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Supports SKI, BCKW, Church numerals, and setting up assertions ('quests') involving all of the above.","maintainers":[{"name":"dallaylaen","email":"khedin@gmail.com"}],"readme":"# Simple Kombinator Interpreter\n\n> **A humane tooling for inhuman logic**\n\nThis package contains a\n[combinatory logic](https://en.wikipedia.org/wiki/Combinatory_logic)\nand [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus)\nparser and interpreter focused on traceability and inspectability.\n\nIt is written in TypeScript and JavaScript\nand can be used in Node.js or in the browser.\n\nA [playground](https://dallaylaen.github.io/ski-interpreter/)\nand a [quest page](https://dallaylaen.github.io/ski-interpreter/quest.html)\ncontaining interactive combinatory logic exercises of increasing difficulty are included.\n\n# Features:\n\n* SKI and BCKW combinators\n* Lambda expressions\n* Church numerals\n* Defining new terms\n* &lambda; &lrarr; SKI conversion\n* Comparison of expressions\n* Includes a class for building and executing test cases for combinators\n\n# Syntax\n\n* Uppercase terms are always single characters and may be lumped together;\n* Lowercase alphanumeric terms may have multiple letters and must therefore be separated by spaces;\n* Whole non-negative numbers are interpreted as Church numerals, e.g. `5 x y` evaluates to `x(x(x(x(x y))))`. They must also be space-separated from other terms;\n* `x y z` is the same as `(x y) z` or `x(y)(z)` but **not** `x (y z)`;\n* Unknown terms are assumed to be free variables;\n* Lambda terms are written as `x->y->z->expr`, which is equivalent to\n`x->(y->(z->expr))` (aka right associative). Free variables in a lambda expression ~~stay in Vegas~~ are isolated from terms with the same name outside it;\n* X = y z defines a new term.\n\n## Starting combinators:\n\n* <code>I x &mapsto; x</code> _// identity_;\n* <code>K x y &mapsto; x</code> _//constant_;\n* <code>S x y z &mapsto; x z (y z)</code> _// fusion_;\n* <code>B x y z &mapsto; x (y z)</code> _// composition_;\n* <code>C x y z &mapsto; x z y</code> _// swapping_;\n* <code>W x y &mapsto; x y y</code> _//duplication_;\n\nThe special combinator `+` will increment Church numerals,\nif they happen to come directly after it:\n\n* `+ 0` // 1\n* `2 + 3` // -> `+(+(3))` -> `+(4)` -> `5`\n\nThe `term + 0` idiom may be used to convert\nnumbers obtained via computation (e.g. factorials)\nback to human readable form.\n\n# Execution strategy\n\nApplications and native terms use leftmost-outermost strategy, i.e. the first term in the tree\nthat has enough arguments is executed and the step ends there.\n\nLambda terms are lazy, i.e. the body is not touched whatsoever\nuntil all the free variables are bound.\nThis is consistent with combinator behavior under LO order.\n\n# Playground\n\n* [Interactive interpreter](https://dallaylaen.github.io/ski-interpreter/)\n\n  * all of the above features (except comparison and JS-native terms) in your browser\n  * expressions have permalinks\n  * can configure verbosity and execution speed\n  * switchable visual highlighting of redexes and outline of subexpressions\n\n* [Quests](https://dallaylaen.github.io/ski-interpreter/quest.html)\n\nThis page contains small combinatory logic exercises of increasing (hopefully) difficulty.\nEach task requires the user to build a combinator with specific properties.\nNew combinators are unlocked as the user progresses.\n\n# Installation\n\n```bash\nnpm install @dallaylaen/ski-interpreter\n```\n\n# CLI\n\n[bin/ski.js](bin/ski.js) - also available as `npx ski` - contains several subcommands:\n\n## Subcommands\n\n* **`repl`** - Start an interactive REPL\n  * `--verbose` - Show all evaluation steps\n  * Built-in commands (type `!help` in REPL):\n    * `!ls` - List all defined terms\n    * `!help` - Show available commands\n\n* **`eval <expression>`** - Evaluate a single expression\n  * `--verbose` - Show all evaluation steps\n  * Example: `ski eval \"S K K x\"`\n\n* **`file <filepath>`** - Evaluate expressions from a file\n  * `--verbose` - Show all evaluation steps\n  * Example: `ski file script.ski`\n\n* **`infer <expression>`** - try to find equivalent lambda expression and display its properties if found.\n\n* **`extract <expression> <known term> ...`** -\n  Replace parts of the expression that are equivalent to the known terms with the respective terms. Known terms must be normalizable.\n\n* **`search <expression> <known term> ...`** -\n  Attempt to brute force an equivalent of the _expression_ using only the _known terms_.\n  Only normalizable terms are currently supported.\n\n* **`quest-lint <files...>`** - Validate quest definition files\n  * `--solution <file>` - Load solutions from a JSON file for verification\n  * Example: `ski quest-lint quest1.json quest2.json --solution solutions.json`\n\nIf no subcommand is provided, help is displayed.\n\nRunning `SKI_REPL=1 node -r @dallaylaen/ski-interpreter/bin/ski.js`\nwill start a node shell with the `SKI` class available as a global variable.\n\n# Usage\n\nSee the [complete API reference](https://dallaylaen.github.io/ski-interpreter/man/) for gory details.\n\n## A minimal example\n\n```javascript\n#!node\n\nconst { SKI } = require('@dallaylaen/ski-interpreter');\n\n// Create a parser instance\nconst ski = new SKI();\n\n// Parse an expression\nconst expr = ski.parse(process.argv[2]);\n\n// Evaluate it step by step\nfor (const step of expr.walk({max: 100})) {\n  console.log(`[${step.steps}] ${step.expr}`);\n}\n```\n\n## Main features\n\n```javascript\nconst { SKI } = require('@dallaylaen/ski-interpreter');\nconst ski = new SKI();\n\nconst expr = ski.parse(src);\n\n// evaluating expressions\nconst next = expr.step(); // { steps: 1, expr: '...' }\nconst final = expr.run({max: 1000}); // { steps: 42, expr: '...' }\nconst iterator = expr.walk();\n\n// applying expressions\nconst result = expr.run({max: 1000}, arg1, arg2, ...);\n// same as\nexpr.apply(arg1).apply(arg2).run();\n// or simply\nexpr.apply(arg1, arg2).run();\n\n// equality check\nski.parse('x->y->x').equals(ski.parse('a->b->a')); // true\nski.parse('S').equals(SKI.S); // true\nski.parse('x').apply(ski.parse('y')).equals(ski.parse('x y')); // also true\n\n// defining new terms\nski.add('T', 'CI'); // T x y = C I x y = I y x = y\nski.add('M', 'x->x x'); // M x = x x\n\n// also with native JavaScript implementations:\nski.add('V', x=>y=>f=>f.apply(x, y), 'pair constructor');\n\nski.getTerms(); // all of the above as an object\n\n// converting lambda expressions to SKI\nconst lambdaExpr = ski.parse('x->y->x y');\nconst steps = [...SKI.extras.toSKI(lambdaExpr)];\n// steps[steps.length - 1].expr only contains S, K, I, and free variables, if any\n\n// converting SKI expressions to lambda\nconst skiExpr = ski.parse('S K K');\nconst lambdaSteps = [...SKI.extras.toLambda(skiExpr)];\n// lambdaSteps[lambdaSteps.length - 1].expr only contains lambda abstractions and applications\n```\n\n## Fancy formatting\n\n`expr.format(options?)` converts an expression to a string with fine-grained\ncontrol over notation. Called without arguments it is equivalent to\n`expr.toString()`.\n\n```javascript\nconst expr = ski.parse('S K K');\n\nexpr.format()                        // 'S K K'  (default, terse)\nexpr.format({ terse: false })        // 'S(K)(K)' — every argument gets parentheses\nexpr.format({ html: true })          // HTML-safe: free vars wrapped in <var>,\n                                     // '->' becomes '-&gt;', fancyName used when set\n\n// Custom lambda notation\nexpr.format({ lambda: ['', '=>', ''], terse: false })    // JavaScript style\nexpr.format({ lambda: ['&lambda;', '.', ''] })           // math style\nexpr.format({ lambda: ['(', '->', ')'], around: ['(', ')'], brackets: ['', ''] })\n                                                         // Lisp style, still parseable\n\n// Redex highlighting (e.g. for step-by-step HTML output)\nski.parse('I x').format({ html: true, redex: ['<b>', '</b>'] })\n// '<b>I</b> <var>x</var>'\n\n// inventory: show listed aliases by name, expand everything else\nconst { T } = ski.getTerms();\nexpr.format({ inventory: { T } })    // keeps T as 'T', expands any other aliases\n```\n\nThe `brackets`, `var`, `around`, and `redex` options each take a `[open, close]`\npair of strings; `lambda` takes a `[prefix, separator, suffix]` triple.\n\n`expr.diag()` will instead output an indented expression tree (breadth-first)\nwith class information and variables labeled for disambiguation.\n\n## Variable scoping\n\nBy default, parsed free variables are global and equal to any other variable with the same name.\nVariables inside lambdas are local to said lambda and will not be equal to anything except themselves.\n\nA special `scope` argument may be given to parse to limit the scope. It can be any object.\n\n```javascript\nconst scope1 = {};\nconst scope2 = {};\nconst expr1 = ski.parse('x y', {scope: scope1});\nconst expr2 = ski.parse('x y', {scope: scope2}); // not equal\nconst expr3 = ski.parse('x y'); // equal to neither\nconst expr4 = ski.parse('x', {scope: scope1}).apply(ski.parse('y', {scope: scope1})); // equal to expr1\n```\n\nVariables can also be created using magic `SKI.vars(scope)` method:\n\n```javascript\nconst scope = {};\nconst {x, y, z} = SKI.vars(scope); // no need to specify names\n```\n\n## Querying the expressions\n\nExpressions are trees, so they can be traversed.\n\n```javascript\nexpr.any(e => e.equals(SKI.S)); // true if any subexpression is S\n\nexpr.traverse(e => e.equals(SKI.I) ? SKI.S.apply(SKI.K, SKI.K) : null);\n// replaces all I's with S K K\n// here a returned `Expr` object replaces the subexpression,\n// whereas `null` means \"leave it alone and descend if possible\"\n\nexpr.fold(0, (acc, e) => acc + (e.equals(SKI.K) ? acc+1 : acc));\n// counts the number of K's in the expression\n```\n\n## Test cases\n\nThe `Quest` class may be used to build and execute test cases for combinators.\n\n```javascript\nconst { SKI } = require('@dallaylaen/ski-interpreter');\nconst { Quest } = SKI.quest;\n\nconst q = new Quest({\n    name: 'Test combinator T',\n    description: 'T x y should equal y x',\n    input: 'T',\n    cases: [\n        ['T x y', 'y x'],\n    ],\n});\n\nq.check('CI'); // pass\nq.check('a->b->b a'); // ditto\nq.check('K'); // fail\nq.check('K(K(y x))') // nope! The variable scopes won't match\n```\n\nSee also [the quest guide](quest-authoring.md) for more details on building your own quests or even interactive quest pages.\n\n# Package contents\n\n* `lib/ski-interpreter.cjs.js` - main entry point for Node.js;\n* `lib/ski-interpreter.esm.js` - main entry point for ES modules;\n* `lib/ski-interpreter.min.js` - minified version for browsers;\n* `lib/ski-quest.min.js` - script with the interpreter\nplus `QuestBox`, `QuestChapter`, and `QuestPage` classes\nfor building interactive quest pages from JSON-encoded quest data;\n* `bin/ski.js` - a CLI REPL;\n* `types` - TypeScript type definitions.\n\n# Thanks\n\n* [@ivanaxe](https://github.com/ivanaxe) for luring me into [icfpc 2011](http://icfpc2011.blogspot.com/2011/06/task-description-contest-starts-now.html) where I was introduced to combinators.\n* [@akuklev](https://github.com/akuklev) for explaining functional programming to me so many times that I actually got some idea.\n* [One happy fellow](https://github.com/happyfellow-one) whose [riddle](https://blog.happyfellow.dev/a-riddle/) trolled me into writing an early `traverse` prototype.\n* [Darkwing3125](https://github.com/Darkwing3125) for posting multiple bug reports and feature requests.\n* [@dokutan](https://github.com/dokutan) for quest bug reports and contributions.\n* [@mikevoronov](https://github.com/mikevoronov) - chief demand officer\n\n# Prior art, inspiration, and similar projects\n\n* \"To Mock The Mockingbird\" by Raymond Smullyan.\n* [combinator birds](https://www.angelfire.com/tx4/cus/combinator/birds.html) by [Chris Rathman](https://www.angelfire.com/tx4/cus/index.html);\n* [Fun with combinators](https://doisinkidney.com/posts/2020-10-17-ski.html) by [@oisdk](https://github.com/oisdk);\n* [Combinatris](https://dirk.rave.org/combinatris/) by Dirk van Deun;\n* [Combinate](https://combinate.app/) by [Matthías Páll Gissurarson](https://github.com/Tritlo).\n\n# License and copyright\n\nThis software is free and available under the MIT license.\n\n&copy; Konstantin Uvarin 2024&ndash;2026\n","readmeFilename":"README.md"}