package main import ( "slices" ) const EPSILON int = 0 type assertType int const ( NONE assertType = iota SOS EOS WBOUND NONWBOUND PLA // Positive lookahead NLA // Negative lookahead PLB // Positive lookbehind NLB // Negative lookbehind ) type State struct { content stateContents // Contents of current state isEmpty bool // If it is empty - Union operator and Kleene star states will be empty isLast bool // If it is the last state (acept state) output []*State // The outputs of the current state ie. the 'outward arrows'. A union operator state will have more than one of these. transitions map[int][]*State // Transitions to different states (maps a character (int representation) to a _list of states. This is useful if one character can lead multiple states eg. ab|aa) isKleene bool // Identifies whether current node is a 0-state representing Kleene star assert assertType // Type of assertion of current node - NONE means that the node doesn't assert anything zeroMatchFound bool // Whether or not the state has been used for a zero-length match - only relevant for zero states allChars bool // Whether or not the state represents all characters (eg. a 'dot' metacharacter). A 'dot' node doesn't store any contents directly, as it would take up too much space except []rune // Only valid if allChars is true - match all characters _except_ the ones in this block. Useful for inverting character classes. lookaroundRegex string // Only for lookaround states - Contents of the regex that the lookaround state holds } // Clones the NFA starting from the given state. func cloneState(start *State) *State { return cloneStateHelper(start, make(map[*State]*State)) } // Helper function for clone. The map is used to keep track of which states have // already been copied, and which ones haven't. // This function was created using output from Llama3.1:405B. func cloneStateHelper(state *State, cloneMap map[*State]*State) *State { // Base case - if the clone exists in our map, return it. if clone, exists := cloneMap[state]; exists { return clone } // Recursive case - if the clone doesn't exist, create it, add it to the map, // and recursively call for each of the transition states. clone := &State{ content: append([]int{}, state.content...), isEmpty: state.isEmpty, isLast: state.isLast, output: make([]*State, len(state.output)), transitions: make(map[int][]*State), isKleene: state.isKleene, assert: state.assert, zeroMatchFound: state.zeroMatchFound, allChars: state.allChars, except: append([]rune{}, state.except...), lookaroundRegex: state.lookaroundRegex, } cloneMap[state] = clone for i, s := range state.output { if s == state { clone.output[i] = clone } else { clone.output[i] = cloneStateHelper(s, cloneMap) } } for k, v := range state.transitions { clone.transitions[k] = make([]*State, len(v)) for i, s := range v { if s == state { clone.transitions[k][i] = clone } else { clone.transitions[k][i] = cloneStateHelper(s, cloneMap) } } } return clone } // Checks if the given state's assertion is true. Returns true if the given // state doesn't have an assertion. func (s State) checkAssertion(str []rune, idx int) bool { if s.assert == SOS { return idx == 0 } if s.assert == EOS { return idx == len(str) } if s.assert == WBOUND { return isWordBoundary(str, idx) } if s.assert == NONWBOUND { return !isWordBoundary(str, idx) } if s.assert == PLA || s.assert == PLB || s.assert == NLA || s.assert == NLB { // Lookaround // The process here is simple: // 1. Compile the regex stored in the state's contents. // 2. Run it on the test string. // 3. Based on the kind of lookaround (and the indices we get), determine what action to take. regex := s.lookaroundRegex re_postfix := shuntingYard(regex) startState := thompson(re_postfix) matchIndices := findAllMatches(startState, str) numMatchesFound := 0 for _, matchIdx := range matchIndices { if s.assert == PLA || s.assert == NLA { // Lookahead - return true (or false) if at least one match starts at the current index if matchIdx.startIdx == idx { numMatchesFound++ } } if s.assert == PLB || s.assert == NLB { // Lookbehind - return true (or false) if at least one match _ends_ at the current index. if matchIdx.endIdx == idx { numMatchesFound++ } } } if s.assert == PLA || s.assert == PLB { // Positive assertions want at least one match return numMatchesFound > 0 } if s.assert == NLA || s.assert == NLB { // Negative assertions only want zero matches return numMatchesFound == 0 } } return true } // Returns true if the contents of 's' contain the value at the given index of the given string func (s State) contentContains(str []rune, idx int) bool { if s.assert != NONE { return s.checkAssertion(str, idx) } if s.allChars { return !slices.Contains(slices.Concat(notDotChars, s.except), str[idx]) // Return true only if the index isn't a 'notDotChar', or isn't one of the exception characters for the current node. } // Default - s.assert must be NONE return slices.Contains(s.content, int(str[idx])) } // Returns the matches for the character at the given index of the given string. // Also returns the number of matches. Returns -1 if an assertion failed. func (s State) matchesFor(str []rune, idx int) ([]*State, int) { // Assertions can be viewed as 'checks'. If the check fails, we return // an empty array and 0. // If it passes, we treat it like any other state, and return all the transitions. if s.assert != NONE { if s.checkAssertion(str, idx) == false { return make([]*State, 0), -1 } } listTransitions := s.transitions[int(str[idx])] for _, dest := range s.transitions[int(ANY_CHAR)] { if !slices.Contains(slices.Concat(notDotChars, dest.except), str[idx]) { // Add an allChar state to the list of matches if: // a. The current character isn't a 'notDotChars' character. In single line mode, this includes newline. In multiline mode, it doesn't. // b. The current character isn't the state's exception list. listTransitions = append(listTransitions, dest) } } numTransitions := len(listTransitions) return listTransitions, numTransitions } type NFA struct { start State outputs []State } // verifyLastStatesHelper performs the depth-first recursion needed for verifyLastStates func verifyLastStatesHelper(state *State, visited map[*State]bool) { if len(state.transitions) == 0 { state.isLast = true return } // if len(state.transitions) == 1 && len(state.transitions[state.content]) == 1 && state.transitions[state.content][0] == state { // Eg. a* if len(state.transitions) == 1 { // Eg. a* var moreThanOneTrans bool // Dummy variable, check if all the transitions for the current's state's contents have a length of one for _, c := range state.content { if len(state.transitions[c]) != 1 || state.transitions[c][0] != state { moreThanOneTrans = true } } state.isLast = !moreThanOneTrans } if state.isKleene { // A State representing a Kleene Star has transitions going out, which loop back to it. If all those transitions point to the same (single) state, then it must be a last state transitionDests := make([]*State, 0) for _, v := range state.transitions { transitionDests = append(transitionDests, v...) } if allEqual(transitionDests...) { state.isLast = true return } } if visited[state] == true { return } visited[state] = true for _, states := range state.transitions { for i := range states { if states[i] != state { verifyLastStatesHelper(states[i], visited) } } } } // verifyLastStates enables the 'isLast' flag for the leaf nodes (last states) func verifyLastStates(start []*State) { verifyLastStatesHelper(start[0], make(map[*State]bool)) } // Concatenates s1 and s2, returns the start of the concatenation. func concatenate(s1 *State, s2 *State) *State { if s1 == nil { return s2 } for i := range s1.output { for _, c := range s2.content { // Create transitions for every element in s1's content to s2' s1.output[i].transitions[c], _ = unique_append(s1.output[i].transitions[c], s2) } } s1.output = s2.output return s1 } func kleene(s1 State) *State { toReturn := &State{} toReturn.transitions = make(map[int][]*State) toReturn.content = newContents(EPSILON) toReturn.isEmpty = true toReturn.isKleene = true toReturn.output = append(toReturn.output, toReturn) for i := range s1.output { for _, c := range toReturn.content { s1.output[i].transitions[c], _ = unique_append(s1.output[i].transitions[c], toReturn) } } for _, c := range s1.content { toReturn.transitions[c], _ = unique_append(toReturn.transitions[c], &s1) } return toReturn } func alternate(s1 *State, s2 *State) *State { toReturn := &State{} toReturn.transitions = make(map[int][]*State) toReturn.output = append(toReturn.output, s1.output...) toReturn.output = append(toReturn.output, s2.output...) // Unique append is used here (and elsewhere) to ensure that, // for any given transition, a state can only be mentioned once. // For example, given the transition 'a', the state 's1' can only be mentioned once. // This would lead to multiple instances of the same set of match indices, since both // 's1' states would be considered to match. for _, c := range s1.content { toReturn.transitions[c], _ = unique_append(toReturn.transitions[c], s1) } for _, c := range s2.content { toReturn.transitions[c], _ = unique_append(toReturn.transitions[c], s2) } toReturn.content = newContents(EPSILON) toReturn.isEmpty = true return toReturn } func question(s1 *State) *State { // Use the fact that ab? == a(b|) s2 := &State{} s2.transitions = make(map[int][]*State) s2.content = newContents(EPSILON) s2.output = append(s2.output, s2) s2.isEmpty = true s3 := alternate(s1, s2) return s3 }