Fixed Point Intersection or involution in #calculus ever wonder how #lambdacalculus handles such cases , plain vanilla lc doesn't butits fixed point combinator : a means to allow for recursive definitions.
untyped lambda calculus, the function to apply the fixed-point combinator to may be expressed using an encoding, like Church encoding. In this case particular lambda terms (which define functions) are considered as values. "Running" (beta reducing) the fixed-point combinator on the encoding gives a lambda term for the result, which may then be interpreted as fixed-point value.
In lambda calculus function (or term) is an implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition of a fixed-point combinator.
A combinator is a closed lambda expression, meaning that it has no free variables. The combinators may be combined to direct values to their correct places in the expression without ever naming them as variable