Type inference discovers types consistent with a program's structure and typing context. In our examples, it introduces fresh type variables, generates equations from typing judgments, and solves them by type unification. For , if initially has unknown type and the result has fresh type , lambda application requires .

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Type inference is a feature of some programming languages that allows the compiler or interpreter to automatically deduce the types of expressions based on the context in which they are used, instead of requiring the programmer to explicitly specify types. This can lead to more concise and readable code, as it reduces the amount of boilerplate type annotations needed.