Programming Language Theory Flashcard

What is the definition of the fixed-point combinator?

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Deckpure-lambda-calculus

Question

What is the definition of the fixed-point combinator?

Answer

A fixed-point combinator is a function that finds the fixed-point of any given function regarding the Evaluation/Reduction relation.

That is, given $fix$ as a fixed-point combinator and $f$ as any arbitrary function, we have:

fix f \to^{*} f (fix f)