Binding operators in type-theory of algorithms for algorithmic binding of functional neuro-receptors

This paper is on a new approach to mathematics of the notion of algorithm. We extend the higher-order, type-theory of acyclic recursion, i.e., of typed, state-dependent algorithms, which was originally introduced by Moschovakis in [1]. We introduce the concept of recursive λ-binding of argument slots across a sequence of mutually recursive assignments. The primary applications of the extended theory are to computational semantics of formal and natural languages, and to computational neuroscience. We investigate some properties of algorithmic equivalence of functions and relations that bind argument slots of other functions and relations across the recursion operator acting via mutually recursive assignments.