Concept

Arrow type

Modified just now
Books JourneyProgramming Language Theory Statuslearning Tags
  • formal system
  • language-feature-design
  • type theory

This generalization unifies simple function types, universal types (forallalpha.T\\forall\\alpha.T), and dependent function types under a single constructor.

  • In simple type systems: T1TT_1 \to T₂, classifying functions from T1T_1 to T2T_2, where the result type is independent of the input.
  • In Pure type systems: generalized to the Dependent type product Π(x:T1).T2\Pi(x:T_1).T_2, where the result type T2T_2 may depend on the input value xx.
  • The simple arrow T1T2T_1 \to T_2 is the special case where T2T_2 does not mention xx.

This generalization unifies simple function types, universal types (α.T\forall\alpha.T), and dependent function types under a single constructor.