In type theory a typing environment (or variable assignment) represents the association between variables names and data types. More formally an environment Γ{\displaystyle \Gamma } is a set or ordered list of pairs ⟨x,τ⟩{\displaystyle \langle x,\tau \rangle }, usually written as x:τ{\displaystyle x:\tau }, where x{\displaystyle x} is a variable and τ{\displaystyle \tau } its type.