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Occurs check : ウィキペディア英語版
Occurs check
In computer science, the occurs check is a part of algorithms for syntactic unification. It causes unification of a variable ''V'' and a structure ''S'' to fail if ''S'' contains ''V''.
==Application in theorem proving==

In theorem proving, unification without the occurs check can lead to unsound inference. For example, the Prolog goal
X = f(X)
will succeed, binding ''X'' to a cyclic structure which has no counterpart in the Herbrand universe.
As another example,
〔; here: p.143〕
without occurs-check, a resolution proof can be found for the non-theorem
〔Informally, and taking p(x,y) to mean e.g. "''x loves y''", the formula reads "''If everybody loves somebody, then a single person must exist that is loved by everyone.''"〕
(\forall x \exists y. p(x,y)) \rightarrow (\exists y \forall x. p(x,y)): the negation of that formula has the conjunctive normal form p(X,f(X)) \land \lnot p(g(Y),Y), with f and g denoting the Skolem function for the first and second existential quantifier, respectively; the literals p(X,f(X)) and p(g(Y),Y) are unifiable without occurs check, producing the refuting empty clause.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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