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Strong normalization proofs by CPS-translations. (English) Zbl 1185.68625
Summary: This paper proposes a new proof method for strong normalization of classical natural deduction and calculi with control operators. For this purpose, we introduce a new CPS-translation, continuation and garbage passing style \((CGPS )\) translation. We show that this CGPS-translation method gives simple proofs of strong normalization of \(\lambda \mu ^{\rightarrow \wedge \vee \perp }\), which is introduced in [P. de Groote, in: Typed lambda calculi and applications. 5th international conference, TLCA 2001, Kraków, Poland, May 2–5, 2001. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2044, 182–196 (2001; Zbl 0981.03027)] by de Groote and corresponds to the classical natural deduction with disjunctions and permutative conversions.

MSC:
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B40 Combinatory logic and lambda calculus
68N18 Functional programming and lambda calculus
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