Type systems in programming languages are sets of rules that operate on the syntax of the language. The syntax includes expressions and types, and a type system defines the relationship between them. The typing relation, written as e:τ, represents that expression e has type τ. Typing rules capture the intuitive understanding of what expressions make sense and what do not. They can be used to construct formal proofs about the properties of a type system. Judgments can be interpreted as an algorithm for typechecking, mapping an expression to its type. Contexts are used to keep track of the types of variables in scope.
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