1 Patterns

(require redex/reduction-semantics)

This section covers Redex’s pattern language, used in many of Redex’s forms.

Note that pattern matching is caching (including caching the results of side-conditions). This means that once a pattern has matched a given term, Redex assumes that it will always match that term.

This is the grammar for the Redex pattern language. Non-terminal references are wrapped with angle brackets; otherwise identifiers in the grammar are terminals.

pattern		=		any
		|		number
		|		natural
		|		integer
		|		real
		|		string
		|		variable
		|		(variable-except <id> ...)
		|		(variable-prefix <id>)
		|		variable-not-otherwise-mentioned
		|		hole
		|		symbol
		|		(name <id> <pattern>)
		|		(in-hole <pattern> <pattern>)
		|		(hide-hole <pattern>)
		|		(side-condition <pattern> guard)
		|		(cross <id>)
		|		(<pattern-sequence> ...)
		|		<racket-constant>
pattern-sequence		=		<pattern>
		|		... ; literal ellipsis
		|		..._id

• The any pattern matches any sexpression. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The number pattern matches any number. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The natural pattern matches any exact non-negative integer. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The integer pattern matches any exact integer. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The real pattern matches any real number. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The string pattern matches any string. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The variable pattern matches any symbol. This pattern may also be suffixed with an underscore and another identifier, in which case they bind the full name (as if it were an implicit name pattern) and match the portion before the underscore.

• The variable-except pattern matches any symbol except those listed in its argument. This is useful for ensuring that keywords in the language are not accidentally captured by variables.

• The variable-prefix pattern matches any symbol that begins with the given prefix.

• The variable-not-otherwise-mentioned pattern matches any symbol except those that are used as literals elsewhere in the language.

• The hole pattern matches anything when inside the first argument to an in-hole pattern. Otherwise, it matches only a hole.

• The symbol pattern stands for a literal symbol that must match exactly, unless it is the name of a non-terminal in a relevant language or contains an underscore.

  If it is a non-terminal, it matches any of the right-hand sides of that non-terminal. If the non-terminal appears twice in a single pattern, then the match is constrained to expressions that are the same, unless the pattern is part of a grammar, in which case there is no constraint.

  If the symbol is a non-terminal followed by an underscore, for example e_1, it is implicitly the same as a name pattern that matches only the non-terminal, (name e_1 e) for the example. Accordingly, repeated uses of the same name are constrainted to match the same expression.

  If the symbol is a non-terminal followed by _!_, for example e_!_1, it is also treated as a pattern, but repeated uses of the same pattern are constrained to be different. For example, this pattern:

  (e_!_1 e_!_1 e_!_1)

  matches lists of three es, but where all three of them are distinct.

  Unlike a _ pattern, the _!_ patterns do not bind names.

  If _ names and _!_ are mixed, they are treated as separate. That is, this pattern (e_1 e_!_1) matches just the same things as (e e), but the second doesn’t bind any variables.

  If the symbol otherwise has an underscore, it is an error.

• The pattern (name symbol pattern) matches pattern and binds using it to the name symbol.

• The (in-hole pattern pattern) pattern matches the first pattern. This match must include exactly one match against the second pattern. If there are zero matches or more than one match, an exception is raised.

  When matching the first argument of in-hole, the hole pattern matches any sexpression. Then, the sexpression that matched the hole pattern is used to match against the second pattern.

• The (hide-hole pattern) pattern matches what the embedded pattern matches but if the pattern matcher is looking for a decomposition, it ignores any holes found in that pattern.

• The (side-condition pattern guard) pattern matches what the embedded pattern matches, and then the guard expression is evaluated. If it returns #f, the pattern fails to match, and if it returns anything else, the pattern matches. Any occurrences of name in the pattern (including those implicitly there via _ pattersn) are bound using term-let in the guard.

• The (cross symbol) pattern is used for the compatible closure functions. If the language contains a non-terminal with the same name as symbol, the pattern (cross symbol) matches the context that corresponds to the compatible closure of that non-terminal.

• The (pattern-sequence ...) pattern matches a sexpression list, where each pattern-sequence element matches an element of the list. In addition, if a list pattern contains an ellipsis, the ellipsis is not treated as a literal, instead it matches any number of duplications of the pattern that came before the ellipses (including 0). Furthermore, each (name symbol pattern) in the duplicated pattern binds a list of matches to symbol, instead of a single match. (A nested duplicated pattern creates a list of list matches, etc.) Ellipses may be placed anywhere inside the row of patterns, except in the first position or immediately after another ellipses.

  Multiple ellipses are allowed. For example, this pattern:

  ((name x a) ... (name y a) ...)

  matches this sexpression:

  (term (a a))

  three different ways. One where the first a in the pattern matches nothing, and the second matches both of the occurrences of a, one where each named pattern matches a single a and one where the first matches both and the second matches nothing.

  If the ellipses is named (ie, has an underscore and a name following it, like a variable may), the pattern matcher records the length of the list and ensures that any other occurrences of the same named ellipses must have the same length.

  As an example, this pattern:

  ((name x a) ..._1 (name y a) ..._1)

  only matches this sexpression:

  (term (a a))

  one way, with each named pattern matching a single a. Unlike the above, the two patterns with mismatched lengths is ruled out, due to the underscores following the ellipses.

  Also, like underscore patterns above, if an underscore pattern begins with ..._!_, then the lengths must be different.

  Thus, with the pattern:

  ((name x a) ..._!_1 (name y a) ..._!_1)

  and the expression

  (term (a a))

  two matches occur, one where x is bound to '() and y is bound to '(a a) and one where x is bound to '(a a) and y is bound to '().

If redex-match receives only two arguments, it builds a procedure for efficiently testing if expressions match the pattern, using the language lang. The procedures accepts a single expression and if the expresion matches, it returns a list of match structures describing the matches. If the match fails, the procedure returns #f.

Caching should be disabled when matching a pattern that depends on values other than the in-scope pattern variables or evaluating a metafunction that reads or writes mutable external state.