Combinators in Array Languages
Combinators in Array Languages Raymond Smullyan’s "To Mock a Mockingbird" book's aviary of combinator birds implemented in APL-derived languages and the problem implementing the Sage bird (Fixed Point or Y combinator) in an eagerly evaluated language. Newer APLs support lazy evaluation. My eager language has a workaround for this. The Z combinator is the standard strict-language fix: wrap the self-application in one extra function layer (λv. x x v), so the recursion is a value (a delayed call) rather than an executing expression. sw-MLPL expresses that delay as a named partial — z_step/z_recur/applicative_sage — because the language has no anonymous lambdas. Z has no Smullyan name (and no zebra in the aviary, despite the letter). The book predates and ignores the strictness problem, so it has no applicative-order variant. "Z combinator" is programmer folklore for the eta-expanded Y