By A. R. D. Mathias, H. Rogers

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**Extra resources for Cambridge Summer School in Mathematical Logic, Cambridge, 1971**

**Sample text**

Antoy and M. Hanus sequence of tokens that remain to be parsed. The Extensions of [9] are a form of this pattern. The reference contains a comparison with the monadic approach. This pattern is not available in functional languages since they lack free variables. Logic languages typically return information by instantiating free variables passed as arguments to predicates, but predicates do not return information, except for succeeding. 2 Many-to-Many Name Intent Applicability Structure Many-to-many encode a many-to-many relation with a single simple function a relation is computed in both directions a non-deterministic function deﬁnes a one-to-many relation; a functional pattern deﬁnes the inverse relation Consequences avoid structures to deﬁne a relation Known uses See also We consider a many-to-many relation R between two sets A and B.

XPath can also be optimized (see [10] for more details). The rest of the paper is organized as follows. Section 2 brieﬂy introduces the XPath subset presented in [10]. M. Almendros-Jiménez et al. T OY. Section 4 shows how to use T OY for the optimization of XQuery. Finally, Section 5 presents some conclusions. XPath in T OY 2 This section introduces the functional-logic language T OY [22] and the subset of XPath that we intend to integrate with T OY, omitting all the feaures of XPath that are supported by T OY but not used in this paper, such as ﬁlters, abbreviations, attributes and preprocessing of reverse axes.

The deﬁnition of for relies on the non-deterministic function member deﬁned in Section 2. /. M. Almendros-Jiménez et al. /. name "item")==R can be tried. Let us remark that XPath expressions have been modiﬁed in XQuery as follows. A new operator <$– is deﬁned in terms of <–: infixr 35 <$-(<$--) :: string -> xPath -> xQuery (<$--) Doc Path = [(<--) Doc Path] The function <$– returns (non deterministically) unitary lists with the elements of the given document in the corresponding path. Therefore, XPath and for expressions have the same behavior in the T OY implementation of XQuery.