5 research outputs found
On properties of -terms
-terms are built from the combinator alone defined by , which is well known as a function composition operator. This
paper investigates an interesting property of -terms, that is, whether
repetitive right applications of a -term cycles or not. We discuss
conditions for -terms to have and not to have the property through a sound
and complete equational axiomatization. Specifically, we give examples of
-terms which have the cyclic property and show that there are infinitely
many -terms which do not have the property. Also, we introduce another
interesting property about a canonical representation of -terms that is
useful to detect cycles, or equivalently, to prove the cyclic property, with an
efficient algorithm.Comment: Journal version in Logical Methods in Computer Science. arXiv admin
note: substantial text overlap with arXiv:1703.1093
On properties of -terms
-terms are built from the combinator alone defined by , which is well known as a function composition operator. This
paper investigates an interesting property of -terms, that is, whether
repetitive right applications of a -term cycles or not. We discuss
conditions for -terms to have and not to have the property through a sound
and complete equational axiomatization. Specifically, we give examples of
-terms which have the cyclic property and show that there are infinitely
many -terms which do not have the property. Also, we introduce another
interesting property about a canonical representation of -terms that is
useful to detect cycles, or equivalently, to prove the cyclic property, with an
efficient algorithm
On Repetitive Right Application of B-Terms
B-terms are built from the B combinator alone defined by B == lambda f.lambda g.lambda x. f~(g~x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications of a B-term cycles or not. We discuss conditions for B-terms to have and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of B-terms which have the property and show that there are infinitely many B-terms which do not have the property. Also, we introduce a canonical representation of B-terms that is useful to detect cycles, or equivalently, to prove the property, with an efficient algorithm