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Shine On You Crazy Diamond

Dependent type theory illuminated with one paragraph (Theorem Proving in Lean):

This is an instance of a Pi type, or dependent function type. Given α : Type and β : α → Type, think of β as a family of types over α, that is, a type β a for each a : α. In that case, the type Π x : α, β x denotes the type of functions f with the property that, for each a : α, f a is an element of β a. In other words, the type of the value returned by f depends on its input.


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Good mathematicians see analogies between theorems;
great mathematicians see analogies between analogies.

-Banach

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