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<Paper uid="E06-1048">
  <Title>Unifying Synchronous Tree-Adjoining Grammars and Tree Transducers via Bimorphisms</Title>
  <Section position="3" start_page="377" end_page="377" type="intro">
    <SectionTitle>
TION OF t1,...,tn INTO C, notated C[t1,...,tn], is
</SectionTitle>
    <Paragraph position="0"> defined inductively as follows:</Paragraph>
    <Paragraph position="2"> A tree t [?] T(F,X) is LINEAR if and only if no variable in X occurs more than once in t.</Paragraph>
    <Paragraph position="3"> We will use a notation akin to BNF to specify equations defining functional programs of various sorts. As an introduction to the notation we will use, here is a grammar defining trees over a ranked alphabet and variables (essentially identically to the definition given above):</Paragraph>
    <Paragraph position="5"> The notation allows definition of classes of expressions (e.g., F(n)) and specifies metavariables over them (f(n)). These classes can be primitive (F(n)) or defined (X), even inductively in terms of other classes or themselves (T(F,X)). We use the metavariables and subscripted variants on the right-hand side to represent an arbitrary element of the corresponding class. Thus, the elements t1,...,tm stand for arbitrary trees in T(F,X), and x an arbitrary variable in X. Because numerically subscripted versions of x appear explicitly on the right hand side of the rule defining variables, numerically subscripted variables (e.g., x1) on the right-hand side of all rules are taken to refer to the specific elements of x, whereas otherwise subscripted elements (e.g., xi) are taken generically.</Paragraph>
  </Section>
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