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Combinators in Array Languages

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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

HN · launched Sep 21, 2026 · 11 upvotes (top 38%) · 0 views

Niche: specialized algorithms and computing libraries · 230 launches, 4 in the last 7 days ▼ -73% · Explore this niche →

Category and tags
  • Horizontal
  • Dev tools
  • Developer
  • Not AI
  • Hobby / open-source project

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More like this: all 230 launches in specialized algorithms and computing libraries →

Could you build this?

No This is specialized theoretical computer science and language design research focusing on combinator calculus and fixed-point semantics within array-oriented programming paradigms.

What it would actually take: This project requires deep expertise in functional programming theory, lambda calculus, combinatory logic (Smullyan's SKI/B/C/W/Y birds), and interpreter internals of APL/BQN/J array languages. Implementing fixed-point combinators in eager evaluation requires designing special evaluation strategies, trampolining, or custom primitive AST rewriting rules within the language compiler.

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Competitors

Other products that read as similar to this one : 68 launches clear the similarity bar, closest 8 shown.

Attention rank: #27 of 69 (itself plus its competitors, highest first, normalized so YC and Product Hunt are compared fairly).

Launched 314 days after the earliest competitor.

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