702 lines
22 KiB
Standard ML
702 lines
22 KiB
Standard ML
structure DfaGen =
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struct
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datatype regex =
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CHAR_LITERAL of {char: char, position: int}
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| WILDCARD of int
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| IS_ANY_CHARACTER of {chars: char vector, position: int}
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| NOT_ANY_CHARACTER of {chars: char vector, position: int}
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| CONCAT of {l: regex, r: regex, leftMaxState: int, rightMaxState: int}
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| ALTERNATION of {l: regex, r: regex, leftMaxState: int, rightMaxState: int}
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| ZERO_OR_ONE of regex
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| ZERO_OR_MORE of regex
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| ONE_OR_MORE of regex
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| GROUP of regex
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val endMarker = #"\^@"
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structure Set =
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struct
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datatype 'a set = BRANCH of 'a set * int * 'a * 'a set | LEAF
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fun insertOrReplace (newKey, newVal, tree) =
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case tree of
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BRANCH (l, curKey, curVal, r) =>
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if newKey > curKey then
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let val r = insertOrReplace (newKey, newVal, r)
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in BRANCH (l, curKey, curVal, r)
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end
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else if newKey < curKey then
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let val l = insertOrReplace (newKey, newVal, l)
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in BRANCH (l, curKey, curVal, r)
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end
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else
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BRANCH (l, newKey, newVal, r)
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| LEAF => BRANCH (LEAF, newKey, newVal, LEAF)
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fun getOrDefault (findKey, tree, default) =
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case tree of
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BRANCH (l, curKey, curVal, r) =>
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if findKey > curKey then getOrDefault (findKey, r, default)
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else if findKey < curKey then getOrDefault (findKey, l, default)
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else curVal
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| LEAF => default
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fun helpToList (tree, acc) =
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case tree of
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BRANCH (l, curKey, curVal, r) =>
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let
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val acc = helpToList (r, acc)
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val acc = (curKey, curVal) :: acc
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in
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helpToList (l, acc)
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end
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| LEAF => acc
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fun toList tree = helpToList (tree, [])
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fun helpKeysToList (tree, acc) =
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case tree of
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BRANCH (l, curKey, _, r) =>
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let
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val acc = helpKeysToList (r, acc)
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val acc = curKey :: acc
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in
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helpKeysToList (l, acc)
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end
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| LEAF => acc
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fun keysToList tree = helpKeysToList (tree, [])
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fun map (f, tree) =
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case tree of
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BRANCH (l, key, value, r) =>
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let
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val r = map (f, r)
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val l = map (f, l)
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val value = f value
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in
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BRANCH (l, key, value, r)
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end
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| LEAF => LEAF
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fun foldl (f, tree, acc) =
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case tree of
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BRANCH (l, k, v, r) =>
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let
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val acc = foldl (f, l, acc)
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val acc = f (v, acc)
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in
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foldl (f, r, acc)
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end
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| LEAF => acc
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end
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structure ParseDfa =
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struct
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(* parsing through precedence climbing algorithm. *)
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val postfixLevel = 1
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val concatLevel = 2
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val altLevel = 3
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local
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fun loop (pos, str, openParens, closeParens) =
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if pos = String.size str then
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NONE
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else
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case String.sub (str, pos) of
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#"(" => loop (pos + 1, str, openParens + 1, closeParens)
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| #")" =>
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if closeParens + 1 = openParens then SOME pos
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else loop (pos + 1, str, openParens, closeParens + 1)
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| _ => loop (pos + 1, str, openParens, closeParens)
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in
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fun getRightParenIdx (pos, str) = loop (pos, str, 1, 0)
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end
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(* assumes previous char is a backslash *)
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fun isValidEscapeSequence chr =
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case chr of
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(* regex metacharacters *)
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#"(" => (true, chr)
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| #")" => (true, chr)
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| #"[" => (true, chr)
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| #"]" => (true, chr)
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| #"+" => (true, chr)
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| #"*" => (true, chr)
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| #"|" => (true, chr)
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| #"?" => (true, chr)
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| #"." => (true, chr)
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| #"-" => (true, chr)
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(* standard escape sequences *)
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| #"a" => (true, #"\a")
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| #"b" => (true, #"\b")
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| #"t" => (true, #"\t")
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| #"n" => (true, #"\n")
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| #"v" => (true, #"\v")
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| #"f" => (true, #"\f")
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| #"r" => (true, #"\r")
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| #"\\" => (true, chr)
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| #"\"" => (true, chr)
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| _ => (false, chr)
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fun getCharsBetween (lowChr, highChr, acc) =
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if lowChr = highChr then
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highChr :: acc
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else
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let
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val acc = lowChr :: acc
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val lowChr = Char.succ lowChr
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in
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getCharsBetween (lowChr, highChr, acc)
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end
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fun getCharsInBrackets (pos, str, acc) =
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if pos = String.size str then
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NONE
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else
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case String.sub (str, pos) of
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#"\\" =>
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(* escape sequences *)
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if pos + 1 = String.size str then
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NONE
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else
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let
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val chr = String.sub (str, pos + 1)
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val (isValid, chr) = isValidEscapeSequence chr
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in
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if isValid then getCharsInBrackets (pos + 2, str, chr :: acc)
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else NONE
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end
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| #"]" =>
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let val chars = Vector.fromList acc
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in SOME (pos + 1, chars)
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end
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| #"-" => NONE
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| chr =>
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if
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pos + 1 < String.size str andalso String.sub (str, pos + 1) = #"-"
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andalso pos + 2 < String.size str
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then
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(* handle character ranges like a-z *)
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let
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val chr2 = String.sub (str, pos + 2)
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val lowChr = if chr < chr2 then chr else chr2
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val highChr = if chr > chr2 then chr else chr2
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val acc = getCharsBetween (lowChr, highChr, acc)
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in
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getCharsInBrackets (pos + 3, str, acc)
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end
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else
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getCharsInBrackets (pos + 1, str, chr :: acc)
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fun parseCharacterClass (pos, str, stateNum) =
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case getCharsInBrackets (pos, str, []) of
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SOME (pos, chars) =>
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let
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val node = IS_ANY_CHARACTER {chars = chars, position = stateNum + 1}
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in
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SOME (pos, node, stateNum + 1)
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end
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| NONE => NONE
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fun parseNegateCharacterClass (pos, str, stateNum) =
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case getCharsInBrackets (pos, str, []) of
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SOME (pos, chars) =>
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let
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val node =
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NOT_ANY_CHARACTER {chars = chars, position = stateNum + 1}
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in
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SOME (pos, node, stateNum + 1)
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end
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| NONE => NONE
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fun computeAtom (pos, str, stateNum) =
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if pos = String.size str then
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NONE
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else
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case String.sub (str, pos) of
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#"(" =>
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(case getRightParenIdx (pos + 1, str) of
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SOME groupEndIdx =>
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let
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val substr = String.substring
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(str, pos + 1, groupEndIdx - pos - 1)
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in
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case parse (substr, stateNum) of
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SOME (rhs, stateNum) =>
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SOME (groupEndIdx + 1, rhs, stateNum)
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| NONE => NONE
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end
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| NONE => NONE)
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| #"\\" =>
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(* escape sequences *)
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if pos + 1 = String.size str then
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NONE
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else
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let
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val chr = String.sub (str, pos + 1)
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val (isValid, chr) = isValidEscapeSequence chr
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in
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if isValid then
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let
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val chr = CHAR_LITERAL {char = chr, position = stateNum + 1}
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in
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SOME (pos + 2, chr, stateNum + 1)
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end
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else
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NONE
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end
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| #"." => SOME (pos + 1, WILDCARD (stateNum + 1), stateNum + 1)
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| #")" => NONE
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| #"?" => NONE
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| #"*" => NONE
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| #"+" => NONE
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| #"[" =>
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if pos + 1 = String.size str then
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NONE
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else if String.sub (str, pos + 1) = #"^" then
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parseNegateCharacterClass (pos + 2, str, stateNum)
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else
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parseCharacterClass (pos + 1, str, stateNum)
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| chr =>
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let val chr = CHAR_LITERAL {char = chr, position = stateNum + 1}
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in SOME (pos + 1, chr, stateNum + 1)
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end
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and climb (pos, str, lhs, level, stateNum) : (int * regex * int) option =
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if pos = String.size str then
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SOME (pos, lhs, stateNum)
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else
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case String.sub (str, pos) of
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#"|" =>
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if level < altLevel then
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SOME (pos, lhs, stateNum)
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else if pos + 1 < String.size str then
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let
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val chr = String.sub (str, pos + 1)
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val chr = CHAR_LITERAL {char = chr, position = stateNum + 1}
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in
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case climb (pos + 2, str, chr, altLevel, stateNum + 1) of
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SOME (pos, rhs, rightStateNum) =>
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let
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val result = ALTERNATION
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{ l = lhs
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, r = rhs
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, leftMaxState = stateNum
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, rightMaxState = rightStateNum
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}
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in
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SOME (pos, result, rightStateNum)
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end
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| NONE => NONE
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end
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else
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NONE
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| #"?" =>
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if level < postfixLevel then
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SOME (pos, lhs, stateNum)
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else
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let val lhs = ZERO_OR_ONE lhs
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in climb (pos + 1, str, lhs, postfixLevel, stateNum)
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end
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| #"*" =>
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if level < postfixLevel then
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SOME (pos, lhs, stateNum)
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else
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let val lhs = ZERO_OR_MORE lhs
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in climb (pos + 1, str, lhs, postfixLevel, stateNum)
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end
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| #"+" =>
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if level < postfixLevel then
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SOME (pos, lhs, stateNum)
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else
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let val lhs = ONE_OR_MORE lhs
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in climb (pos + 1, str, lhs, postfixLevel, stateNum)
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end
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| chr =>
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if level < concatLevel then
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SOME (pos, lhs, stateNum)
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else
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case computeAtom (pos, str, stateNum) of
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SOME (nextPos, curAtom, atomStateNum) =>
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(case climb (nextPos, str, curAtom, concatLevel, atomStateNum) of
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SOME (pos, rhs, rightStateNum) =>
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let
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val result = CONCAT
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{ l = lhs
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, r = rhs
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, leftMaxState = stateNum
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, rightMaxState = rightStateNum
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}
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in
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SOME (pos, result, rightStateNum)
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end
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| NONE => NONE)
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| NONE => NONE
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and loop (pos, str, ast, stateNum) =
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if pos = String.size str then
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SOME (ast, stateNum)
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else
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case climb (pos, str, ast, altLevel, stateNum) of
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SOME (pos, ast, stateNum) => loop (pos, str, ast, stateNum)
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| NONE => NONE
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and parse (str, stateNum) =
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if String.size str > 0 then
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case computeAtom (0, str, stateNum) of
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SOME (nextPos, lhs, stateNum) => loop (nextPos, str, lhs, stateNum)
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| NONE => NONE
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else
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NONE
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end
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structure ToDfa =
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struct
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fun isNullable tree =
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case tree of
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CHAR_LITERAL _ => false
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| WILDCARD _ => false
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| IS_ANY_CHARACTER _ => false
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| NOT_ANY_CHARACTER _ => false
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| CONCAT {l, r, ...} => isNullable l andalso isNullable r
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| ALTERNATION {l, r, ...} => isNullable l orelse isNullable r
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| ZERO_OR_ONE _ => true
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| ZERO_OR_MORE _ => true
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| ONE_OR_MORE regex => isNullable regex
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| GROUP regex => isNullable regex
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fun firstpos (tree, acc) =
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case tree of
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CHAR_LITERAL {position, ...} => position :: acc
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| IS_ANY_CHARACTER {position, ...} => position :: acc
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| NOT_ANY_CHARACTER {position, ...} => position :: acc
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| WILDCARD i => i :: acc
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| CONCAT {l, r, ...} =>
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if isNullable l then
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let val acc = firstpos (l, acc)
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in firstpos (r, acc)
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end
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else
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firstpos (l, acc)
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| ALTERNATION {l, r, ...} =>
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let val acc = firstpos (l, acc)
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in firstpos (r, acc)
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end
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| ZERO_OR_ONE regex => firstpos (regex, acc)
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| ZERO_OR_MORE regex => firstpos (regex, acc)
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| ONE_OR_MORE regex => firstpos (regex, acc)
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| GROUP regex => firstpos (regex, acc)
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fun lastpos (tree, acc) =
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case tree of
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CHAR_LITERAL {position, ...} => position :: acc
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| IS_ANY_CHARACTER {position, ...} => position :: acc
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| NOT_ANY_CHARACTER {position, ...} => position :: acc
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| WILDCARD i => i :: acc
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| CONCAT {l, r, ...} =>
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if isNullable r then
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let val acc = lastpos (l, acc)
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in lastpos (r, acc)
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end
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else
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lastpos (r, acc)
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| ALTERNATION {l, r, ...} =>
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let val acc = lastpos (l, acc)
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in lastpos (r, acc)
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end
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| ZERO_OR_ONE regex => lastpos (regex, acc)
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| ZERO_OR_MORE regex => lastpos (regex, acc)
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| ONE_OR_MORE regex => lastpos (regex, acc)
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| GROUP regex => lastpos (regex, acc)
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fun followpos (char, regex, acc) =
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case regex of
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CONCAT {r, ...} => firstpos (r, acc)
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| ZERO_OR_MORE r => firstpos (r, acc)
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| ONE_OR_MORE r => firstpos (r, acc)
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| _ => acc
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fun chrExistsInVec (idx, vec, curChr) =
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if idx = Vector.length vec then
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false
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else
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Vector.sub (vec, idx) = curChr
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orelse chrExistsInVec (idx + 1, vec, curChr)
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(* Does two things:
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* 1. Descends to the leaf matching 'pos'.
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* 2. If the character at 'pos' matches the current character,
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* calls followpos at the appropriate nodes.
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* In the end, we get a list of positions to follow. *)
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fun getFollowsForPositionAndChar (regex: regex, pos, curChr) =
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case regex of
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CHAR_LITERAL {char, position = _} =>
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if char = curChr then
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{sawConcat = false, follows = [], charIsMatch = true}
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else
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{sawConcat = false, follows = [], charIsMatch = false}
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| WILDCARD _ =>
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(* we are treating a char that has ASCII code 0
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* as an end marker which will not appear anywhere else.
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* So we don't want to match it, but the wildcard can match
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* any other character that has a different ASCII code. *)
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{sawConcat = false, follows = [], charIsMatch = curChr <> endMarker}
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| IS_ANY_CHARACTER {chars, ...} =>
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let val chrExists = chrExistsInVec (0, chars, curChr)
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in {sawConcat = false, follows = [], charIsMatch = chrExists}
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end
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| NOT_ANY_CHARACTER {chars, ...} =>
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let
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val charIsValid = chrExistsInVec (0, chars, curChr)
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val charIsValid = not charIsValid andalso curChr <> endMarker
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in
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{sawConcat = false, follows = [], charIsMatch = charIsValid}
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end
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| ALTERNATION {l, r, leftMaxState, rightMaxState} =>
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let val nodeToFollow = if pos <= leftMaxState then l else r
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in getFollowsForPositionAndChar (nodeToFollow, pos, curChr)
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end
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| GROUP regex => getFollowsForPositionAndChar (regex, pos, curChr)
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| CONCAT {l, r, leftMaxState, ...} =>
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if pos <= leftMaxState then
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let
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val result = getFollowsForPositionAndChar (l, pos, curChr)
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val {sawConcat, follows, charIsMatch} = result
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in
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if charIsMatch then
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if sawConcat then
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(* we already saw a concat and got followpos *)
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result
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else
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let val fp = followpos (curChr, regex, follows)
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in {sawConcat = true, follows = fp, charIsMatch = true}
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end
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else
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(* char is not match, so don't get follow pos *)
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result
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end
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else
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getFollowsForPositionAndChar (r, pos, curChr)
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| ZERO_OR_MORE child =>
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let
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val result = getFollowsForPositionAndChar (child, pos, curChr)
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val {sawConcat, follows, charIsMatch} = result
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in
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if charIsMatch then
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{ sawConcat = false
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, follows = firstpos (child, follows)
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, charIsMatch = true
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}
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else
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result
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end
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| ZERO_OR_ONE child => getFollowsForPositionAndChar (child, pos, curChr)
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| ONE_OR_MORE child =>
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let
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val result = getFollowsForPositionAndChar (child, pos, curChr)
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val {sawConcat, follows, charIsMatch} = result
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in
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if charIsMatch then
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{ sawConcat = false
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, follows = firstpos (child, follows)
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, charIsMatch = true
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}
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else
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result
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end
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fun getFollowPositionsFromList (lst: int list, regex, char, followSet) =
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case lst of
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hd :: tl =>
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let
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|
val fpList = getFollowsForPositionAndChar (regex, hd, char)
|
|
val {sawConcat, follows, charIsMatch} = fpList
|
|
val follows =
|
|
if charIsMatch andalso not sawConcat then 0 :: follows
|
|
else follows
|
|
|
|
val followSet =
|
|
List.foldl
|
|
(fn (fp, followSet) => Set.insertOrReplace (fp, (), followSet))
|
|
followSet follows
|
|
in
|
|
getFollowPositionsFromList (tl, regex, char, followSet)
|
|
end
|
|
| [] => Set.keysToList followSet
|
|
|
|
fun appendIfNew (pos, dstates, newStates) =
|
|
if pos = Vector.length dstates then
|
|
let
|
|
val record = {transitions = newStates, marked = false}
|
|
val dstates = Vector.concat [dstates, Vector.fromList [record]]
|
|
in
|
|
(pos, dstates)
|
|
end
|
|
else
|
|
let
|
|
val {transitions: int list, marked = _} = Vector.sub (dstates, pos)
|
|
in
|
|
if transitions = newStates then (pos, dstates)
|
|
else appendIfNew (pos + 1, dstates, newStates)
|
|
end
|
|
|
|
fun getUnmarkedTransitionsIfExists (pos, dstates) =
|
|
if pos = Vector.length dstates then
|
|
NONE
|
|
else
|
|
let
|
|
val record = Vector.sub (dstates, pos)
|
|
in
|
|
if #marked record then
|
|
getUnmarkedTransitionsIfExists (pos + 1, dstates)
|
|
else
|
|
SOME (pos, #transitions record)
|
|
end
|
|
|
|
(* the int key in dtran refers to the char code
|
|
* while the int value refers to the idx from dstates
|
|
* that this char transitions to *)
|
|
type dtran = int Set.set
|
|
|
|
fun makeEmptyVec _ = ~1
|
|
|
|
fun convertChar
|
|
( char
|
|
, regex
|
|
, dstates
|
|
, dtran: dtran vector
|
|
, curStates
|
|
, curStatesIdx
|
|
, setForCurStates
|
|
) =
|
|
if char < 0 then
|
|
let
|
|
(* append setForCurStates which was accumulated in this function
|
|
* to the end of dtran. *)
|
|
val dtran = Vector.concat [dtran, Vector.fromList [setForCurStates]]
|
|
in
|
|
(dstates, dtran)
|
|
end
|
|
else
|
|
let
|
|
(* get union of all follow positions *)
|
|
val u =
|
|
getFollowPositionsFromList
|
|
(curStates, regex, Char.chr char, Set.LEAF)
|
|
in
|
|
case u of
|
|
[] =>
|
|
(* no follow positions from here, so don't add to dstates *)
|
|
convertChar
|
|
( char - 1
|
|
, regex
|
|
, dstates
|
|
, dtran
|
|
, curStates
|
|
, curStatesIdx
|
|
, setForCurStates
|
|
)
|
|
| _ =>
|
|
let
|
|
(* add follow positions to dstates if they are not already inside
|
|
* and if follow is not empty *)
|
|
val (newStateIdx, dstates) = appendIfNew (0, dstates, u)
|
|
|
|
(* update dtran to include transitions for char. *)
|
|
val setForCurStates =
|
|
Set.insertOrReplace (char, newStateIdx, setForCurStates)
|
|
in
|
|
convertChar
|
|
( char - 1
|
|
, regex
|
|
, dstates
|
|
, dtran
|
|
, curStates
|
|
, curStatesIdx
|
|
, setForCurStates
|
|
)
|
|
end
|
|
end
|
|
|
|
fun convertLoop (regex, dstates, dtran) =
|
|
case getUnmarkedTransitionsIfExists (0, dstates) of
|
|
SOME (unmarkedIdx, unamarkedTransition) =>
|
|
let
|
|
(* mark transition *)
|
|
val dstates =
|
|
let
|
|
val newMark = {marked = true, transitions = unamarkedTransition}
|
|
in
|
|
Vector.update (dstates, unmarkedIdx, newMark)
|
|
end
|
|
|
|
val (dstates, dtran) = convertChar
|
|
( 255
|
|
, regex
|
|
, dstates
|
|
, dtran
|
|
, unamarkedTransition
|
|
, unmarkedIdx
|
|
, Set.LEAF
|
|
)
|
|
in
|
|
convertLoop (regex, dstates, dtran)
|
|
end
|
|
| NONE =>
|
|
Vector.map
|
|
(fn set =>
|
|
Vector.tabulate (256, fn i => Set.getOrDefault (i, set, ~1)))
|
|
dtran
|
|
|
|
fun convert regex =
|
|
let
|
|
val first = List.rev (firstpos (regex, []))
|
|
val dstates = Vector.fromList [{transitions = first, marked = false}]
|
|
in
|
|
convertLoop (regex, dstates, Vector.fromList [])
|
|
end
|
|
end
|
|
|
|
fun fromString str =
|
|
case ParseDfa.parse (str, 0) of
|
|
SOME (ast, numStates) =>
|
|
let
|
|
val endMarker =
|
|
CHAR_LITERAL {char = endMarker, position = numStates + 1}
|
|
val ast = CONCAT
|
|
{ l = ast
|
|
, leftMaxState = numStates
|
|
, r = endMarker
|
|
, rightMaxState = numStates + 1
|
|
}
|
|
in
|
|
ToDfa.convert ast
|
|
end
|
|
| NONE => Vector.fromList []
|
|
|
|
type dfa = int vector vector
|
|
|
|
fun nextState (dfa: dfa, curState, chr) =
|
|
let val curTable = Vector.sub (dfa, curState)
|
|
in Vector.sub (curTable, Char.ord chr)
|
|
end
|
|
|
|
fun isFinal (dfa: dfa, curState) =
|
|
curState <> ~1
|
|
andalso
|
|
let val curTable = Vector.sub (dfa, curState)
|
|
in Vector.sub (curTable, 0) <> ~1
|
|
end
|
|
|
|
fun isDead curState = curState = ~1
|
|
end
|