Call-by-Value λμ-calculus and Its Simulation by the Cut-Elimination Procedure for LKQ
BibTeX
@MISC{Ogata_call-by-valueλμ-calculus,
author = {Ichiro Ogata},
title = {Call-by-Value λμ-calculus and Its Simulation by the Cut-Elimination Procedure for LKQ},
year = {}
}
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Abstract
We show Call-By-Value(CBV) normalization for CND (Parigot 92) can be simulated by by cut-elimination for LKQ (Danos-JoinetSchellinx 93), namely q-protocol. For this, a new term calculus was made for each classical logic. A term calculus for CND is a CBV version of Parigot's #-calculus. A completely new term calculus for LKQ is presented in a style of classical extension of #-calculus with a let construct. We then define a translation from CND into LKQ and show how our version of CBV normalization procedure can be simulated by q-protocol. We claim that this translation-simulation relation is closely related to the familiar CBV CPS-translation. keywords: Constructive Classical Logic, Classical Natural Deduction, LKQ, Call-By-Value, CPS-translation, classical proof theory. 1
