M. Widera and C. Beierle. Function Types in Complete Type Inference. In Sharon Curtis and Kevin Hammond, editors, Proceedings of the 3rd Scottish Functional Programming Workshop, 2001.


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We study type checking that is complete in the sense that it accepts every program whose subexpressions can all be executed without raising a type error at runtime. In a complete type checker for every function call (f a) of a function f with an argument expression a of type t_a it is checked whether f is applicable to one of the possible values of a, i.e.\ whether <[t_a]> \cap dom(f) \not= Ø holds where <[t]> denotes the semantics of a type t. When approximating dom(f) by a type t_{in} it turns out that the usual function type constructor is not appropriate for complete type checking: for a function type t_f = t_{in} -> t_{out} of f the input type t_{in} is usually not guaranteed to contain all values of dom(f) and the test for common elements can erroneously fail. We therefore introduce an alternative notion of function types, called I/O-representation, where the input types cover a superset of the domain of the denoted functions. We show that this notion of function types fits into the framework of complete type checking much better than the usual function type constructor. Moreover, we argue that complete type checking overcomes the disadvantages of soft-typing approaches by enabling the rejection of programs instead of just raising a warning.

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