Church’s Semigroup Is Sq-Universal

Author Rick Statman

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Rick Statman
  • Carnegie Mellon University, Pittsburgh, PA, USA

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Rick Statman. Church’s Semigroup Is Sq-Universal. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 6:1-6:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We prove Church’s lambda calculus semigroup is sq-universal.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • lambda calculus
  • Church’s semigroup
  • sq-universal


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  1. Hendrik Pieter Barendregt. The Lambda Calculus - Its Syntax and Semantics, volume 103 of Studies in logic and the foundations of mathematics. North-Holland, 1985. Google Scholar
  2. Alonzo Church. The Calculi of Lambda Conversion. Princeton University Press, 1941. Google Scholar
  3. Haskell B. Curry and Robert Feys. Combinatory Logic, volume 1. North Holland, 1958. Google Scholar
  4. Mariangiola Dezani-Ciancaglini. Characterization of Normal Forms Possessing Inverse in the lambda-beta-eta-Calculus. Theor. Comput. Sci., 2(3):323-337, 1976. URL:
  5. Giuseppe Jacopini. A condition for identifying two elements of whatever model of combinatory logic. In Corrado Böhm, editor, Lambda-Calculus and Computer Science Theory, Proceedings of the Symposium Held in Rome, Italy, March 25-27, 1975, volume 37 of Lecture Notes in Computer Science, pages 213-219. Springer, 1975. URL:
  6. P. Neumann. The SQ-universality of some finitely presented groups. J. Austral. Math. Soc., 16:1-6, 1973. Google Scholar
  7. Richard Statman. Morphisms and Partitions of V-Sets. In Georg Gottlob, Etienne Grandjean, and Katrin Seyr, editors, Computer Science Logic, 12th International Workshop, CSL '98, Annual Conference of the EACSL, Brno, Czech Republic, August 24-28, 1998, Proceedings, volume 1584 of Lecture Notes in Computer Science, pages 313-322. Springer, 1998. URL:
  8. Richard Statman. Consequences of Jacopini’s Theorem: Consistent Equalities and Equations. In Jean-Yves Girard, editor, Typed Lambda Calculi and Applications, 4th International Conference, TLCA'99, L'Aquila, Italy, April 7-9, 1999, Proceedings, volume 1581 of Lecture Notes in Computer Science, pages 355-364. Springer, 1999. URL: