David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 70 (2):536 - 556 (2005)
Symmetic combinatory logic with the symmetric analogue of a combinatorially complete base (in the form of symmetric λ-calculus) is known to lack the Church-Rosser property. We prove a much stronger theorem that no symmetric combinatory logic that contains at least two proper symmetric combinators has the Church-Rosser property. Although the statement of the result looks similar to an earlier one concerning dual combinatory logic, the proof is different because symmetric combinators may form redexes in both left and right associated terms. Perhaps surprisingly, we are also able to show that certain symmetric combinatory logics that include just one particular constant are not confluent. This result (beyond other differences) clearly sets apart symmetric combinatory logic from dual combinatory logic, since all dual combinatory systems with a single combinator or a single dual combinator are Church-Rosser. Lastly, we prove that a symmetric combinatory logic that contains the fixed point and the one-place identity combinator has the Church-Rosser property
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Katalin Bombó (2005). The Church-Rosser Property in Symmetric Combinatory Logic. Journal of Symbolic Logic 70 (2):536 - 556.
Katalin Bimbó (2003). The Church-Rosser Property in Dual Combinatory Logic. Journal of Symbolic Logic 68 (1):132-152.
Katalin Bimb� (2003). The Church-Rosser Property in Dual Combinatory Logic. Journal of Symbolic Logic 68 (1):132 - 152.
Katalin Bimbó (2000). Investigation Into Combinatory Systems with Dual Combinators. Studia Logica 66 (2):285-296.
M. W. Bunder (1988). Arithmetic Based on the Church Numerals in Illative Combinatory Logic. Studia Logica 47 (2):129 - 143.
Katalin Bimbó (2004). Semantics for Dual and Symmetric Combinatory Calculi. Journal of Philosophical Logic 33 (2):125-153.
Kenneth Loewen (1968). The Church Rosser Theorem for Strong Reduction in Combinatory Logic. Notre Dame Journal of Formal Logic 9 (4):299-302.
E. G. K. López-Escobar (1990). Remarks on the Church-Rosser Property. Journal of Symbolic Logic 55 (1):106-112.
Katalin Bimbó (2012). Combinatory Logic: Pure, Applied, and Typed. Taylor & Francis.
C. Barry Jay (1991). Coherence in Category Theory and the Church-Rosser Property. Notre Dame Journal of Formal Logic 33 (1):140-143.
Barkley Rosser (1942). New Sets of Postulates for Combinatory Logics. Journal of Symbolic Logic 7 (1):18-27.
Yuichi Komori, Naosuke Matsuda & Fumika Yamakawa (2014). A Simplified Proof of the Church–Rosser Theorem. Studia Logica 102 (1):175-183.
J. Roger Hindley (1972). Introduction to Combinatory Logic. Cambridge [Eng.]University Press.
Haskell B. Curry (1958). Combinatory Logic. Amsterdam, North-Holland Pub. Co..
Katalin Bimbó, Combinatory Logic. Stanford Encyclopedia of Philosophy.
Sorry, there are not enough data points to plot this chart.
Added to index2010-08-24
Recent downloads (6 months)0
How can I increase my downloads?