Programming with visual expressions

The lambda calculus is a formal symbolic term rewriting system that has been used for many years both as a mechanism for defining the semantics of programming languages and as the basis for functional programming languages. In this paper, we describe a completely visual representation for lambda expressions, VEX (Visual EXpressions), that has several advantages over traditional textual lambda calculus. Although VEX is designed as an expression-oriented component of VIPR (VIsual PRogramming language), it can also be used in teaching the concepts of the lambda calculus as a replacement for or augmentation to the teaching of traditional textual rewrite rules. Many semantic issues in the lambda calculus that are confusing to students, including substitution, free variables and binding, become apparent and explicit in VEX.