Solving Equations in Lambda-Calculus

Abstract Part 1 reviews principal solvable and unsolvable equations and equation systems encountered in λ-calculus and Combinatory Logic. Particular emphasis is given to the solvability of discriminability, separability and X-separability problems. All these problems are special cases of (and are improved by) the predicate “F is X-weakly separable”, whose decidability is proved in part 2. The more general X-weak separability problem still remains open.