S combinator ( $S \equiv λ x yz . x z (yz)$ )

In lambda calculus,

S \equiv λ x yz . x z (yz)

distributes its third argument to its first two arguments. In combinatory logic, its primitive constant satisfies

S A BC = A C (BC)

and implements the application clause of bracket abstraction.

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I combinator
Past exam of the computer science course of the University of Oxford / 2015 / Lambda calculus and types / 3 / a / Solution
Past exam of the computer science course of the University of Oxford / 2015 / Lambda calculus and types / 3 / b / Solution
Past exam of the computer science course of the University of Oxford / 2015 / Lambda calculus and types / 3 / c / Solution
Past exam of the computer science course of the University of Oxford / 2015 / Lambda calculus and types / 3 / d / Solution

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