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Kleene equality

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In mathematics, Kleene equality,[1] or strong equality, () is an equality operator on partial functions, that states that on a given argument either both functions are undefined, or both are defined and their values on that arguments are equal.

For example, if we have partial functions and , means that for every :[2]

  • and are both defined and
  • or and are both undefined.

Some authors[3] are using "quasi-equality", which is defined like this: where the down arrow means that the term on the left side of it is defined. Then it becomes possible to define the strong equality in the following way:

References

[edit]
  1. ^ "Kleene equality in nLab". ncatlab.org.
  2. ^ Cutland 1980, p. 3.
  3. ^ Farmer, William M.; Guttman, Joshua D. (2000). "A Set Theory with Support for Partial Functions". Studia Logica: An International Journal for Symbolic Logic. 66 (1): 59–78. JSTOR 20016214.