lambda/src/lambda.ts at main · clikuki/lambda · GitHub

History

321 lines (285 loc) · 7.59 KB

Raw

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

import { getID, ID } from "./utils.js";

const id = getID();

export interface Abstraction {

type: "ABSTRACTION";

param: symbol;

body: Term;

id: ID;

}

export interface Application {

type: "APPLICATION";

left: Term;

right: Term;

id: ID;

}

export interface Variable {

type: "VARIABLE";

symbol: symbol;

id: ID;

}

export type Term = Application | Abstraction | Variable;

export interface Replacer {

by?: Term;

at: Term[];

}

const REDUCTION_STEP_LIMIT = 10000;

export class Lambda {

tree: Term;

constructor(code: string) {

this.tree = parseString(code);

}

betaReduce(attemptNominal = false) {

let reduced: Term | null;

let steps = REDUCTION_STEP_LIMIT;

const replaced: Replacer = { at: [] };

do {

reduced = attemptNominal

? this._greedyReductionStep(this.tree)

: this._shallowReductionStep(this.tree, replaced);

if (reduced) this.tree = reduced;

} while (attemptNominal && reduced && --steps > 0);

return replaced;

}

/** Performs as much reduction as possible in a single step */

_greedyReductionStep(tree: Term): Term | null {

switch (tree.type) {

case "APPLICATION":

// Reduce application

const { left, right } = tree;

const leftReduct = this._greedyReductionStep(left) ?? left;

const rightReduct = this._greedyReductionStep(right) ?? right;

if (left.type === "ABSTRACTION") {

return this._substitute(left.body, left.param, right);

} else {

return {

id: tree.id,

type: "APPLICATION",

left: leftReduct,

right: rightReduct,

};

}

case "ABSTRACTION":

// Reduce abstraction body

const bodyReduct = this._greedyReductionStep(tree.body);

if (bodyReduct) {

return {

id: tree.id,

type: "ABSTRACTION",

param: tree.param,

body: bodyReduct,

};

}

return null;

}

/** Perform one step of beta reduction */

_shallowReductionStep(tree: Term, replaced: Replacer): Term | null {

switch (tree.type) {

case "APPLICATION":

// Reduce application

const { left, right } = tree;

if (left.type === "ABSTRACTION") {

replaced.by = right;

return this._substitute(left.body, left.param, right, replaced);

}

const leftReduct = this._shallowReductionStep(left, replaced);

if (leftReduct) {

return {

id: tree.id,

type: "APPLICATION",

left: leftReduct,

right,

};

}

const rightReduct = this._shallowReductionStep(right, replaced);

if (rightReduct) {

return {

id: tree.id,

type: "APPLICATION",

left,

right: rightReduct,

};

}

break;

case "ABSTRACTION":

// Reduce abstraction body

const bodyReduct = this._shallowReductionStep(tree.body, replaced);

if (bodyReduct) {

return {

id: tree.id,

type: "ABSTRACTION",

param: tree.param,

body: bodyReduct,

};

}

return null;

}

_substitute(tree: Term, from: symbol, to: Term, replaced?: Replacer): Term {

// Quick escape for strings

if (tree.type === "VARIABLE") {

if (tree.symbol === from) {

const copy = this.copy(to);

replaced?.at!.push(copy);

return copy;

}

return tree;

}

let sub: Term;

if (tree.type === "APPLICATION") {

// Dealing with application

const { left, right } = tree;

sub = {

id: tree.id,

type: "APPLICATION",

left: this._substitute(left, from, to, replaced),

right: this._substitute(right, from, to, replaced),

};

} else if (tree.param !== from) {

// Dealing with abstraction

sub = {

id: tree.id,

type: "ABSTRACTION",

param: tree.param,

body: this._substitute(tree.body, from, to, replaced),

};

} else {

// Is abstraction, but shadows the term that we are trying to substitute

sub = tree;

}

return sub;

}

copy(tree: Term, changeID = true): Term {

switch (tree.type) {

case "VARIABLE":

return {

id: changeID ? id.next().value : tree.id,

type: "VARIABLE",

symbol: tree.symbol,

};

case "APPLICATION":

return {

id: changeID ? id.next().value : tree.id,

type: "APPLICATION",

left: this.copy(tree.left, changeID),

right: this.copy(tree.right, changeID),

};

case "ABSTRACTION":

return {

id: changeID ? id.next().value : tree.id,

type: "ABSTRACTION",

param: tree.param,

body: this.copy(tree.body, changeID),

};

}

toString(collectParameters = false) {

return stringifyTree(this.tree, collectParameters);

}

export const func_char = "@";

export function parseString(

code: string,

mapping = new Map<string, symbol>()

): Term {

let left: Term | null = null;

let right: Term | null = null;

for (let i = 0; i < code.length; i++) {

const char = code[i];

if (char === " ") throw SyntaxError("No spaces allowed in code string");

if (char === func_char) {

// abstraction declaration

const start = i + 3;

const end = code.length;

const paramChar = code[i + 1];

const param = Symbol(paramChar);

const localMapping = new Map(mapping);

localMapping.set(paramChar, param);

// All characters at this point must be consumed

const body = parseString(code.slice(start, end), localMapping);

const abstraction: Abstraction = {

type: "ABSTRACTION",

param,

body,

id: id.next().value,

};

if (!left) left = abstraction;

else right = abstraction;

i = end;

} else if (char === "(") {

// Perform parse within bracket group, this usually occurs before abstraction declarations

const start = i + 1;

const end = findBracketPair(code, i);

let term = parseString(code.slice(start, end), mapping);

if (!left) left = term;

else right = term;

i = end;

} else {

// Get correspnding symbol of variable

const sym = mapping.get(char) ?? Symbol(char);

if (!mapping.has(char)) mapping.set(char, sym);

// Add single character as variable

const variable: Term = {

type: "VARIABLE",

symbol: sym,

id: id.next().value,

};

if (!left) left = variable;

else right = variable;

}

if (right) {

// Group a and b into an application

left = { type: "APPLICATION", left, right, id: id.next().value };

right = null;

}

if (!left) throw "Cannot parse empty string";

return left;

}

export function stringifyTree(tree: Term, combineParameters = false): string {

let str = "";

if (tree.type === "VARIABLE") {

// Is this a dangerous assumption?

str = tree.symbol.description!;

} else if (tree.type === "APPLICATION") {

// Dealing with application

const { left, right } = tree;

str += stringifyTree(left, combineParameters);

// If the second term is an application itself, then explicitly parenthesize

if (right.type === "APPLICATION")

str += `(${stringifyTree(right, combineParameters)})`;

else str += `${stringifyTree(right, combineParameters)}`;

} else {

// Dealing with abstraction

// Shorthand: Collect parameters of consecutively nested abstractions

let node: Term = tree.body;

let parameters = tree.param.description!;

while (combineParameters && node.type === "ABSTRACTION") {

parameters += node.param.description;

node = node.body;

}

str = `(${func_char}${parameters}.${stringifyTree(node, combineParameters)})`;

}

return str;

}

function findBracketPair(str: string, at: number): number {

let count = 1;

for (let i = at + 1; i < str.length; i++) {

const char = str[i];

if (char === "(") count++;

else if (char === ")" && !--count) return i;

}

return -1;

}

export function code(

strings: TemplateStringsArray,

...values: string[]

): string {

let str = "";

for (let i = 0; i < values.length; i++) {

str += strings[i];

str += `(${values[i]})`;

}

str += strings.at(-1);

return str.replaceAll(" ", "");

}

lambda/src/lambda.ts at main · clikuki/lambda · GitHub

Expand file tree

Breadcrumbs

lambda.ts

Latest commit

History

Breadcrumbs

lambda.ts

File metadata and controls