For the electronic dance music artist, see Ferry Corsten. System F, also known as the polymorphic lambda calculus or the second-order lambda calculus, is a typed lambda calculus. It was discovered independently by the logician Jean-Yves Girard and the computer scientist John C. Reynolds. System F formalizes the notion of parametric polymorphism in programming languages. Just as the lambda calculus has variables ranging over functions, and binders for them,the second-order lambda calculus has variables ranging over types, and binders for them. As an example, the fact that the identity function can have any type of the form A? Awould be formalized in System F as the judgement vdash Lambdaalpha. lambda x^alpha.x: forallalpha.alpha to alpha where ? is a type variable. Under the Curry-Howard isomorphism

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