Mirasyedioğlu, Şeref; Güyer, Tolga A symbolic and algebraic computation based lambda-Boolean reduction machine via PROLOG. (English) Zbl 1095.68751 Appl. Math. Comput. 176, No. 1, 65-75 (2006). Summary: In this paper we introduce a new lambda-Boolean reduction machine for lambda-Boolean and lambda-beta Boolean reductions in the context of lambda calculus and investigate the role of Church-Rosser properties and the functional computation model in symbolic and algebraic computation with induction. The algorithm which is improved for lambda-beta Boolean reduction is simulated by the efficient logic programming language Prolog. Cited in 1 ReviewCited in 1 Document MSC: 68W30 Symbolic computation and algebraic computation 03B40 Combinatory logic and lambda calculus 68N17 Logic programming 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68Q42 Grammars and rewriting systems Keywords:lambda calculus; lambda-Boolean reduction; symbolic computation; algebraic computation; Church-Rosser theorem; Prolog PDFBibTeX XMLCite \textit{Ş. Mirasyedioğlu} and \textit{T. Güyer}, Appl. Math. Comput. 176, No. 1, 65--75 (2006; Zbl 1095.68751) Full Text: DOI Link References: [1] Church, A., An unsolvable problem of elementary number theory, American Journal of Mathematics, 58, 345-363 (1936) · JFM 62.0046.01 [2] Warren, D. S., Computing with Logic: Logic Programming with Prolog (1986), Addison-Wesley, January [3] Abramson, H.; Dahl, V., Logic Grammars (1989), Springer-Verlag · Zbl 0672.68032 [4] Barendregt, H., The Lambda Calculus, its Syntax and Semantics (1984), North-Holland · Zbl 0551.03007 [5] Hindley, J. R.; Seldin, J. P., Introduction to Combinators and \(λ\)-Calculus (1986), Cambridge University Press · Zbl 0614.03014 [6] Kleene, S., A theory of positive integers in formal logic, American Journal of Mathematics, 57, 153-173 (1935), 219-244 · JFM 61.0055.02 [7] Mirasyedioğlu, Ş., \(λ\)-Boolean theory, International Logic Review, 35, 13-27 (1987) · Zbl 0656.03008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.