diff --git a/.eslintrc.json b/.eslintrc.json new file mode 100644 index 0000000..2926fe4 --- /dev/null +++ b/.eslintrc.json @@ -0,0 +1,25 @@ +{ + "extends": [ + "standard", + "eslint:recommended", + "plugin:@typescript-eslint/recommended", + "plugin:@typescript-eslint/recommended-requiring-type-checking" + ], + "parser": "@typescript-eslint/parser", + "parserOptions": { + "sourceType": "module", + "project": "./tsconfig.json", + "tsconfigRootDir": "." + }, + "plugins": [ + "@typescript-eslint" + ], + "overrides": [ + { + "files": ["*.mts"], + "rules": { + "max-len": ["error", 80] + } + } + ] +} diff --git a/.github/workflows/node.js.yml b/.github/workflows/node.js.yml new file mode 100644 index 0000000..e83272b --- /dev/null +++ b/.github/workflows/node.js.yml @@ -0,0 +1,21 @@ +name: Node.js CI +on: [push] +jobs: + build: + runs-on: ubuntu-20.04 + + strategy: + matrix: + node-version: ["16.17.0"] + + steps: + - uses: actions/checkout@v2 + - name: Use Node.js ${{ matrix.node-version }} + uses: actions/setup-node@v2 + with: + node-version: ${{ matrix.node-version }} + cache: "npm" + - run: npm ci + - run: npm run lint + - run: npm test + - run: npm run build diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..807d5c6 --- /dev/null +++ b/.gitignore @@ -0,0 +1,5 @@ +node_modules/ +dist/ +.vscode/ +.nyc_output/ +*.tgz \ No newline at end of file diff --git a/.mocharc.json b/.mocharc.json new file mode 100644 index 0000000..ebbb2b2 --- /dev/null +++ b/.mocharc.json @@ -0,0 +1,4 @@ +{ + "extension": ["mts"], + "loader": "ts-node/esm" +} diff --git a/.nvmrc b/.nvmrc new file mode 100644 index 0000000..2a4e4ab --- /dev/null +++ b/.nvmrc @@ -0,0 +1 @@ +16.17.0 diff --git a/AUTHORS b/AUTHORS new file mode 100644 index 0000000..133b406 --- /dev/null +++ b/AUTHORS @@ -0,0 +1,5 @@ +# This is the list of the significant contributors + +Max DeLiso +Alex Matson +Shishir Biyyala diff --git a/CODE_OF_CONDUCT.md b/CODE_OF_CONDUCT.md new file mode 100644 index 0000000..be6edbe --- /dev/null +++ b/CODE_OF_CONDUCT.md @@ -0,0 +1,106 @@ +# Contributor Covenant Code of Conduct + +## Our Pledge + +We as members, contributors, and leaders pledge to make participation in our +community a harassment-free experience for everyone, regardless of age, body +size, visible or invisible disability, ethnicity, sex characteristics, gender +identity and expression, level of experience, education, socio-economic status, +nationality, personal appearance, race, caste, color, religion, or sexual +identity and orientation. +We pledge to act and interact in ways that contribute to an open, welcoming, +diverse, inclusive, and healthy community. + +## Our Standards + +Examples of behavior that contributes to a positive environment for our +community include: + +* Demonstrating empathy and kindness toward other people +* Being respectful of differing opinions, viewpoints, and experiences +* Giving and gracefully accepting constructive feedback +* Accepting responsibility and apologizing to those affected by our mistakes, +and learning from the experience +* Focusing on what is best not just for us as individuals, but for the overall +community + +Examples of unacceptable behavior include: + +* The use of sexualized language or imagery, and sexual attention or advances of +any kind +* Trolling, insulting or derogatory comments, and personal or political attacks +* Public or private harassment +* Publishing others’ private information, such as a physical or email address, +without their explicit permission +* Other conduct which could reasonably be considered inappropriate in a +professional setting + +## Enforcement Responsibilities + +Community leaders are responsible for clarifying and enforcing our standards of +acceptable behavior and will take appropriate and fair corrective action in +response to any behavior that they deem inappropriate, threatening, offensive, +or harmful. +Community leaders have the right and responsibility to remove, edit, or reject +comments, commits, code, wiki edits, issues, and other contributions that are +not aligned to this Code of Conduct, and will communicate reasons for moderation +decisions when appropriate. +Scope +This Code of Conduct applies within all community spaces, and also applies when +an individual is officially representing the community in public spaces. +Examples of representing our community include using an official e-mail address, +posting via an official social media account, or acting as an appointed +representative at an online or offline event. +Enforcement +Instances of abusive, harassing, or otherwise unacceptable behavior may be +reported to the community leaders responsible for enforcement by e-mailing +me@maxdeliso.name with the subject "COC violation." +All complaints will be reviewed and investigated promptly and fairly. +All community leaders are obligated to respect the privacy and security of the +reporter of any incident. + +## Enforcement Guidelines + +Community leaders will follow these Community Impact Guidelines in determining +the consequences for any action they deem in violation of this Code of Conduct: + +1. Correction +Community Impact: Use of inappropriate language or other behavior deemed +unprofessional or unwelcome in the community. +Consequence: A private, written warning from community leaders, providing +clarity around the nature of the violation and an explanation of why the +behavior was inappropriate. A public apology may be requested. +2. Warning +Community Impact: A violation through a single incident or series of +actions. +Consequence: A warning with consequences for continued behavior. No +interaction with the people involved, including unsolicited interaction with +those enforcing the Code of Conduct, for a specified period of time. This +includes avoiding interactions in community spaces as well as external channels +like social media. Violating these terms may lead to a temporary or permanent +ban. +3. Temporary Ban +Community Impact: A serious violation of community standards, including +sustained inappropriate behavior. +Consequence: A temporary ban from any sort of interaction or public +communication with the community for a specified period of time. No public or +private interaction with the people involved, including unsolicited interaction +with those enforcing the Code of Conduct, is allowed during this period. +Violating these terms may lead to a permanent ban. +4. Permanent Ban +Community Impact: Demonstrating a pattern of violation of community +standards, including sustained inappropriate behavior, harassment of an +individual, or aggression toward or disparagement of classes of individuals. +Consequence: A permanent ban from any sort of public interaction within the +community. + +## Attribution + +This Code of Conduct is adapted from the Contributor Covenant, +version 2.1, available at +. +Community Impact Guidelines were inspired by +Mozilla’s code of conduct enforcement ladder. +For answers to common questions about this code of conduct, see the FAQ at +. Translations are available at +. diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..a08c5fa --- /dev/null +++ b/LICENSE @@ -0,0 +1,9 @@ +# The MIT License (MIT) + +Copyright © 2022 Joseph Maximilian DeLiso + +Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..9291e92 --- /dev/null +++ b/README.md @@ -0,0 +1,19 @@ +# SKI in TS + +An implementation of a parser, evaluator, printer, and serializer for the [SKI](https://en.wikipedia.org/wiki/SKI_combinator_calculus) combinators in [Typescript](https://www.typescriptlang.org/). + +## Books + +* [Combinators: A Centennial View, Stephen Wolfram](https://www.amazon.com/dp/1579550436/ref=nosim?tag=YOURASSOCIATEID) +* [To Mock a Mockingbird, Raymond Smullyan](https://www.amazon.com/dp/0192801422/ref=nosim?tag=YOURASSOCIATEID) +* [Combinatory Logic Volume I, Haskell Brooks Curry & Robert Feys](https://www.amazon.com/dp/B0041N5RDC/ref=nosim?tag=YOURASSOCIATEID) + +## Papers + +* Turner, David. “A new implementation technique for applicative languages.” Software: Practice and Experience 9 (1979): n. pag. +* Stoye, William et al. “Some practical methods for rapid combinator reduction.” LFP '84 (1984). + +## Status + +[![Node.js CI](https://github.com/maxdeliso/typed-ski/actions/workflows/node.js.yml/badge.svg?branch=main)](https://github.com/maxdeliso/typed-ski/actions/workflows/node.js.yml) +[![COC](https://img.shields.io/badge/Contributor%20Covenant-2.1-4baaaa.svg)](CODE_OF_CONDUCT.md) diff --git a/lib/evaluator.mts b/lib/evaluator.mts new file mode 100644 index 0000000..a9503ae --- /dev/null +++ b/lib/evaluator.mts @@ -0,0 +1,168 @@ +import { Expression } from './expression.mjs' +import { nt } from './nonterminal.mjs' +import { TerminalSymbol } from './terminal.mjs' + +/** + * the shape of an evaluation result. + * altered is set if the evaluation step changed the input. + * expr is the evaluation output. + */ +export interface Result { + altered: boolean; + expr: E; +} + +/** + * a computation step; takes an expression and returns a result. + */ +export type Step = (expr: E) => Result + +/** + * the SKI combinator single step reduction function. + * @param expr the input expression. + * @returns the evaluation result. + */ +export const stepOnce: Step = + (expr: Expression) => scanStep(expr, [stepOnceI, stepOnceK, stepOnceS]) + +const stepOnceI: Step = + (expr: Expression) => treeStep(expr, stepI) + +const stepOnceK: Step = + (expr: Expression) => treeStep(expr, stepK) + +const stepOnceS: Step = + (expr: Expression) => treeStep(expr, stepS) + +/** + * @param expr the expression to scan with steppers. + * @param steppers a list of steppers to try on the entire expression. + * @returns the expression with the first possible step in the list applied. + * + * NOTE: this is an eagerly returning fold + */ +const scanStep = (expr: Expression, steppers: Array>): + Result => { + for (const step of steppers) { + const result = step(expr) + + if (result.altered) { + return result + } + } + + return { + altered: false, + expr + } +} + +/** + * @param expr the input expression + * @param step a stepper + * @returns the result of traversing the tree to determine if the step + * resulted in an altering. + * + * NOTE: this is an implementation of DFS where the expression + * is the input and a singular function that processes an expression + * and returns either nothing or some result, returning eagerly. + */ +function treeStep (expr: Expression, step: Step): + Result { + switch (expr.kind) { + case 'terminal': + return ({ + altered: false, + expr + }) + + case 'non-terminal': { + const currentResult = step(expr) + + if (currentResult.altered) { + return currentResult + } + + const lftStepResult = treeStep(expr.lft, step) + + if (lftStepResult.altered) { + return ({ + altered: true, + expr: nt(lftStepResult.expr, expr.rgt) + }) + } + + const rgtStepResult = treeStep(expr.rgt, step) + + return { + altered: rgtStepResult.altered, + expr: nt(expr.lft, rgtStepResult.expr) + } + } + } +} + +type ExtractStep = (expr: E) => E | false + +function extractStep (expr: Expression, extractStep: ExtractStep): + Result { + const extractionResult = extractStep(expr) + + if (extractionResult) { + return ({ altered: true, expr: extractionResult }) + } else { + return ({ altered: false, expr }) + } +} + +/* + * identity + * Ix = x + */ +const stepI: Step = (expr: Expression) => + extractStep( + expr, (expr: Expression) => + expr.kind === 'non-terminal' && + expr.lft.kind === 'terminal' && + expr.lft.sym === TerminalSymbol.I && + expr.rgt + ) + +/* + * constant + * Kxy = x + */ +const stepK: Step = (expr: Expression) => + extractStep( + expr, (expr: Expression) => + expr.kind === 'non-terminal' && + expr.lft.kind === 'non-terminal' && + expr.lft.lft.kind === 'terminal' && + expr.lft.lft.sym === TerminalSymbol.K && + expr.lft.rgt + ) + +/* + * fusion + * Sxyz = xz(yz) + */ +const stepS: Step = (expr: Expression) => + extractStep( + expr, (expr: Expression) => { + if ( + expr.kind === 'non-terminal' && + expr.lft.kind === 'non-terminal' && + expr.lft.lft.kind === 'non-terminal' && + expr.lft.lft.lft.kind === 'terminal' && + expr.lft.lft.lft.sym === TerminalSymbol.S + ) { + const x = expr.lft.lft.rgt + const y = expr.lft.rgt + const z = expr.rgt + + return nt(nt(x, z), nt(y, z)) + } else { + return false + } + } + ) diff --git a/lib/expression.mts b/lib/expression.mts new file mode 100644 index 0000000..35fe1ed --- /dev/null +++ b/lib/expression.mts @@ -0,0 +1,134 @@ +import { stepOnce } from './evaluator.mjs' +import { NonTerminal, nt } from './nonterminal.mjs' +import { SyntaxExpression } from './syntaxExpression.mjs' +import { generate as generateTerminal, Terminal } from './terminal.mjs' + +import { RandomSeed } from 'random-seed' + +/** + * EBNF grammar: + * + * terminal = "S" | "K" | "I" + * non-terminal = "(", expression, expression, ")" + * expression = terminal | non-terminal + * + * alphabet: + * + * "S" | "K" | "I" | "(" | ")" + * + * non-terminals: + * + * terminal | non-terminal | expression + */ +export type Expression = Terminal | NonTerminal + +/** + * @param syntaxExpression an expression to pretty print. + * @returns a pretty printed expression. + */ +export function prettyPrint (syntaxExpression: SyntaxExpression): string { + if (syntaxExpression === undefined) return '∅' + + switch (syntaxExpression.kind) { + case 'terminal': + return syntaxExpression.sym + case 'non-terminal': { + const printed = [ + '(', + `${prettyPrint(syntaxExpression.lft)}`, + `${prettyPrint(syntaxExpression.rgt)}`, + ')' + ] + + return printed.join('') + } + } +} + +/** + * @param rs a random seed. + * @param n the number of symbols to include in the expression. + * @returns a randomly generated expression. + */ +export function generate (rs: RandomSeed, n: number): Expression { + if (n === 0) { + throw new Error('A valid expression must contain at least one symbol.') + } + + let result: Expression = generateTerminal(rs) + + for (let i = 0; i < n - 1; i++) { + result = splat(rs, result, generateTerminal(rs)) + } + + return result +} + +/** + * @param exp an abstract expression. + * @returns how many terminals are present in the expression. + */ +export function size (exp: Expression): number { + if (exp.kind === 'terminal') return 1 + else return size(exp.lft) + size(exp.rgt) +} + +/** + * Run reductions continuously, with the supplied parameters. + * Note: when an expression can no longer be reduced, a new + * expression is generated. + * + * @param S the number of symbols in each generated expression. + * @param N the number of reduction steps to take. + * @param rs the random seed to use to regenerate the expr. + * @param onStep a callback function for when a step occurs. + * @param onRegenerate a callback function for when a regeneration occurs. + */ +export function compute ( + S: number, + N: number, + rs: RandomSeed, + onStep: (_: Expression) => void, + onRegenerate: (_: Expression) => void): Expression { + let exp = generate(rs, S) + + for (let i = 0; i < N; i++) { + const stepResult = stepOnce(exp) + + if (stepResult.altered) { + exp = stepResult.expr + onStep(exp) + } else { + exp = generate(rs, S) + onRegenerate(exp) + } + } + + return exp +} + +/** + * Splat a combinator in there randomly. + * + * @param randomSeed entropy source + * @param expr expression + * @param term the combinator to insert. + * @returns an expression with the symbol t added in a "random" but deserving + * location. + */ +const splat = (randomSeed: RandomSeed, expr: Expression, term: Terminal): + Expression => { + const direction = randomSeed.intBetween(0, 1) === 1 + + if (expr.kind === 'terminal') { + if (direction) { + return nt(expr, term) + } else { + return nt(term, expr) + } + } else if (direction) { + return nt(splat(randomSeed, expr.lft, term), expr.rgt) + } else { + return nt(expr.lft, splat(randomSeed, expr.rgt, term)) + } +} diff --git a/lib/index.mts b/lib/index.mts new file mode 100644 index 0000000..30ba130 --- /dev/null +++ b/lib/index.mts @@ -0,0 +1,5 @@ +export * from './expression.mjs' +export * from './syntaxExpression.mjs' +export * from './packer.mjs' +export * from './parser.mjs' +export * from './evaluator.mjs' diff --git a/lib/nonterminal.mts b/lib/nonterminal.mts new file mode 100644 index 0000000..5c5d2e7 --- /dev/null +++ b/lib/nonterminal.mts @@ -0,0 +1,16 @@ +export interface NonTerminal { + kind: 'non-terminal' + lft: E + rgt: E +} + +/** + * @param lft the left subtree. + * @param rgt the right subtree. + * @returns a new non-terminal node, with E as the type of each branch. + */ +export const nt = (lft: E, rgt: E): NonTerminal => ({ + kind: 'non-terminal', + lft, + rgt +}) diff --git a/lib/packer.mts b/lib/packer.mts new file mode 100644 index 0000000..9211d7e --- /dev/null +++ b/lib/packer.mts @@ -0,0 +1,225 @@ +import { Expression } from './expression.mjs' +import { nt } from './nonterminal.mjs' +import { term, TerminalSymbol } from './terminal.mjs' + +export type SymbolHeap = Array; + +export type BinaryHeap = Uint8Array + +const rootIndex = 0 + +function lftIndex (heapIdx: number): number { + return 2 * heapIdx + 1 +} + +function rgtIndex (heapIdx: number): number { + return 2 * heapIdx + 2 +} + +/** + * Transform an expression into a symbol heap. + * + * @param exp an expression. + * @returns a symbol heap. + */ +export function heapify (exp: Expression): SymbolHeap { + const heapLength = maxHeapIndex(exp) + 1 + const result = new Array(heapLength) + const indexes = [rootIndex] + const nodes = [exp] + + while (indexes.length > 0) { + const idx = indexes.pop() + const node = nodes.pop() + + if (idx === undefined || node === undefined) { + throw new Error('stack elements must be defined') + } else if (node.kind === 'non-terminal') { + indexes.push(lftIndex(idx)) + nodes.push(node.lft) + + indexes.push(rgtIndex(idx)) + nodes.push(node.rgt) + } else if (node.kind === 'terminal') { + result[idx] = node.sym + } else { + throw new Error('unexpected node kind') + } + } + + return result +} + +export function maxHeapIndex (exp: Expression): number { + return maxHeapIndexInternal(exp, 0) +} + +function maxHeapIndexInternal (exp: Expression, acc: number): number { + if (exp.kind === 'non-terminal') { + return Math.max( + maxHeapIndexInternal(exp.lft, lftIndex(acc)), + maxHeapIndexInternal(exp.rgt, rgtIndex(acc)) + ) + } else { + return acc + } +} + +export function unheapify (heapSyms: SymbolHeap): Expression { + if (heapSyms.length === 0) { + throw new Error('expression must be non-empty') + } + + return unheapifyFrom(heapSyms, 0) +} + +function unheapifyFrom (heapSyms: SymbolHeap, heapIdx: number): Expression { + if (heapIdx >= heapSyms.length) { + throw new Error(`heap index exceeded: ${heapIdx}. input is corrupt.`) + } + + const heapValue = heapSyms[heapIdx] + + if (heapValue) { + return term(heapValue) + } else { + return nt( + unheapifyFrom(heapSyms, lftIndex(heapIdx)), + unheapifyFrom(heapSyms, rgtIndex(heapIdx)) + ) + } +} + +/** + * ∅ -> b00 + * S -> b01 + * K -> b10 + * I -> b11 + * + * @see unpackSymbol + * @throws this was tossed in here to make the type of this function number + * + * NOTE: here ∅ represents the empty set, or lack of a value. + */ +function packSymbol (sym: TerminalSymbol | undefined): number { + if (sym === undefined) { + return 0b00 + } else if (sym === TerminalSymbol.S) { + return 0b01 + } else if (sym === TerminalSymbol.K) { + return 0b10 + } else if (sym === TerminalSymbol.I) { + return 0b11 + } else { + throw new Error('Impossible.') + } +} + +/** + * b00 -> ∅ + * b01 -> S + * b10 -> K + * b11 -> I + * + * @see packSymbol + */ +function unpackSymbol (n: number): TerminalSymbol | undefined { + if (n === 0b00) { + return undefined + } else if (n === 0b01) { + return TerminalSymbol.S + } else if (n === 0b10) { + return TerminalSymbol.K + } else if (n === 0b11) { + return TerminalSymbol.I + } else { + throw new Error(`The number ${n} does not correspond to a symbol in SKI.`) + } +} + +/** + * Pack a symbol heap into a binary heap. + * @param ts the symbol heap. + * @returns the binary heap. + */ +export function packSymbolHeap (ts: SymbolHeap): BinaryHeap { + /* + * ts byteCount /4 %4 /4+1 %4!=0 + * 0 0 0 0 1 0 + * 1 1 0 1 1 1 + * 2 1 0 2 1 1 + * 3 1 0 3 1 1 + * 4 1 1 0 2 0 + * 5 2 1 1 2 1 + * 6 2 1 2 2 1 + * 7 2 1 3 2 1 + * 8 2 2 0 2 0 + * 9 3 2 1 3 1 + */ + const lenDivFour : number = ts.length / 4 >> 0 + const lenModFourOdd : boolean = ts.length % 4 !== 0 + const packedLength : number = lenDivFour + (lenModFourOdd ? 1 : 0) + const result = new Uint8Array(packedLength) // note: initialized to zero + + for (let i = 0; i < ts.length; i++) { + const maybeValue = ts[i] + const symBits = packSymbol(maybeValue) + const block = (i / 4) >> 0 // prevents a floating point index + const shift = (3 - (i % 4)) * 2 + + result[block] |= (symBits << shift) + } + + return result +} + +/** + * Unpack a binary heap into a symbol heap. + * This is to reduce the in memory size of the symbol heap. + * @param inputBytes a sequence of bytes that contains an encoded symbol heap. + * @returns the corresponding symbol heap. + */ +export function unpackBinaryHeap (inputBytes: BinaryHeap): SymbolHeap { + const result: SymbolHeap = [] + + for (let i = 0; i < inputBytes.length; i++) { + const byte = inputBytes[i] || 0 + + /* + * 0 b 1100 0000 = 0 x C 0 + * 0 b 0011 0000 = 0 x 3 0 + * 0 b 0000 1100 = 0 x 0 C + * 0 b 0000 0011 = 0 x 0 3 + */ + const fourSnakeEyes = [ + (byte & 0xC0) >> 6, + (byte & 0x30) >> 4, + (byte & 0x0C) >> 2, + (byte & 0x03) >> 0 + ] + + fourSnakeEyes + .map(unpackSymbol) + .forEach(maybeSym => result.push(maybeSym)) + } + + return result +} + +/** + * Pack an expression into a contiguous sequence of heap ordered bits. + * @param exp the input expression. + * @returns a binary heap packed result. + */ +export function packHeap (exp: Expression): BinaryHeap { + return packSymbolHeap(heapify(exp)) +} + +/** + * Re-inflate a sequence of packed heap ordered bits into an Expression. + * @param heapBytes the input binary heap. + * @returns an expression. + */ +export function unpackHeap (heapBytes: BinaryHeap): Expression { + return unheapify(unpackBinaryHeap(heapBytes)) +} diff --git a/lib/parser.mts b/lib/parser.mts new file mode 100644 index 0000000..df502ad --- /dev/null +++ b/lib/parser.mts @@ -0,0 +1,68 @@ +import { Expression } from './expression.mjs' +import { nt } from './nonterminal.mjs' +import { SyntaxExpression, append } from './syntaxExpression.mjs' +import { term, TerminalSymbol } from './terminal.mjs' + +export class ParseError extends Error { } + +/** + * @param input a string with an SKI expression to parse. + * @returns an abstract expression corresponding to the parsed input string, + * should one exist. + * @throws {ParseError} if the input string is not a well formed expression. + */ +export function parse (input: string): Expression { + let syn: SyntaxExpression + let parenLevel = 0 + + for (const ch of input) { + if (ch === '(') { + syn = append(syn, { + kind: 'non-terminal', + lft: undefined, + rgt: undefined + }) + parenLevel++ + } else if (ch === ')') { + parenLevel-- + + if (parenLevel < 0) { + throw new ParseError('mismatched parens! (early)') + } + } else if (ch === TerminalSymbol.S || + ch === TerminalSymbol.K || + ch === TerminalSymbol.I) { + syn = append(syn, term(ch)) + } else { + throw new ParseError('unrecognized char: ' + ch) + } + } + + if (parenLevel !== 0) { + throw new ParseError('mismatched parens! (late)') + } + + return flatten(syn) +} + +/** + * @param exp a syntax expression. + * @returns an abstract expression. + * @throws {ParseError} if there are any empty internal nodes in the + * expression. + */ +export const flatten = (exp: SyntaxExpression): Expression => { + if (exp === undefined) { + throw new ParseError('expression undefined (empty)') + } else if (exp.kind === 'terminal') { + return exp + } else if ((exp.lft === undefined) && (exp.rgt !== undefined)) { + return flatten(exp.rgt) + } else if ((exp.lft !== undefined) && (exp.rgt === undefined)) { + return flatten(exp.lft) + } else if ((exp.lft === undefined) || (exp.rgt === undefined)) { + throw new ParseError('expression undefined (hole)') + } else { + return nt(flatten(exp.lft), flatten(exp.rgt)) + } +} diff --git a/lib/syntaxExpression.mts b/lib/syntaxExpression.mts new file mode 100644 index 0000000..bde2347 --- /dev/null +++ b/lib/syntaxExpression.mts @@ -0,0 +1,43 @@ +import { NonTerminal, nt } from './nonterminal.mjs' +import { Terminal } from './terminal.mjs' + +/** + * A variation on the expression type, that allows undefined values. + * This version is used to build up a syntax expression during parsing, + * which is then converted into an abstract expression after the parse, + * while verifying that no undefined values, or 'holes', remain. + */ +export type SyntaxExpression + = Terminal + | NonTerminal + | undefined; + +/** + * @param exp a syntax expression. + * @returns true if there is a hole, false otherwise. + */ +export const hasHole = (exp: SyntaxExpression): boolean => + exp === undefined || + (exp.kind === 'non-terminal' && (hasHole(exp.lft) || hasHole(exp.rgt))) + +/** + * @param lft a syntax expression. + * @param rgt a second syntax expression. + * @returns the two expressions, appended together. + */ +export const append = (lft: SyntaxExpression, rgt: SyntaxExpression): + SyntaxExpression => { + if (lft === undefined) { + return rgt + } else if (rgt === undefined) { + return lft + } else if (lft.kind === 'terminal') { + return nt(lft, rgt) + } else if (hasHole(lft.lft)) { + return nt(append(lft.lft, rgt), lft.rgt) + } else if (hasHole(lft.rgt)) { + return nt(lft.lft, append(lft.rgt, rgt)) + } else { + return nt(lft, rgt) + } +} diff --git a/lib/terminal.mts b/lib/terminal.mts new file mode 100644 index 0000000..b4bb72f --- /dev/null +++ b/lib/terminal.mts @@ -0,0 +1,39 @@ +import { RandomSeed } from 'random-seed' + +export enum TerminalSymbol { + S = 'S', + K = 'K', + I = 'I' +} + +export interface Terminal { + kind: 'terminal'; + sym: TerminalSymbol; +} + +export const term = (sym: TerminalSymbol): Terminal => ({ + kind: 'terminal', + sym +}) + +export const S = term(TerminalSymbol.S) +export const K = term(TerminalSymbol.K) +export const I = term(TerminalSymbol.I) + +/** + * @param rs the random seed to use. + * @returns a randomly selected terminal symbol. + */ +export function generate (rs: RandomSeed): Terminal { + const die = rs.intBetween(1, 3) + + if (die === 1) { + return S + } else if (die === 2) { + return K + } else if (die === 3) { + return I + } else { + throw new Error('error on line twenty eight') + } +} diff --git a/package-lock.json b/package-lock.json new file mode 100644 index 0000000..6b6d534 --- /dev/null +++ b/package-lock.json @@ -0,0 +1,10722 @@ +{ + "name": "typed-ski", + "version": "1.0.0", + "lockfileVersion": 2, + "requires": true, + "packages": { + "": { + "name": "typed-ski", + "version": "1.0.0", + "license": "MIT", + "dependencies": { + "random-seed": "^0.3.0" + }, + "devDependencies": { + "@types/chai": "^4.3.0", + "@types/jest": "^29.1.2", + "@types/mocha": "^10.0.0", + "@types/node": "^18.8.5", + "@types/random-seed": "^0.3.3", + "@typescript-eslint/eslint-plugin": "^5.15.0", + "@typescript-eslint/parser": "^5.15.0", + "chai": "^4.3.6", + "eslint": "^8.25.0", + "eslint-config-standard": "^17.0.0", + "eslint-plugin-import": "^2.25.4", + "eslint-plugin-node": "^11.1.0", + 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"ts-node" + }, + "types": "dist/lib/index.d.mts", + "module": "dist/lib/index.mjs", + "files": [ + "dist" + ], + "type": "module", + "repository": { + "type": "git", + "url": "git@github.com:maxdeliso/typed-ski.git" + }, + "keywords": [ + "SKI", + "combinators" + ], + "author": "Joseph Maximilian DeLiso", + "license": "MIT", + "bugs": { + "url": "https://github.com/maxdeliso/typed-ski/issues" + }, + "homepage": "https://github.com/maxdeliso/typed-ski", + "devDependencies": { + "@types/chai": "^4.3.0", + "@types/jest": "^29.1.2", + "@types/mocha": "^10.0.0", + "@types/node": "^18.8.5", + "@types/random-seed": "^0.3.3", + "@typescript-eslint/eslint-plugin": "^5.15.0", + "@typescript-eslint/parser": "^5.15.0", + "chai": "^4.3.6", + "eslint": "^8.25.0", + "eslint-config-standard": "^17.0.0", + "eslint-plugin-import": "^2.25.4", + "eslint-plugin-node": "^11.1.0", + "eslint-plugin-promise": "^6.0.1", + "jest": "^29.1.2", + "mocha": "^10.0.0", + "ts-node": "^10.7.0", + "typescript": "^4.8.4" + }, + "dependencies": { + "random-seed": "^0.3.0" + } +} diff --git a/test/evaluator.test.mts b/test/evaluator.test.mts new file mode 100644 index 0000000..856878e --- /dev/null +++ b/test/evaluator.test.mts @@ -0,0 +1,77 @@ +import { parse } from '../lib/parser.mjs' +import { stepOnce } from '../lib/evaluator.mjs' +import { prettyPrint } from '../lib/expression.mjs' + +import { describe, it } from 'mocha' +import { assert } from 'chai' + +const first = parse('III') +const second = parse('II') +const third = parse('I') +const fourth = parse('KIS') +const fifth = parse('SKKI') +const sixth = parse('SKKII') +const seventh = parse('KI(KI)') + +describe('stepOnce', () => { + it(`evaluates ${prettyPrint(second)} + => + ${prettyPrint(third)}`, () => { + const result = stepOnce(second) + + assert(result.altered) + + assert.deepStrictEqual(result.expr, third) + }) + + it(`evaluates ${prettyPrint(first)} + => + ${prettyPrint(third)}`, + () => { + const result = stepOnce(stepOnce(first).expr) + + assert(result.altered) + + assert.deepStrictEqual(result.expr, third) + }) + + it(`evaluates ${prettyPrint(fourth)} + => + ${prettyPrint(third)}`, () => { + const result = stepOnce(fourth) + + assert(result.altered) + + assert.deepStrictEqual(result.expr, third) + }) + + it(`evaluates + ${prettyPrint(fifth)} + => + ${prettyPrint(seventh)}`, () => { + const first = stepOnce(fifth) + + assert(first.altered) + + assert.deepStrictEqual(first.expr, seventh) + }) + + it(`${prettyPrint(sixth)} + => + ${prettyPrint(third)}`, + () => { + const firstStep = stepOnce(sixth) + + assert(firstStep.altered) + + const secondStep = stepOnce(firstStep.expr) + + assert(secondStep.altered) + + const thirdStep = stepOnce(secondStep.expr) + + assert(thirdStep.altered) + + assert.deepStrictEqual(thirdStep.expr, third) + }) +}) diff --git a/test/expression.test.mts b/test/expression.test.mts new file mode 100644 index 0000000..ba7e685 --- /dev/null +++ b/test/expression.test.mts @@ -0,0 +1,28 @@ +import { Expression, generate, prettyPrint, size } from '../lib/expression.mjs' +import { nt } from '../lib/nonterminal.mjs' +import { K, S } from '../lib/terminal.mjs' + +import { assert } from 'chai' +import pkg, { RandomSeed } from 'random-seed' +const { create } = pkg + +describe('prettyPrint', () => { + const expr = nt(nt(S, K), K) + const printedExpr = '((SK)K)' + + it('pretty prints a valid expression', + () => assert.deepStrictEqual(prettyPrint(expr), printedExpr) + ) +}) + +describe('generate', () => { + const testSeed = '18477814418' + const n = 8 + + it('generates a random expression with the specified size', () => { + const rs: RandomSeed = create(testSeed) + const generated = generate(rs, n) + + assert.deepStrictEqual(n, size(generated)) + }) +}) diff --git a/test/packer.test.mts b/test/packer.test.mts new file mode 100644 index 0000000..dc38d9a --- /dev/null +++ b/test/packer.test.mts @@ -0,0 +1,78 @@ +import { parse } from '../lib/parser.mjs' +import { + BinaryHeap, + maxHeapIndex, + packHeap, + unpackHeap +} from '../lib/packer.mjs' +import { compute, Expression, size } from '../lib/expression.mjs' + +import { assert } from 'chai' +import { describe, it } from 'mocha' +import { hrtime } from 'process' +import pkg from 'random-seed' +const { create } = pkg + +const eye = parse('I') +const dos = parse('II') +const tres = parse('III') +const quattro = parse('SKKI') +const toTheRight = parse('(I(S(KI)))') +const zipper = parse('((I(S(KI)))I)') + +describe('packHeap and unpackHeap', () => { + const assertRepack = (expr: Expression): BinaryHeap => { + const packed = packHeap(expr) + const unpacked = unpackHeap(packed) + assert.deepStrictEqual(expr, unpacked) + return packed + } + + it('packs an expression composed of four symbols into three bytes', + () => { + const packResult = assertRepack(quattro) + const unpacked = unpackHeap(packResult) + + assert.deepStrictEqual(size(unpacked), 4) + assert.deepStrictEqual(packResult.length, 3) + } + ) + + it('packs and unpacks I to a single byte/symbol', + () => { + const singlePackResult = assertRepack(eye) + const unpackedSingle = unpackHeap(singlePackResult) + + assert.deepStrictEqual(singlePackResult.length, 1) + assert.deepStrictEqual(size(unpackedSingle), 1) + assert.deepStrictEqual(eye, unpackedSingle) + } + ) + + it('packs and unpacks a simple small expression symmetrically', + () => assertRepack(quattro) + ) + + const S = 8 // symbol count in each randomly generated expression + const N = 128 // the total number of reductions to complete + + it('packs and unpacks many randomly generated expressions', () => { + const seed = hrtime.bigint() + const rs = create(`${seed}`) + + compute(S, N, rs, + (expr) => assertRepack(expr), + (expr) => assertRepack(expr)) + }) +}) + +describe('maxHeapIndex', () => { + it('returns the largest heap index of different shapes', + () => { + assert.deepStrictEqual(maxHeapIndex(eye), 0) + assert.deepStrictEqual(maxHeapIndex(dos), 2) + assert.deepStrictEqual(maxHeapIndex(tres), 4) + assert.deepStrictEqual(maxHeapIndex(toTheRight), 14) + assert.deepStrictEqual(maxHeapIndex(zipper), 22) + }) +}) diff --git a/test/parser.test.mts b/test/parser.test.mts new file mode 100644 index 0000000..1b7fd6e --- /dev/null +++ b/test/parser.test.mts @@ -0,0 +1,65 @@ +import { Expression, prettyPrint } from '../lib/expression.mjs' +import { nt } from '../lib/nonterminal.mjs' +import { parse, ParseError } from '../lib/parser.mjs' +import { I, K, S } from '../lib/terminal.mjs' + +import { assert, expect } from 'chai' +import { describe, it } from 'mocha' + +const firstLiteral = '(I(SK))' +const secondLiteral = '(((((SK)I)S)K)I)' + +describe('parse', () => { + it(`should parse ${firstLiteral} and variations`, () => { + const expected = nt(I, nt(S, K)) + + assert.deepStrictEqual(parse(firstLiteral), expected) + assert.deepStrictEqual(parse('I(SK)'), expected) + }) + + it(`should parse ${secondLiteral} and variations`, () => { + const expected = + nt( + nt( + nt( + nt( + nt(S, K), I + ), + S), + K), + I) + + assert.deepStrictEqual(parse(secondLiteral), expected) + assert.deepStrictEqual(parse('SKISKI'), expected) + }) + + it('should parse adjacent chars associating to the left', () => { + assert.deepStrictEqual(parse('SKI'), parse('(SK)I')) + assert.deepStrictEqual(parse('(SK)I'), parse('((SK)I)')) + + assert.notDeepEqual(parse('SKI'), parse('S(KI)')) + }) + + it('should fail to parse mismatched parens', () => { + expect(() => parse('(())(')).to.throw(ParseError, /mismatched/) + expect(() => parse('(')).to.throw(ParseError, /mismatched/) + expect(() => parse('()())')).to.throw(ParseError, /mismatched/) + }) + + const assertReparse = (expr: string) => { + const parsed = parse(expr) + const printed = prettyPrint(parsed) + const reparsed = parse(printed) + const reprinted = prettyPrint(reparsed) + + assert.deepStrictEqual(parsed, reparsed) + assert.deepStrictEqual(printed, reprinted) + } + + it('should reparse complicated expressions', () => { + assertReparse('S(K(SKK))SI') + assertReparse('SK(SKK)SI') + assertReparse('SKI') + assertReparse('(IIII)') + }) +}) diff --git a/test/performance.test.mts b/test/performance.test.mts new file mode 100644 index 0000000..30cc509 --- /dev/null +++ b/test/performance.test.mts @@ -0,0 +1,37 @@ +import { compute } from '../lib/expression.mjs' + +import { hrtime } from 'process' +import { Readable } from 'stream' +import pkg from 'random-seed' +const { create } = pkg + +describe('evaluator performance', () => { + const S = 64 // symbol count in each randomly generated expression + const N = 256 // the total number of reductions to complete + + it('is estimated by measuring the rate of reductions', () => { + const seed = hrtime.bigint() + const rs = create(`${seed}`) + const start = hrtime.bigint() + const testOutput = new Readable() + let generations = 1 // generate upon unaltered evaluation + + compute(S, N, rs, + () => testOutput.push('.'), + () => { + testOutput.push('!') + generations++ + }) + + const final = hrtime.bigint() + const elapsedNs = final - start + const estimatedReductionDurationNs = elapsedNs / BigInt(N) + + testOutput.push( + `\ncompleted in ${elapsedNs} ns +for an estimated ${estimatedReductionDurationNs} ns per reduction +with random seed ${seed} and ${generations} generations.`) + testOutput.push(null) + testOutput.pipe(process.stdout) + }) +}) diff --git a/tsconfig.json b/tsconfig.json new file mode 100644 index 0000000..086940a --- /dev/null +++ b/tsconfig.json @@ -0,0 +1,32 @@ +{ + "compilerOptions": { + "target": "ESNext", + "module": "esnext", + "skipLibCheck": true, + "moduleResolution": "NodeNext", + "forceConsistentCasingInFileNames": true, + "strict": true, + "noImplicitAny": true, + "strictNullChecks": true, + "strictFunctionTypes": true, + "strictBindCallApply": true, + "strictPropertyInitialization": true, + "noImplicitThis": true, + "useUnknownInCatchVariables": true, + "alwaysStrict": true, + "noUnusedLocals": true, + "noUnusedParameters": true, + "exactOptionalPropertyTypes": true, + "noImplicitReturns": true, + "noFallthroughCasesInSwitch": true, + "noUncheckedIndexedAccess": true, + "noImplicitOverride": true, + "noPropertyAccessFromIndexSignature": true, + "allowUnusedLabels": true, + "allowUnreachableCode": true, + "outDir": "./dist", + "declarationDir": "./dist", + "declaration": true, + "declarationMap": true + } +}