Banana Algebra: Compositional syntactic language extension

We propose an algebra of languages and transformations as a means for ex-tending languages syntactically. The algebra provides a layer of high-level ab-stractions built on top of languages (captured by context-free grammars) andtransformations (captured by constructive catamorphisms).The algebra is self-contained in that any term of the algebra specifying atransformation can be reduced to a constant catamorphism, before the transfor-mation is run. Thus, the algebra comes “for free” without sacrificing the strongsafety and efficiency properties of constructive catamorphisms.The entire algebra as presented in the paper is implemented as the BananaAlgebra Tool which may be used to syntactically extend languages in an in-cremental and modular fashion via algebraic composition of previously definedlanguages and transformations. We demonstrate and evaluate the tool via sev-eral kinds of extensions.