On the Representation of Semigroups and Other Congruences in the Lambda Calculus
Rick Statman · Electronic Notes in Theoretical Computer Science · 2016
We show that every semigroup with an RE word problem can be pointwise represented in the lambda calculus. In addition, we show that the free monoid generated by an arbitrary RE subset of combinators can be represented as the monoid of all terms which fix a finite set of points.