Intensional properties of functions—such as how a computation proceeds, not just its input-output behavior—are not preserved under compositional closure, as Kreisel's squeezing arguments reveal.

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Compositional closure(describes what happens when you put functions together): The idea that if you combine or build things together in a certain way, the results should follow the same rules or properties as the parts you started with.
Georg Kreisel(as a key figure in philosophy of mathematics): A 20th-century mathematician and logician who studied how informal mathematical reasoning relates to formal logical systems, and argued that intuitive understanding cannot be completely separated from formal proof.
Input-output behavior(contrasted with intensional properties to show the difference between results and methods): What goes in and what comes out of a process, without caring about the steps in between.
Intensional properties(as opposed to extensional properties, which only care about results): Features of something that depend on *how* it works or what it means, not just what it produces—like how a recipe matters, not just the final dish.

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