Brett Victor has invented an Alligator Eggs game (very loosely resembling Conway's Game of Life), using formal rules to determine feeding and breeding patterns for alligators and their eggs, but the game represents the *untyped* lambda calculus: Alligator Eggs! http://worrydream.com/AlligatorEggs/ I am interested in adapting this to the *simply typed* lambda calculus with Curry-style typing, to aid students of Haskell. Brett Victor's game currently aids students of LISP, and I think that it would be helpful to have a Haskell counterpart (see http://wadler.blogspot.com/2007/05/oh-no-alligators.html for a comment on how the Alligator Eggs game has been used by EE students at Caltech in learning LISP): Simply typed lambda calculus - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus Thereafter, I would like to create a new entry for this Haskell version of Alligator Eggs on HaskellWiki, and create a link to it under a new subsection, "Board Games," under the current "Learning Haskell" category: http://www.haskell.org/haskellwiki/Learning_Haskell In Brett Victor's version, the following representations hold: * a hungry alligator: lambda abstraction * an old alligator: a pair of parentheses * an egg: a variable * the Eating Rule: beta-reduction * the Color Rule: (over-cautious) alpha-conversion * the Old Age Rule: the rule that a pair of parentheses containing a single term may be removed However, in thinking about how to adapt the game, I am not quite sure how to incorporate the representation of "->" (function type): * ???: "->" (function type) What ideas, if any, would anybody have on how "->" (function type) could be represented in a simply-typed lambda calculus version of Brett Victor's Alligator Eggs? Benjamin L. Russell