473 lines
15 KiB
Standard ML
473 lines
15 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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| 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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| WILDCARD of int
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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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fun helpToCharsAndPositionsList (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 = helpToCharsAndPositionsList (r, acc)
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val acc = {char = v, position = k} :: acc
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in
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helpToCharsAndPositionsList (l, acc)
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end
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| LEAF => acc
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fun toCharsAndPositionsList tree = helpToCharsAndPositionsList (tree, [])
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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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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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| #")" => NONE
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| #"?" => NONE
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| #"*" => NONE
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| #"+" => NONE
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| #"." => SOME (pos + 1, WILDCARD (stateNum + 1), stateNum + 1)
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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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| 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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| 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 firstposWithChar (tree, acc) =
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case tree of
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CHAR_LITERAL {position, char} =>
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{position = position, char = Char.ord char} :: acc
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| WILDCARD position => {position = position, char = ~1} :: acc
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| CONCAT {l, r, ...} =>
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if isNullable l then
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let val acc = firstposWithChar (l, acc)
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in firstposWithChar (r, acc)
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end
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else
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firstposWithChar (l, acc)
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| ALTERNATION {l, r, ...} =>
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let val acc = firstposWithChar (l, acc)
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in firstposWithChar (r, acc)
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end
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| ZERO_OR_ONE regex => firstposWithChar (regex, acc)
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| ZERO_OR_MORE regex => firstposWithChar (regex, acc)
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| ONE_OR_MORE regex => firstposWithChar (regex, acc)
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| GROUP regex => firstposWithChar (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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| 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 (l, 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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| ZERO_OR_ONE r => firstpos (r, acc)
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| ONE_OR_MORE r => firstpos (r, acc)
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| _ => acc
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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 _ => {sawConcat = false, follows = [], charIsMatch = true}
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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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let
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val nodeToFollow = if pos <= leftMaxState then l else r
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val result =
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getFollowsForPositionAndChar (nodeToFollow, 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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(* saw concat, so we got follow pos already *)
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result
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else
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(* get followpos *)
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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 does not match, so don't get followpos *)
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result
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end
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| ZERO_OR_ONE child =>
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getFollowsForPositionAndCharLoop (pos, regex, child, curChr)
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| ZERO_OR_MORE child =>
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getFollowsForPositionAndCharLoop (pos, regex, child, curChr)
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| ONE_OR_MORE child =>
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getFollowsForPositionAndCharLoop (pos, regex, child, curChr)
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and getFollowsForPositionAndCharLoop (pos, regex, child, curChr) =
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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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if sawConcat then
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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 = false, follows = fp, charIsMatch = true}
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end
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else
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result
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end
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fun ifStatesInVec (pos, dstates, newStates) =
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if pos = Vector.length dstates then
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false
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else
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let
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val {transitions, marked = _} = Vector.sub (dstates, pos)
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in
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transitions = newStates
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orelse ifStatesInVec (pos + 1, dstates, newStates)
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end
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fun getUnmarkedTransitionsIfExists (pos, dstates) =
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if pos = Vector.length dstates then
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NONE
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else
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let
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val record = Vector.sub (dstates, pos)
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in
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if #marked record then
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getUnmarkedTransitionsIfExists (pos + 1, dstates)
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else
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SOME (pos, #transitions record)
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end
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fun convertLoop (regex, dstates) =
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case getUnmarkedTransitionsIfExists (0, dstates) of
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SOME (unmarkedIdx, unamarkedTransition) =>
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let
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(* mark transition *)
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val dstates =
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let
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val newMark = {marked = true, transitions = unamarkedTransition}
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in
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Vector.update (dstates, unmarkedIdx, newMark)
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end
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(* get follow transitions *)
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val nodes = raise Fail "todo"
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val follows = raise Fail "todo"
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(* add any new transitions we find *)
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val newdstates = Set.foldl
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( fn (subtree, acc) =>
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let
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val subtreeStates = Set.toCharsAndPositionsList subtree
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in
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if ifStatesInVec (0, dstates, subtreeStates) then
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acc
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else
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let
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val record =
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{marked = false, transitions = subtreeStates}
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in
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Vector.concat [acc, Vector.fromList [record]]
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end
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end
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, follows
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, dstates
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)
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in
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convertLoop (regex, newdstates)
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end
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| NONE => dstates
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fun convert regex =
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let
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val first = List.rev (firstposWithChar (regex, []))
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val dstates = Vector.fromList [{transitions = first, marked = false}]
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in
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convertLoop (regex, dstates)
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end
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end
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fun fromString str =
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case ParseDfa.parse (str, 0) of
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SOME (ast, _) => ToDfa.convert ast
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| NONE => Vector.fromList []
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end
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val dfa = DfaGen.fromString "(a|b)*abb#"
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