December 10, 2008

Alligator Eggs!

Some time ago I had already written about a nice visualization of lambda calculus called VEX (visual expressions). In VEX the variable bindings are made explicit by using connecting lines. In contrast, in conventional lambda calculus bindings are implicitly given by the names of the variables. From my experience this is difficult to understand for students, in particular if alpha conversion comes into play. Today I have seen an even nicer visualization for the representation and execution of lambda expressions called Alligator Eggs!.

For motivation, here is an example expression from the Alligator Eggs! website:

Very briefly: A hungry alligator is an abstraction, an old (=uncolored and non-hungry) alligator can be used for bracketing, and eggs represent variables. There is an eating rule, which corresponds to beta-reduction, and a color rule for over-cautious alpha-conversion. Finally, for clean-up, there is an old age rule, which says that if a pair of parentheses contains a single term, the parentheses can be removed.

I really look forward to empirical results whether this approach helps in teaching lambda calculus.