Computer Science > Logic in Computer Science
[Submitted on 7 Jul 2020 (v1), last revised 14 May 2021 (this version, v4)]
Title:The Vectorial Lambda Calculus Revisited
View PDFAbstract:We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) has been originally designed for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and linear combinations of types are also types. In its first presentation, Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial Lambda Calculus supports the standard version of said property, answering a long standing issue. In addition we also introduce the concept of weight of types and terms, and prove a relation between the weight of terms and of its types.
Submission history
From: Alejandro Díaz-Caro [view email][v1] Tue, 7 Jul 2020 17:37:51 UTC (39 KB)
[v2] Wed, 8 Jul 2020 12:21:29 UTC (39 KB)
[v3] Tue, 27 Oct 2020 00:35:41 UTC (36 KB)
[v4] Fri, 14 May 2021 12:59:48 UTC (32 KB)
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