Typing environment

In type theory, a typing environment (or typing context) represents the association between variable names and data types.

More formally, an environment

is a set or ordered list of pairs

The judgement is read as "

[1] For each function body type checks: Typing Rules Example:

{\displaystyle {\begin{array}{c}\Gamma \vdash b:Bool,\Gamma \vdash t_{1}:\tau ,\Gamma \vdash t_{2}:\tau \\\hline \Gamma \vdash ({\text{if}}(b)t_{1}{\text{else}}t_{2}):\tau \\\end{array}}}

In statically typed programming languages, these environments are used and maintained by typing rules to type check a given program or expression.

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