6.9 Conclusion
We have introduced the essence of functions: that they map arguments of their definition set into (i.e., yield) results of their range, and that they can be expressed (i.e., defined), named, applied and abstracted. We have also introduced the notion that functions have type — from (type of) definition set into (type of) range set. Together with the name of the function, this is called the signature of the function. We have seen that functions are either total or partial, and that functions can be further attributed as either being surjective, injective or bijective.
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6.10 Bibliographical Notes
H.R. Rogers: Theory of Recursive Functions and Effective Computability (McGraw-Hill, 1967)
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© 2006 Springer-Verlag Berlin Heidelberg
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(2006). Functions. In: Software Engineering 1. Texts in Theoretical Computer Science an EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31288-9_6
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