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The automatic deduction of the type of a program fragment

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A programming language implementation may perform type inference to compensate for the lack of explicitly declared type signatures such that type checking is still feasible. Typically, type inference happens at compile time. Consider, for example, the following function for negating Booleans in Language:Haskell:

not True = False
not False = True

The Language:Haskell type system is perfectly confident to infer, even without any type signature at hand, that not is of the following type:

not :: Bool -> Bool

Type inference becomes enormously more powerful, once higher-order functions are taken into account.


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