|
| 1 | +function first(G, A) { |
| 2 | + let result = new Set |
| 3 | + let visited = new Set |
| 4 | + let stack = [A] |
| 5 | + while (stack.length > 0) { |
| 6 | + let X = stack.pop() |
| 7 | + if (visited.has(X)) continue |
| 8 | + visited.add(X) |
| 9 | + if (!/^[A-Z]/.test(X) || X === '$') { |
| 10 | + result.add(X) |
| 11 | + continue |
| 12 | + } |
| 13 | + for (let i = 0; i < G.length; i++) { |
| 14 | + let r = G[i] |
| 15 | + if (r[0] === X && r[1] !== X) { |
| 16 | + stack.push(r[1]) |
| 17 | + } |
| 18 | + } |
| 19 | + } |
| 20 | + return result |
| 21 | +} |
| 22 | + |
| 23 | +function closure(G, items) { |
| 24 | + let stack = items.slice() |
| 25 | + let state = items.slice() |
| 26 | + let visited = new Set |
| 27 | + while (true) { |
| 28 | + if (stack.length === 0) break |
| 29 | + let item = stack.shift() |
| 30 | + let key = item.rule + ',' + item.dot + ',' + item.lookahead |
| 31 | + if (visited.has(key)) { |
| 32 | + continue |
| 33 | + } |
| 34 | + visited.add(key) |
| 35 | + state.push(item) |
| 36 | + let r = G[item.rule] |
| 37 | + let X1 = r[item.dot + 1] |
| 38 | + let X2 = r[item.dot + 2] |
| 39 | + for (let i = 0; i < G.length; i++) { |
| 40 | + if (G[i][0] !== X1) continue |
| 41 | + let ls = item.dot + 2 === r.length |
| 42 | + ? new Set([item.lookahead]) |
| 43 | + : union(first(G, X1), first(G, X2)) |
| 44 | + for (let lookahead of ls) { |
| 45 | + let nitem = { |
| 46 | + rule: i, |
| 47 | + dot: 0, |
| 48 | + lookahead, |
| 49 | + next: -1, |
| 50 | + index: -1, |
| 51 | + } |
| 52 | + stack.push(nitem) |
| 53 | + } |
| 54 | + } |
| 55 | + } |
| 56 | + return state |
| 57 | +} |
| 58 | + |
| 59 | +function union(A, B) { |
| 60 | + // :( |
| 61 | + return new Set(Array.from(A).concat(Array.from(B))) |
| 62 | +} |
| 63 | + |
| 64 | +class States { |
| 65 | + static key(items) { |
| 66 | + return items.map(item => { |
| 67 | + return item.rule + ',' + item.dot + ',' + item.lookahead |
| 68 | + }).sort().join('_') |
| 69 | + } |
| 70 | + constructor(G) { |
| 71 | + this.G = G |
| 72 | + this.states = [] |
| 73 | + this._stateKeys = new Map |
| 74 | + } |
| 75 | + add(items) { |
| 76 | + let key = States.key(items) |
| 77 | + |
| 78 | + let i = this._stateKeys.get(key) |
| 79 | + if (i !== undefined) return i |
| 80 | + i = this.states.length |
| 81 | + this.states.push(items) |
| 82 | + this._stateKeys.set(key, i) |
| 83 | + return i |
| 84 | + } |
| 85 | + has(items) { |
| 86 | + return this._stateKeys.has(States.key(items)) |
| 87 | + } |
| 88 | +} |
| 89 | + |
| 90 | +function groupNext(G, state) { |
| 91 | + let groups = new Map |
| 92 | + for (let i = 0; i < state.length; i++) { |
| 93 | + let s = state[i] |
| 94 | + let rule = G[s.rule] |
| 95 | + if (s.dot + 1 >= rule.length) continue |
| 96 | + let X0 = rule[0] |
| 97 | + let X1 = rule[s.dot + 1] |
| 98 | + let gs = groups.get(X1) |
| 99 | + if (gs == null) gs = [] |
| 100 | + gs.push({ |
| 101 | + rule: s.rule, |
| 102 | + dot: s.dot + 1, |
| 103 | + lookahead: s.lookahead, |
| 104 | + index: i, |
| 105 | + next: -1, |
| 106 | + }) |
| 107 | + groups.set(X1, gs) |
| 108 | + } |
| 109 | + return groups |
| 110 | +} |
| 111 | + |
| 112 | +function itemSets(G) { |
| 113 | + let states = new States(G) |
| 114 | + let I0 = closure(G, [{ rule: 0, dot: 0, lookahead: '$', index: 0, next: -1 }]) |
| 115 | + let i0 = states.add(I0) |
| 116 | + let stack = [I0] |
| 117 | + while (true) { |
| 118 | + if (stack.length === 0) break |
| 119 | + let I = stack.shift() |
| 120 | + let groups = groupNext(G, I) |
| 121 | + for (let T of Array.from(groups.keys()).sort()) { |
| 122 | + let gs = groups.get(T) |
| 123 | + let J = closure(G, gs) |
| 124 | + if (!states.has(J)) stack.push(J) |
| 125 | + let j = states.add(J) |
| 126 | + for (let si = 0; si < gs.length; si++) { |
| 127 | + let g = gs[si] |
| 128 | + I[g.index].next = j |
| 129 | + } |
| 130 | + } |
| 131 | + } |
| 132 | + return states.states |
| 133 | +} |
| 134 | + |
| 135 | +function createTable(G, states) { |
| 136 | + let action = Array(states.length).fill(null).map(x => new Map) |
| 137 | + let goTo = Array(states.length).fill(null).map(x => new Map) |
| 138 | + |
| 139 | + for (let i = 0; i < states.length; i++) { |
| 140 | + let I = states[i] |
| 141 | + for (let j = 0; j < I.length; j++) { |
| 142 | + let item = I[j] |
| 143 | + if (item.rule === 0 && item.dot + 1 === G[item.rule].length && item.lookahead === '$') { |
| 144 | + action[i].set('$', 'acc') |
| 145 | + } else if (item.dot + 1 === G[item.rule].length) { |
| 146 | + let a = item.lookahead |
| 147 | + action[i].set(a, 'r' + item.rule) |
| 148 | + } else { |
| 149 | + let a = G[item.rule][item.dot + 1] |
| 150 | + action[i].set(a, 's' + item.next) |
| 151 | + } |
| 152 | + let A = G[item.rule][item.dot + 1] |
| 153 | + if (/^[A-Z]/.test(A)) { |
| 154 | + goTo[i].set(A, item.next) |
| 155 | + } |
| 156 | + } |
| 157 | + } |
| 158 | + return { action, goTo } |
| 159 | +} |
| 160 | + |
| 161 | +function parse(G, { action, goTo }, input) { |
| 162 | + let firstSymbol = G[0][0] |
| 163 | + let offset = 0 |
| 164 | + let stack = [0] |
| 165 | + let nodes = [] |
| 166 | + let lookahead = input[0] |
| 167 | + |
| 168 | + while (true) { |
| 169 | + let state = stack[stack.length - 1] |
| 170 | + let a = action[state].get(lookahead) |
| 171 | + if (a === undefined) throw new Error(`no action for state: ${state} lookahead: ${lookahead}`) |
| 172 | + let n = Number(a.slice(1)) |
| 173 | + if (/^s/.test(a)) { |
| 174 | + nodes.push({ symbol: lookahead, offset }) |
| 175 | + stack.push(n) |
| 176 | + lookahead = input[++offset] |
| 177 | + } else if (/^r/.test(a)) { |
| 178 | + let symbol = G[n][0] |
| 179 | + let arity = G[n].length - 1 |
| 180 | + let children = Array(arity) |
| 181 | + for (let i = 0; i < arity; i++) { |
| 182 | + children[arity - 1 - i] = nodes.pop() |
| 183 | + stack.pop() |
| 184 | + } |
| 185 | + nodes.push({ symbol, children }) |
| 186 | + |
| 187 | + state = stack[stack.length - 1] |
| 188 | + let gt = goTo[state].get(symbol) |
| 189 | + if (gt === undefined) throw new Error(`undefined goto for state=${state} symbol=${symbol}`) |
| 190 | + stack.push(gt) |
| 191 | + } else if (a === 'acc') { |
| 192 | + return { symbol: firstSymbol, children: nodes } |
| 193 | + } else { |
| 194 | + throw new Error(`unexpected value for action ${a}`) |
| 195 | + } |
| 196 | + } |
| 197 | +} |
| 198 | + |
| 199 | +let grammar = [ |
| 200 | + [ "S", "S" ], |
| 201 | + [ "S", "X", "X" ], |
| 202 | + [ "X", "a", "X" ], |
| 203 | + [ "X", "b" ] |
| 204 | +] |
| 205 | +let sets = itemSets(grammar) |
| 206 | +// console.log(sets) |
| 207 | +let tab = createTable(grammar, sets) |
| 208 | +console.log(tab) |
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