Solving Equations in the

-Calculus using Syntactic Encapsulation

Mayer Goldberg

September 1995

Abstract:

Syntactic encapsulation is a relation between an expression and one of its sub-expressions, that constraints how the given sub-expression can be used throughout the reduction of the expression. In this paper, we present a class of systems of equations, in which the right-hand side of each equation is syntactically encapsulated in the left-hand side. This class is general enough to allow equations to contain self-application, and to allow unknowns to appear on both sides of the equation. Yet such a system is simple enough to be solvable, and for a solution (though of course not its normal form) to be obtainable in constant time.

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