# polymorphic function

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Related to polymorphic function: polymer

## polymorphic function

n
(Computer Science) computing a function in a computer program that can deal with a number of different types of data
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The type fh is held abstract by encoding the client as a polymorphic function:
Intuitively, the independence of nonlocal procedures from local state corresponds to the parametricity of a polymorphic function whose type argument ranges over possible pieces of local state [Reynolds 1983; O'Hearn and Tennent 1995].
(The translation could be arranged so that each M* was a polymorphic function of type [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
A generic function, or polymorphic function as it is sometimes called, is one whose implementation depends on the types of its arguments.
For example, C++ provides mechanisms for user-defined compile time and run-time polymorphic functions, but Fortran does not provide any means for user-defined polymorphic operators.
This means that the checking rule will perform significantly better on polymorphic function types such as All (X) () [right arrow] (X [right arrow] X), where the result type mentions a polymorphic variable in both positive and negative positions.
The ability to eliminate variables in this way is a crucial reason for choosing the "Kernel" variant of F [is less than is equal] rather than the "full F [is less than is equal to]" variant where two polymorphic function types with different upper bounds for their type components are allowed to stand in the subtype relation under appropriate conditions; in the latter system, it can be shown that variables cannot always be eliminated in a most general way [Ghelli and Pierce 1998].
Polymorphic functions are written [Lambda][Alpha].e, where [Alpha] is the abstracted type, and e is the body of the polymorphic function.
In the absence of polymorphic functions, our approach to typing closure conversion is based on Minamide et al.
Such a function specifies a form of type-safe dynamic type dispatch, wherein a polymorphic function dispatches at run-time on the basis of type arguments.
The rule demonstrates that the typerec defines a polymorphic function of type [inverted]A[Alpha] [is less than]: [Rho].[Sigma] The kind constraint on [Alpha] restricts the domain of applicability of this function, to types for which the cases in dynamic type dispatch are defined.
Algorithm S does not attempt to find the right type schemes of polymorphic functions. Algorithm R, on the other hand, generates no new variables, but uses Mycroft iteration to resolve the type schemes of recursive functions.

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