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  <tmdoc-title|Matching regular expressions>

  Regular expressions naturally generalize from strings to trees and allow to
  test whether a given tree matches a given pattern. <TeXmacs> implements the
  primitives <scm|match?> and <scm|match> for this purpose, which also
  provide support for wildcards, user-defined grammars and more.

  <\explain>
    <scm|(match? <scm-arg|expr> <scm-arg|pattern>)><explain-synopsis|check
    whether a scheme expression satisfies a pattern>
  <|explain>
    This function determines whether a scheme expression <scm-arg|expr>
    satisfies a given <scm-arg|pattern>. It will be detailed below how to
    form valid patterns. The pattern may contain named wildcards, in case of
    success, we return a list with matches for these wildcards. In case of
    failure, we return<nbsp><scm|#f>. The expression <scm|expr> may contain
    trees, in which case we understand that such tree subexpressions should
    match their scheme counterparts. For instance, <scm|(match? (tree "x")
    "x<name|">)> will return<nbsp><scm|(())>, whereas <scm|(match? (tree "x")
    "y<name|">)> returns <scm|#f>.
  </explain>

  <\explain>
    <scm|(match <scm-arg|l> <scm-arg|pattern>
    <scm-arg|bindings>)><explain-synopsis|solutions to a given pattern under
    bindings>
  <|explain>
    Given a list <scm-arg|l> of scheme expressions, a <scm-arg|pattern> with
    free variables and an association list of <scm-arg|bindings>, this
    routine determines all substitutions of free variables by values
    (extending the given <scm-arg|bindings>), for which <scm-arg|l> matches
    the <scm-arg|pattern>.
  </explain>

  <\explain>
    <scm|(define-regexp-grammar <scm-args|rules>)><explain-synopsis|user
    defined matching grammars>
  <|explain>
    Given a list of rules of the form <scm|(:<scm-arg|var>
    <scm-arg|pattern-1> ... <scm-arg|pattern-n>)>, this instruction defines a
    new terminal symbol <scm|:<scm-arg|var>> for each such rule, which
    matches the disjunction of the patterns <scm-arg|pattern-1> until
    <scm-arg|pattern-n>. This terminal symbol can then be used as an
    abbreviation in matching patterns. Grammar rules may be interdependent.
    See example below.
  </explain>

  Valid patterns are formed in the following ways:

  <\explain>
    <scm-arg|leaf><explain-synopsis|symbols, strings, etc.>
  <|explain>
    A <scm-arg|leaf> is only matched against itself.
  </explain>

  <\explain>
    <scm|(<scm-arg|pattern-1> ... <scm-arg|pattern-n>)><explain-synopsis|lists>
  <|explain>
    In the case when lists <scm|l-1> until <scm|l-n> match
    <scm-arg|pattern-1> until <scm-arg|pattern-n>, their concatenation
    matches the pattern <scm|(<scm-arg|pattern-1> ... <scm-arg|pattern-n>)>.
  </explain>

  <\explain>
    <scm|:%1>, <scm|:%2>, <scm|:%3> ..., <scm|:*><explain-synopsis|wildcards>
  <|explain>
    The wildcard <scm|:%n>, where <scm|n> is a number matches any list of
    length <scm|n>. The wildcard <scm|:*> matches any list, including the
    empty list.
  </explain>

  <\explain>
    <scm|'<scm-arg|var>><explain-synopsis|variables>
  <|explain>
    This pattern attempts to bind the variable <scm-arg|var> against the
    expression. If <scm-arg|var> is used only once, then it essentially
    behaves as a wildcard. More generally, it can be used to form patterns
    with identical subexpressions. For instance, the pattern <scm|(frac 'x
    'x)> will match all fractions <math|<frac|x|x>>.
  </explain>

  <\explain>
    <scm|:<scm-arg|var>><explain-synopsis|user-provided grammar rules>
  <|explain>
    In the case when <scm|:<scm-arg|var>> is a user-provided terminal symbol
    (see <scm|define-regexp-grammar> above), this pattern matches the
    corresponding grammar.
  </explain>

  <\explain>
    <scm|:<scm-arg|pred?>><explain-synopsis|arbitrary <scheme> predicates>
  <|explain>
    Given a <scheme> predicate <scm-arg|pred?>, such as <scm|string?>, this
    pattern matches any scheme expression which satisfies the predicate.
  </explain>

  <\explain>
    <scm|(:not <scm-arg|pattern>)>

    <scm|(:or <scm-arg|pattern-1> ... <scm-arg|pattern-n>)>

    <scm|(:and <scm-arg|pattern-1> ... <scm-arg|pattern-n>)><explain-synopsis|logical
    operations>
  <|explain>
    Negation, disjunction and conjunction of patterns.
  </explain>

  <\explain>
    <scm|(:repeat <scm-arg|pattern>)><explain-synopsis|repetition>
  <|explain>
    Given lists <scm|l-1> until <scm|l-n> which match <scm-arg|pattern>,
    their concatenation matches the repetition <scm|(:repeat
    <scm-arg|pattern>)>. In particular, the empty list is matched.
  </explain>

  <\explain>
    <scm|(:group <scm-arg|pattern-1> ... <scm-arg|pattern-n>)><explain-synopsis|grouping>
  <|explain>
    Groups a concatenation of patterns into a new list patterns. For
    instance, all lists of the form <scm|(a b a b ... a b)> are matched by
    <scm|(:repeat (:group a b))>, whereas <scm|(:repeat (a b))> rather
    matches all lists of the form <scm|((a b) (a b) ... (a b))>.
  </explain>

  <\explain>
    <scm|(:quote <scm-arg|expr>)><explain-synopsis|quotation>
  <|explain>
    Only matches a given expression <scm-arg|expr>.
  </explain>

  <\example>
    The tree

    <\scm-code>
      (define t '(foo (bar "x") (bar "y") (option "z")))
    </scm-code>

    matches the pattern <scm|(foo (:repeat (bar :%1)) :*)>, but not <scm|(foo
    (:repeat (bar 'x)) :*)>. The call <scm|(match t '(foo 'x 'y :*))> will
    return <scm|(((x . (bar "x")) (y . (bar "y"))))>. Notice that <scm|(x .
    (bar "x"))> will be displayed as <scm|(x bar "x")>:

    <\session|scheme|default>
      <\input|Scheme] >
        (define t '(foo (bar "x") (bar "y") (option "z")))
      </input>

      <\unfolded-io|Scheme] >
        (match? t '(foo 'x 'y :*))
      <|unfolded-io>
        (((y bar "y") (x bar "x")))
      </unfolded-io>
    </session>
  </example>

  <\example>
    Consider the grammar

    <\scm-code>
      (define-regexp-grammar

      \ \ (:a a b c)

      \ \ (:b (:repeat :a)))
    </scm-code>

    Then the list <scm|(a b x y c a a)> matches the pattern <scm|(:b :%2
    :b)>.
  </example>

  <tmdoc-copyright|2007|Joris van der Hoeven>

  <tmdoc-license|Permission is granted to copy, distribute and/or modify this
  document under the terms of the GNU Free Documentation License, Version 1.1
  or any later version published by the Free Software Foundation; with no
  Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
  Texts. A copy of the license is included in the section entitled "GNU Free
  Documentation License".>
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