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2020•DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)Open access

The Call-By-Value Lambda-Calculus with Generalized Applications

José Espírito Santo

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Abstract

The lambda-calculus with generalized applications is the Curry-Howard counterpart to the system of natural deduction with generalized elimination rules for intuitionistic implicational logic. In this paper we identify a call-by-value variant of the system and prove confluence, strong normalization, and standardization. In the end, we show that the cbn and cbv variants of the system simulate each other via mappings based on extensions of the "protecting-by-a-lambda" compilation technique.

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What this paper is about

The lambda-calculus with generalized applications is the Curry-Howard counterpart to the system of natural deduction with generalized elimination rules for intuitionistic implicational logic. In this paper we identify a call-by-value variant of the system and prove confluence, strong normalization, and standardization. In the end, we show that the cbn and cbv variants of the system simulate each other via mappings based on extensions of the "protecting-by-a-lambda" compilation technique.

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Available abstract

The lambda-calculus with generalized applications is the Curry-Howard counterpart to the system of natural deduction with generalized elimination rules for intuitionistic implicational logic. In this paper we identify a call-by-value variant of the system and prove confluence, strong normalization, and standardization. In the end, we show that the cbn and cbv variants of the system simulate each other via mappings based on extensions of the "protecting-by-a-lambda" compilation technique.

Key concepts: Natural deduction, Church encoding, Curry–Howard correspondence, Typed lambda calculus, Calculus (dental), Confluence, Normalization (sociology), System F

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