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polymorphic lambda-calculus
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(Or "second order typed lambda-calculus"). An extension of
typed lambda-calculus allowing functions which take types as
parameters. E.g. the polymorphic function "twice" may be
twice = / t . (f :: t -@# t) . (x :: t) . f (f x)
(where "/" is an upper case Greek lambda and "(v :: T)" is
usually written as v with subscript T). The parameter t will
be bound to the type to which twice is applied, e.g.:
twice Int
takes and returns a function of type Int -@# Int. (Actual type
arguments are often written in square brackets [ ]). Function
twice itself has a higher type:
twice :: Delta t . (t -@# t) -@# (t -@# t)
(where Delta is an upper case Greek delta). Thus /
introduces an object which is a function of a type and Delta
introduces a type which is a function of a type. Polymorphic
lambda-calculus was invented by Jean-Yves Girard in 1971 and
independently by John C. Reynolds in 1974.