practically useful constructions like explicit substitutions and expected type annotations. The calculus stands just on two notions, i.e., bound rt-reduction and parametric validity, and has the expressive power of $\lambda\rightarrow$. Thus, while not aiming at being a logical framework by itself, it does enjoy many desired invariants of logical frameworks including confluence of reduction, strong normalization, preservation of type by reduction, decidability, correctness of types and uniqueness of types up to conversion. This calculus belongs to the $\lambda\delta$ family of formal systems, which borrow some features from the pure type systems and some from the languages of the Automath tradition, but stand outside both families. In particular, the calculus includes and evolves two earlier systems of this family. Moreover, a machine-checked specification of its theory is available.
Submission history
From: Ferruccio Guidi Dr [view email][v1] Thu, 28 Nov 2019 15:23:52 UTC (448 KB)
[v2] Wed, 25 Mar 2020 16:34:42 UTC (400 KB)
[v3] Wed, 28 Oct 2020 16:04:40 UTC (48 KB)
[v4] Wed, 16 Dec 2020 16:12:34 UTC (51 KB)
[v5] Fri, 7 May 2021 22:43:23 UTC (52 KB)
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