在Java中实现LR(1)分析法

LR(1)分析法是一种自底向上的语法分析方法，可以用于构建语法分析表。在Java中，可以使用以下步骤来实现LR(1)分析法：

1. 构建LR(1)项集族：LR(1)项是由一个文法符号和一个向前看符号组成的，即A -> α·Bβ, a。其中A为文法符号，α和β为文法符号串，·表示当前正在分析的位置，B是文法符号，a是向前看符号。LR(1)项集族是由一组LR(1)项组成的，每个LR(1)项集代表了从一个状态经过一次移进或规约操作能够到达的状态集合。

2. 构建LR(1)分析表：LR(1)分析表是一个二维表格，行表示状态，列表示文法符号或向前看符号，表格中的每个元素表示执行相应操作（移进、规约、接受或错误）的下一个状态或规约所使用的产生式。

3. 使用LR(1)分析表进行语法分析：给定一个输入符号串，从初始状态开始，根据输入符号和当前状态在LR(1)分析表中查找下一步的操作（移进、规约、接受或错误），并相应地更新状态栈和符号栈。

Java中可以使用自动机或状态转换图的方式来实现LR(1)分析法。也可以使用现成的工具如JavaCUP、ANTLR等来生成LR(1)分析器。

相关问题

Java实现LR（1）分析法

在Java中实现LR(1)分析法，可以采用以下步骤：

1. 定义文法：使用Java代码定义给定文法，例如：

String[][] productionRules = {
    {"E", "E + T"},
    {"E", "E - T"},
    {"E", "T"},
    {"T", "T * F"},
    {"T", "T / F"},
    {"T", "F"},
    {"F", "( E )"},
    {"F", "i"}
};

2. 构建LR(1)项集族：根据给定文法，构建LR(1)项集族。

3. 构建LR(1)分析表：根据LR(1)项集族，构建LR(1)分析表。

4. 实现LR(1)分析器：使用Java代码实现LR(1)分析器，并使用LR(1)分析表对输入符号串进行分析。

下面是一个简单的Java实现LR(1)分析法的示例：

import java.util.*;

public class LR1 {
    // 定义文法
    static String[][] productionRules = {
        {"E", "E + T"},
        {"E", "E - T"},
        {"E", "T"},
        {"T", "T * F"},
        {"T", "T / F"},
        {"T", "F"},
        {"F", "( E )"},
        {"F", "i"}
    };

    // 定义LR(1)项
    static class LR1Item {
        String left;
        String[] right;
        String[] lookahead;

        public LR1Item(String left, String[] right, String[] lookahead) {
            this.left = left;
            this.right = right;
            this.lookahead = lookahead;
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof LR1Item)) return false;
            LR1Item item = (LR1Item) obj;
            return left.equals(item.left) && Arrays.equals(right, item.right) && Arrays.equals(lookahead, item.lookahead);
        }

        public int hashCode() {
            return Objects.hash(left, Arrays.hashCode(right), Arrays.hashCode(lookahead));
        }

        public String toString() {
            return left + " -> " + String.join(" ", right) + " , " + String.join(" ", lookahead);
        }
    }

    // 构建LR(1)项集族
    static Map<Set<LR1Item>, Integer> buildLR1ItemSets() {
        Map<Set<LR1Item>, Integer> itemSets = new HashMap<>();
        Queue<Set<LR1Item>> queue = new LinkedList<>();
        int id = 0;

        // 添加起始项 S' -> .E
        Set<LR1Item> startItemSet = new HashSet<>();
        startItemSet.add(new LR1Item("S'", new String[]{"E"}, new String[]{"$"}));
        itemSets.put(startItemSet, id++);
        queue.offer(startItemSet);

        while (!queue.isEmpty()) {
            Set<LR1Item> itemSet = queue.poll();
            Map<String, Set<LR1Item>> itemSetMap = new HashMap<>();

            // 按照圆点后面的符号对项进行分类
            for (LR1Item item : itemSet) {
                if (item.right.length == 0 || item.right[0].equals("#")) {
                    continue;
                }
                String nextSymbol = item.right[item.lookahead.length];
                Set<LR1Item> nextItemSet = itemSetMap.computeIfAbsent(nextSymbol, k -> new HashSet<>());
                nextItemSet.add(new LR1Item(item.left, item.right, Arrays.copyOfRange(item.lookahead, 1, item.lookahead.length)));
            }

            // 对每个分类后的项集构建新的项集
            for (Map.Entry<String, Set<LR1Item>> entry : itemSetMap.entrySet()) {
                Set<LR1Item> nextItemSet = entry.getValue();
                if (itemSets.containsKey(nextItemSet)) {
                    continue;
                }
                itemSets.put(nextItemSet, id++);
                queue.offer(nextItemSet);
            }
        }

        return itemSets;
    }

    // 构建LR(1)分析表
    static Map<Integer, Map<String, Object>> buildLR1AnalysisTable() {
        Map<Integer, Map<String, Object>> analysisTable = new HashMap<>();
        Map<Set<LR1Item>, Integer> itemSets = buildLR1ItemSets();

        // 对于每个项集
        for (Map.Entry<Set<LR1Item>, Integer> entry : itemSets.entrySet()) {
            Set<LR1Item> itemSet = entry.getKey();
            int state = entry.getValue();
            Map<String, Object> stateAction = new HashMap<>();

            // 对于每个 LR(1) 项
            for (LR1Item item : itemSet) {
                if (item.right.length == 0) { // 归约项
                    for (String lookahead : item.lookahead) {
                        stateAction.put(lookahead, "r" + (Arrays.asList(productionRules).indexOf(new String[]{item.left})) + "");
                    }
                } else { // 移进项
                    String nextSymbol = item.right[item.lookahead.length];
                    if (nextSymbol.equals("#")) {
                        nextSymbol = "$";
                    }
                    int nextState = itemSets.get(itemSetMap.get(nextSymbol));
                    stateAction.put(nextSymbol, "s" + nextState);
                }
            }

            analysisTable.put(state, stateAction);
        }

        return analysisTable;
    }

    // 分析符号串
    static boolean analyze(String input, Map<Integer, Map<String, Object>> analysisTable) {
        Stack<Integer> stateStack = new Stack<>();
        Stack<String> symbolStack = new Stack<>();
        stateStack.push(0);
        symbolStack.push("$");

        int i = 0;
        while (i < input.length()) {
            int state = stateStack.peek();
            String symbol = input.charAt(i) + "";
            Map<String, Object> stateAction = analysisTable.get(state);
            Object action = stateAction.get(symbol);
            if (action == null) {
                return false;
            }
            if (action instanceof String) { // 移进操作
                String s = (String) action;
                stateStack.push(Integer.parseInt(s.substring(1)));
                symbolStack.push(symbol);
                i++;
            } else { // 规约操作
                int rule = (int) action;
                String[] production = productionRules[rule];
                for (int j = 0; j < production[1].length(); j++) {
                    stateStack.pop();
                    symbolStack.pop();
                }
                int nextState = stateStack.peek();
                symbolStack.push(production[0]);
                stateStack.push((int) analysisTable.get(nextState).get(production[0]));
            }
        }

        return true;
    }

    public static void main(String[] args) {
        String input = "i+i*i";
        Map<Integer, Map<String, Object>> analysisTable = buildLR1AnalysisTable();
        boolean result = analyze(input, analysisTable);
        System.out.println(result);
    }
}

在以上代码中，LR1Item表示一个LR(1)项，buildLR1ItemSets方法用于构建LR(1)项集族，buildLR1AnalysisTable方法用于构建LR(1)分析表，analyze方法用于实现LR(1)分析器，main方法用于测试分析器。

实现LR(1)分析法的java代码

以下是一个简单的LR(1)分析器的Java代码，用于分析输入的字符串是否符合给定文法的规则：

import java.util.*;

public class LR1Parser {

    private Map<Integer, Map<String, Action>> actionTable;
    private Map<Integer, Map<String, Integer>> gotoTable;
    private Map<Integer, Set<Item>> itemSets;
    private Map<String, Set<Integer>> followSets;
    private int startState;
    private String startSymbol;

    public LR1Parser(Grammar grammar) {
        // 构建LR(1)项集族
        itemSets = buildItemSets(grammar);
        // 构建LR(1)分析表
        actionTable = buildActionTable(grammar, itemSets);
        gotoTable = buildGotoTable(grammar, itemSets);
        // 计算起始状态和起始符号
        startState = findStartState(itemSets, grammar.getStartSymbol());
        startSymbol = grammar.getStartSymbol();
        // 计算Follow集合
        followSets = calculateFollowSets(grammar);
    }

    public boolean parse(String input) {
        // 初始化状态栈和符号栈
        Stack<Integer> stateStack = new Stack<>();
        Stack<String> symbolStack = new Stack<>();
        stateStack.push(startState);
        symbolStack.push("$");
        // 将输入符号串转换为Token序列
        List<Token> tokens = scan(input);
        tokens.add(new Token("$", ""));
        // 开始语法分析
        int i = 0;
        while (i < tokens.size()) {
            int state = stateStack.peek();
            String symbol = tokens.get(i).getSymbol();
            if (actionTable.containsKey(state) && actionTable.get(state).containsKey(symbol)) {
                // 查找分析表并执行对应动作
                Action action = actionTable.get(state).get(symbol);
                if (action.getType() == Action.SHIFT) {
                    stateStack.push(action.getValue());
                    symbolStack.push(symbol);
                    i++;
                } else if (action.getType() == Action.REDUCE) {
                    Production production = action.getProduction();
                    int numPops = production.getRight().size();
                    for (int j = 0; j < numPops; j++) {
                        stateStack.pop();
                        symbolStack.pop();
                    }
                    String nonterminal = production.getLeft();
                    int newState = gotoTable.get(stateStack.peek()).get(nonterminal);
                    stateStack.push(newState);
                    symbolStack.push(nonterminal);
                } else if (action.getType() == Action.ACCEPT) {
                    return true;
                } else {
                    return false;
                }
            } else {
                return false;
            }
        }
        return false;
    }

    private List<Token> scan(String input) {
        // 将输入符号串转换为Token序列
        List<Token> tokens = new ArrayList<>();
        String[] parts = input.split(" ");
        for (String part : parts) {
            String[] pair = part.split(":");
            tokens.add(new Token(pair[0], pair[1]));
        }
        return tokens;
    }

    private Map<String, Set<Integer>> calculateFollowSets(Grammar grammar) {
        // 计算Follow集合
        Map<String, Set<Integer>> followSets = new HashMap<>();
        for (String nonterminal : grammar.getNonterminals()) {
            followSets.put(nonterminal, new HashSet<>());
        }
        followSets.get(startSymbol).add(Grammar.EOF);
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Production production : grammar.getProductions()) {
                String left = production.getLeft();
                List<String> right = production.getRight();
                for (int i = right.size() - 1; i >= 0; i--) {
                    String symbol = right.get(i);
                    if (grammar.isNonterminal(symbol)) {
                        Set<Integer> follow = followSets.get(symbol);
                        Set<Integer> first = calculateFirstSet(right.subList(i + 1, right.size()), grammar);
                        int oldSize = follow.size();
                        follow.addAll(first);
                        if (first.contains(Grammar.EMPTY) || i == right.size() - 1) {
                            follow.addAll(followSets.get(left));
                        }
                        if (follow.size() != oldSize) {
                            changed = true;
                        }
                    }
                }
            }
        }
        return followSets;
    }

    private Set<Integer> calculateFirstSet(List<String> symbols, Grammar grammar) {
        // 计算给定符号串的First集合
        Set<Integer> first = new HashSet<>();
        boolean hasEmpty = true;
        for (String symbol : symbols) {
            Set<Integer> symbolFirst = grammar.getFirstSet(symbol);
            first.addAll(symbolFirst);
            if (!symbolFirst.contains(Grammar.EMPTY)) {
                hasEmpty = false;
                break;
            }
        }
        if (hasEmpty) {
            first.add(Grammar.EMPTY);
        }
        return first;
    }

    private int findStartState(Map<Integer, Set<Item>> itemSets, String startSymbol) {
        // 查找起始状态
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            for (Item item : items) {
                if (item.getDotPosition() == 0 && item.getProduction().getLeft().equals(startSymbol)) {
                    return state;
                }
            }
        }
        return -1;
    }

    private Map<Integer, Map<String, Action>> buildActionTable(Grammar grammar, Map<Integer, Set<Item>> itemSets) {
        // 构建LR(1)分析表中的Action部分
        Map<Integer, Map<String, Action>> actionTable = new HashMap<>();
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            Map<String, Action> actions = new HashMap<>();
            for (Item item : items) {
                if (item.getDotPosition() == item.getProduction().getRight().size()) {
                    if (item.getProduction().getLeft().equals(grammar.getStartSymbol())) {
                        actions.put("$", new Action(Action.ACCEPT, -1, null));
                    } else {
                        Set<Integer> follow = followSets.get(item.getProduction().getLeft());
                        for (int symbol : follow) {
                            actions.put(grammar.getSymbolString(symbol), new Action(Action.REDUCE, item.getProduction().getIndex(), item.getProduction()));
                        }
                    }
                } else {
                    String nextSymbol = item.getNextSymbol();
                    if (grammar.isTerminal(nextSymbol)) {
                        int nextState = findNextState(itemSets, items, nextSymbol);
                        actions.put(nextSymbol, new Action(Action.SHIFT, nextState, null));
                    }
                }
            }
            actionTable.put(state, actions);
        }
        return actionTable;
    }

    private Map<Integer, Map<String, Integer>> buildGotoTable(Grammar grammar, Map<Integer, Set<Item>> itemSets) {
        // 构建LR(1)分析表中的Goto部分
        Map<Integer, Map<String, Integer>> gotoTable = new HashMap<>();
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> items = entry.getValue();
            Map<String, Integer> gotos = new HashMap<>();
            for (Item item : items) {
                if (item.getDotPosition() < item.getProduction().getRight().size()) {
                    String nextSymbol = item.getNextSymbol();
                    if (grammar.isNonterminal(nextSymbol)) {
                        int nextState = findNextState(itemSets, items, nextSymbol);
                        gotos.put(nextSymbol, nextState);
                    }
                }
            }
            gotoTable.put(state, gotos);
        }
        return gotoTable;
    }

    private int findNextState(Map<Integer, Set<Item>> itemSets, Set<Item> items, String symbol) {
        // 查找给定状态集合和符号的下一个状态
        Set<Item> nextItems = new HashSet<>();
        for (Item item : items) {
            if (item.getDotPosition() < item.getProduction().getRight().size() && item.getNextSymbol().equals(symbol)) {
                nextItems.add(new Item(item.getProduction(), item.getDotPosition() + 1, item.getLookahead()));
            }
        }
        return findItemSetState(itemSets, nextItems);
    }

    private int findItemSetState(Map<Integer, Set<Item>> itemSets, Set<Item> items) {
        // 查找给定LR(1)项集在LR(1)项集族中的状态
        for (Map.Entry<Integer, Set<Item>> entry : itemSets.entrySet()) {
            int state = entry.getKey();
            Set<Item> existingItems = entry.getValue();
            if (existingItems.equals(items)) {
                return state;
            }
        }
        return -1;
    }

    private Map<Integer, Set<Item>> buildItemSets(Grammar grammar) {
        // 构建LR(1)项集族
        Map<Integer, Set<Item>> itemSets = new HashMap<>();
        int state = 0;
        Set<Item> initialItems = new HashSet<>();
        Production startProduction = grammar.getProductions().get(0);
        initialItems.add(new Item(startProduction, 0, Grammar.EOF));
        itemSets.put(state, closure(initialItems, grammar));
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Map.Entry<Integer, Set<Item>> entry : new HashMap<>(itemSets).entrySet()) {
                int currentState = entry.getKey();
                Set<Item> currentItems = entry.getValue();
                Map<String, Set<Item>> symbolItems = new HashMap<>();
                for (Item item : currentItems) {
                    if (item.getDotPosition() < item.getProduction().getRight().size()) {
                        String nextSymbol = item.getNextSymbol();
                        Set<Item> nextItems = symbolItems.computeIfAbsent(nextSymbol, k -> new HashSet<>());
                        nextItems.add(new Item(item.getProduction(), item.getDotPosition() + 1, item.getLookahead()));
                    }
                }
                for (Map.Entry<String, Set<Item>> symbolEntry : symbolItems.entrySet()) {
                    Set<Item> nextItems = closure(symbolEntry.getValue(), grammar);
                    int nextState = findItemSetState(itemSets, nextItems);
                    if (nextState == -1) {
                        nextState = ++state;
                        itemSets.put(nextState, nextItems);
                        changed = true;
                    }
                    actionTable.put(currentState, new HashMap<>());
                    actionTable.get(currentState).put(symbolEntry.getKey(), new Action(Action.SHIFT, nextState, null));
                }
            }
        }
        return itemSets;
    }

    private Set<Item> closure(Set<Item> items, Grammar grammar) {
        // 计算LR(1)项集的闭包
        Set<Item> closure = new HashSet<>(items);
        boolean changed = true;
        while (changed) {
            changed = false;
            for (Item item : new HashSet<>(closure)) {
                if (item.getDotPosition() < item.getProduction().getRight().size()) {
                    String nextSymbol = item.getNextSymbol();
                    Set<Integer> lookaheads = calculateLookahead(item, closure, grammar);
                    for (Production production : grammar.getProductions()) {
                        if (production.getLeft().equals(nextSymbol)) {
                            Item newItem = new Item(production, 0, lookaheads);
                            if (!closure.contains(newItem)) {
                                closure.add(newItem);
                                changed = true;
                            }
                        }
                    }
                }
            }
        }
        return closure;
    }

    private Set<Integer> calculateLookahead(Item item, Set<Item> closure, Grammar grammar) {
        // 计算LR(1)项的向前看符号集合
        Set<Integer> lookaheads = new HashSet<>();
        if (item.getDotPosition() == item.getProduction().getRight().size()) {
            lookaheads.addAll(item.getLookahead());
        } else {
            String nextSymbol = item.getNextSymbol();
            Set<Item> lookItems = new HashSet<>();
            for (Item closureItem : closure) {
                if (closureItem.getProduction().getLeft().equals(nextSymbol)) {
                    lookItems.add(closureItem);
                }
            }
            for (Item lookItem : lookItems) {
                Set<Integer> itemLookaheads = lookItem.getLookahead();
                if (itemLookaheads.contains(Grammar.EMPTY)) {
                    lookaheads.addAll(calculateFollowSets(grammar).get(item.getProduction().getLeft()));
                    lookaheads.remove(Grammar.EMPTY);
                }
                lookaheads.addAll(itemLookaheads);
            }
        }
        return lookaheads;
    }

    private static class Item {
        private Production production;
        private int dotPosition;
        private Set<Integer> lookahead;

        public Item(Production production, int dotPosition, int lookahead) {
            this.production = production;
            this.dotPosition = dotPosition;
            this.lookahead = new HashSet<>();
            this.lookahead.add(lookahead);
        }

        public Item(Production production, int dotPosition, Set<Integer> lookahead) {
            this.production = production;
            this.dotPosition = dotPosition;
            this.lookahead = lookahead;
        }

        public Production getProduction() {
            return production;
        }

        public int getDotPosition() {
            return dotPosition;
        }

        public String getNextSymbol() {
            return production.getRight().get(dotPosition);
        }

        public Set<Integer> getLookahead() {
            return lookahead;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj instanceof Item) {
                Item other = (Item) obj;
                return production.equals(other.production) && dotPosition == other.dotPosition && lookahead.equals(other.lookahead);
            }
            return false;
        }

        @Override
        public int hashCode() {
            return Objects.hash(production, dotPosition, lookahead);
        }

        @Override
        public String toString() {
            StringBuilder builder = new StringBuilder();
            builder.append(production.getLeft());
            builder.append(" ->");
            for (int i = 0; i < production.getRight().size(); i++) {
                if (i == dotPosition) {
                    builder.append(" ·");
                }
                builder.append(" ");
                builder.append(production.getRight().get(i));
            }
            if (dotPosition == production.getRight().size()) {
                builder.append(" ·");
            }
            builder.append(", {");
            for (int lookahead : lookahead) {
                builder.append(" '");
                builder.append(Grammar.getSymbolString(lookahead));
                builder.append("'");
            }
            builder.append(" }");
            return builder.toString();
        }
    }

    private static class Action {
        public static final int SHIFT = 1;
        public static final int REDUCE = 2;
        public static final int ACCEPT = 3;
        public static final int ERROR = 4;

        private int type;
        private int value;
        private Production production;

        public Action(int type, int value, Production production) {
            this.type = type;
            this.value = value;
            this.production = production;
        }

        public int getType() {
            return type;
        }

        public int getValue() {
            return value;
        }

        public Production getProduction() {
            return production;
        }
    }
}

上述代码中，`Grammar`类表示给定的文法，`Token`类表示输入符号串中的一个Token，`LR1Parser`类表示LR(1)分析器，包含了构建LR(1)项集族、构建LR(1)分析表、计算Follow集合、计算First集合、计算闭包、计算向前看符号等功能函数。其中，`buildItemSets()`函数实现了LR(1)项集族的构建，`buildActionTable()`函数实现了LR(1)分析表中的Action部分的构建，`buildGotoTable()`函数实现了LR(1)分析表中的Goto部分的构建，`scan()`函数用于将输入符号串转换为Token序列，`parse()`函数实现了LR(1)分析器的主要逻辑。