Call-By-Value λμ-calculus and Its Simulation by the Cut-Elimination Procedure for LKQ
نویسنده
چکیده
We show Call-By-Value(CBV) normalization forCND (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 λμ-calculus. A completely new term calculus for LKQ is presented in a style of classical extension of λ-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.
منابع مشابه
A Proof Theoretical Account of Continuation Passing Style
We study “classical proofs as programs” paradigm in CallBy-Value (CBV) setting. Specifically, we show the CBV normalization for CND (Parigot 92) can be simulated by the cut-elimination procedure for LKQ (Danos-Joinet-Schellinx 93), namely the q-protocol. We use proof-term assignment system to prove this fact. The term calculus for CND we use follows Parigot’s λμ-calculus with new CBV normalizat...
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