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A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X.
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Plus d’exemples (3)
1967 [John Wiley & Sons], Stephen Cole Kleene, Mathematical Logic, 2002, Dover, page 244, The Church-Turing thesis applies to partial functions on the same grounds as to total functions (§ 41).
1991, Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella (editors), Algebraic System Specification and Development: A Survey and Annotated Bibliography, Springer, LNCS 501, page 15, Nowadays it seems quite clear that if algebraic specifications are to be used as a powerful and realistic tool for the development of complex systems they should permit the specification of partial functions. […] There are essentially two ways of specifying partial functions.
2006, Paulo Oliva, Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, John V. Tucker (editors), Logical Approaches to Computational Barriers: 2nd Conference on Computability in Europe, Proceedings, Springer, LNCS 3988, page 432, In the following σ and τ will denote finite partial functions from N to N , i.e. partial functions which are defined on a finite domain. A partial function which is everywhere undefined is denoted by ⟨⟩, whereas a partial function defined only at position k (with value n) is denoted by ⟨k,n⟩.