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Lexikon


occurs check


A feature of some implementations of ref="module.php?name=Lexikon&file=search&eid=1&query=unification">unification which causes unification of a ref="module.php?name=Lexikon&file=search&eid=1&query=logic variable">logic variable V and a structure S to fail if S contains V. Binding a variable to a structure containing that variable results in a cyclic structure which may subsequently cause unification to loop forever. Some implementations use extra pointer comparisons to avoid this. Most implementations of ref="module.php?name=Lexikon&file=search&eid=1&query=Prolog">Prolog do not perform the occurs check for reasons of efficiency. Without occurs check the ref="module.php?name=Lexikon&file=search&eid=1&query=complexity">complexity of ref="module.php?name=Lexikon&file=search&eid=1&query=unification">unification is O(min(size(term1), size(term2))) with occurs check it' s O(max(size(term1), size(term2))) In ref="module.php?name=Lexikon&file=search&eid=1&query=theorem proving">theorem proving unification without the occurs check can lead to unsound inference. For example, in ref="module.php?name=Lexikon&file=search&eid=1&query=Prolog">Prolog it is quite valid to write X = f(X). which will succeed, binding X to a cyclic structure. Clearly however, if f is taken to stand for a function rather than a ref="module.php?name=Lexikon&file=search&eid=1&query=constructor">constructor, then the above equality is only valid if f is the ref="module.php?name=Lexikon&file=search&eid=1&query=identity function">identity function. Weijland calls unification without occur check, "complete unification". The reference below describes a complete unification algorithm in terms of Colmerauer' s consistency algorithm. ["Semantics for Logic Programs without Occur Check", W.P. Weijland, Theoretical Computer Science 71 (1990) pp 155-174]. (1996-01-11)

In addition suitable contents:
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