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Search - lambda calculus calculator javascript
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xholonWorkbook.xml
<?xml version="1.0" encoding="UTF-8"?>
<!--Xholon Workbook http://www.primordion.com/Xholon/gwt/ MIT License, Copyright (C) Ken Webb, Thu Dec 11 2025 15:35:34 GMT-0500 (Eastern Standard Time)-->
<XholonWorkbook>
<Notes><![CDATA[
Xholon
------
Title: Search - lambda calculus calculator javascript
Description:
Url: http://www.primordion.com/Xholon/gwt/
InternalName: 50573ad10d0e0e2ef8b78ec2d55979cf
Keywords:
My Notes
--------
2025 Dec 6
I searched for the following with DuckDuckGo:
lambda calculus calculator javascript
It provided a bunch of interesting looking hits, which I will explore in this workbook.
to test this workbook, with the code in ref[1]:
http://127.0.0.1:8080/XholonLambdaCalc.html?app=Search+-+lambda+calculus+calculator+javascript&src=lstr&gui=clsc
http://127.0.0.1:8080/XholonLambdaCalc.html?app=50573ad10d0e0e2ef8b78ec2d55979cf&src=gist&gui=clsc
TODO:
https://primordion.com/XholonLambdaCalc.html?app=50573ad10d0e0e2ef8b78ec2d55979cf&src=gist&gui=clsc
### References
(1) https://github.com/VictorTaelin/lambda-calculus
A simple, clean and fast implementation of the λ-calculus on JavaScript.
It has zero dependencies and only 2.65KB gzipped.
It evaluates terms very efficiently by using native JS functions, which is possible thanks to a clever compile/readback algorithm based on JS semantics.
It includes the most relevant IO formats - bruijn-indices, binary, base64 and the usual "Wikipedia syntax" - so you can easily export to/from other tools.
You can also convert native JS functions to terms and back.
npm install lambda-calculus
) https://github.com/VictorTaelin/lambda-calculus/issues/1
a cleaner implementation
KSW - I am not using this
(2) https://github.com/gmfc/lambda-calculus-js
) https://github.com/gmfc/lambda-calculus-js/tree/main
Lambda Calculus with JavaScript
This repository is dedicated to demonstrating the principles of lambda calculus using JavaScript.
a collection of simple lambda calculus stuff as javascript functions
similar to stuff I have done while learning
useful
(3) https://iwilare.com/lambda-js/
A minimal JavaScript interpreter for λ‑calculus in less than 60 characters.
(4) https://m1el.github.io/smallest-lambda-eval/
The smallest lambda interpreter in JavaScript
uses De Bruijn indices
worth taking a closer look at sometime
(5) https://tromp.github.io/cl/Binary_lambda_calculus.html
Binary Lambda Calculus
Binary lambda calculus (BLC) is a minimal, pure functional programming language invented by John Tromp in 2004,1
based on a binary encoding of the untyped lambda calculus in De Bruijn index notation.
KSW interesting
(6) https://medium.com/@axdemelas/lambda-calculus-with-javascript-897f7e81f259
Lambda Calculus with JavaScript
An introduction to the roots of functional programming
Alexandre Demelas
Oct 1, 2017
The objective of this article is to present the main concepts of Lambda Calculus with the aid of JavaScript syntax (ES2015),
showing its influence in modern languages and its importance for the future of programming.
(7) https://sshwy.github.io/lamcalc/en/playground.html
λ-Calculus Online Playground
Try writing your lambda expression! We've defined some basic expressions for you:
- unclear what this is about
(8) https://lambda-calculus-interpreter.vercel.app/
parses, shows tree
(9) https://www.cl.cam.ac.uk/~rmk35/lambda_calculus/lambda_calculus.html#org98242d7
Lambda-Calculus Evaluator
- hard to know if this would be useful for me ?
(10) https://lambdacalc.dev/
- might be useful
(11) https://plato.stanford.edu/entries/lambda-calculus/
comprehensive
includes a section on Combinatory logic
Applications in the semantics of natural language, thanks to developments by Montague and other linguists, helped to ‘spread the word’ about the subject.
Since then the λ-calculus enjoys a respectable place in mathematical logic, computer science, linguistics (see, e.g., Heim and Kratzer 1998), and kindred fields.
- see ref[14] below
(12) http://lambdacalculator.com/
- old, http only
The Lambda Calculator
For students and teachers of natural language semantics.
By Lucas Champollion, Josh Tauberer, Maribel Romero, Dylan Bumford, Alex Warstadt, Anna Alsop, Raef Khan, and Nigel Flower
The Lambda Calculator is an interactive, graphical application to help students of natural language semantics practice derivations in the typed lambda calculus.
It is designed for both students and teachers, with modules for online classroom instruction, graded homework assignments, and self-guided practice.
The primary function is to assist in the computation of natural language denotations up a syntactic tree in the style of Heim & Kratzer (1998).
To this end, the program detects common errors and attempts to provide intelligent feedback to the student user and a record of performance for the instructor.
(13) https://github.com/nyusemantics/LambdaCalculatorPublic
) https://github.com/nyusemantics/LambdaCalculatorPublic/wiki/Documentation
public version of ref[12]
(14) https://en.wikipedia.org/wiki/Montague_grammar
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague.
The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus,
and makes use of the notions of intensional logic, via Kripke models.
Montague pioneered this approach in the 1960s and early 1970s.
(15) https://theory.stanford.edu/~blynn/lambda/
Lambda Calculus
lots of topics, a parser, etc.
(16) https://lambster.dev/
Lambster
A lambda calculus interpreter
]]></Notes>
<_-.XholonClass>
<PhysicalSystem/>
<Block/>
<Lam/>
<!-- examples from Greg Michaelson book -->
<GMich superClass="Script"/>
<GMich2 superClass="Script"/>
<GMich3 superClass="Script"/>
<FunctionTester/>
</_-.XholonClass>
<xholonClassDetails>
<GMich><Color>orange</Color></GMich>
<Avatar><Color>red</Color></Avatar>
<GMich2>
<DefaultContent><![CDATA[
var me, beh = {
postConfigure: function() {
me = this.cnode;
const lam = $wnd.xh.lam;
var funk = lam.toFunction(lam.reduce(lam.fromString(me.expr)));
console.log(me.name(), me.expr, funk(33)(77)); // ccc:gMich2 (λa.λb.a) 33
}
}
//# sourceURL=GMich2_ccc.js
]]></DefaultContent>
<Color>gold</Color>
</GMich2>
<GMich3>
<DefaultContent><![CDATA[
var me, args, beh = {
postConfigure: function() {
me = this.cnode;
args = me.args.split(",").map((item) => isNaN(item) ? item : Number(item), []);
console.log("args", args);
const lam = $wnd.xh.lam;
/*if (isNaN(Number(args[0]))) {
console.log("GMich3 1");
var xa = lam.fromString(args[0]);
console.log(xa);
var xb = lam.reduce(xa);
console.log(xb);
var xc = lam.toString(xb);
console.log(xc);
}*/
var funk = lam.toFunction(lam.reduce(lam.fromString(me.expr)));
console.log(me.name(), me.expr, funk(args[0])(args[1]));
}
}
//# sourceURL=GMich3_ddd.js
]]></DefaultContent>
<Color>gold</Color>
</GMich3>
</xholonClassDetails>
<PhysicalSystem>
<Block/>
<FunctionTester funk="(a,b) => a + b" args="981,5"/>
<FunctionTester funk="() => $wnd.xh.root().name()" args=""/>
<Lam/>
<GMich roleName="aaa"><![CDATA[
var beh = {};
console.log("GMich aaa");
const lam = $wnd.xh.lam;
console.log(lam.toString(lam.reduce(lam.fromString("(λa.λb.b)"))));
var second = lam.toFunction(lam.reduce(lam.fromString("(λa.λb.b)")));
console.log(second);
console.log(second(4)(5)); // 5
//# sourceURL=GMich_aaa.js
]]></GMich>
<GMich roleName="bbb"><![CDATA[
var beh = {};
console.log("GMich bbb");
const lam = $wnd.xh.lam;
console.log(lam.toString(lam.reduce(lam.fromString("(λa.λb.a)"))));
var first = lam.toFunction(lam.reduce(lam.fromString("(λa.λb.a)")));
console.log(first);
console.log(first(4)(5)); // 4
//# sourceURL=GMich_bbb.js
]]></GMich>
<GMich roleName="ccc" expr="(λa.λb.λc.a)" args="123,14,98"><![CDATA[
var me, args, beh = {
postConfigure: function() {
me = this.cnode;
args = me.args.split(",").map((item) => Number(item), []);
var numa = args[0];
var numb = args[1];
const lam = $wnd.xh.lam;
var funk = lam.toFunction(lam.reduce(lam.fromString(me.expr)));
console.log(me.name(), me.expr, funk(numa)(numb)(args[2])); // ccc:gMich_50 (λa.λb.λc.a) 123
}
}
//# sourceURL=GMich_ccc.js
]]></GMich>
<GMich2 expr="(λa.λb.a)"/>
<GMich2 expr="(λa.λb.b)"/>
<!--<GMich3 expr="(λa.λb.(a b))" args="x => x+3,210"/>--> <!-- Uncaught TypeError: a is not a function -->
<!--<GMich3 expr="(λa.λb.(a b))" args="λx.x+3,210"/>--> <!-- NO -->
</PhysicalSystem>
<Blockbehavior implName="org.primordion.xholon.base.Behavior_gwtjs"><![CDATA[
// test of code in ref[1] this works!
const lam = $wnd.xh.lam;
console.log(lam.toString(lam.reduce(lam.fromString("(λa.λb.(a (a b)) λa.λb.(a (a b)))")))); // a.b.(a (a (a (a b))))
const funk = lam.toFunction(lam.reduce(lam.fromString("(λa.λb.(a (a b)) λa.λb.(a (a b)))")));
console.log(funk);
console.log(funk(x => x+1)(5)); // 9
$wnd.xh.root().println(funk(x => x+1)(5)); // 9
//# sourceURL=Blockbehavior.js
]]></Blockbehavior>
<Lambehavior implName="org.primordion.xholon.base.Behavior_gwtjs"><![CDATA[
var me, lam, funk, beh = {
postConfigure: function() {
me = this.cnode.parent();
lam = $wnd.xh.lam;
funk = lam.toFunction(lam.reduce(lam.fromString("(λa.λb.(a (a b)) λa.λb.(a (a b)))")));
},
act: function() {
me.println(funk(x => x+3)(30)); // 42
me.println(funk(new Function("return (x) => x+3"))()(31)); // 34
}
}
//# sourceURL=Lambehavior.js
]]></Lambehavior>
<FunctionTesterbehavior implName="org.primordion.xholon.base.Behavior_gwtjs"><![CDATA[
console.log("FunctionTesterbehavior");
// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Function/Function
// testing Function
const sum = Function("a", "b", "return a + b");
console.log(sum(2, 6));
// Expected output: 8 YES
const plus1 = Function("x", "return x + 1");
console.log(plus1(88)); // 89 YES
const findLargestNumber = new Function(
"function findLargestNumber (arr) { return Math.max(...arr) }; return findLargestNumber",
);
// call the function
console.log(findLargestNumber.call({}).call({}, [2, 4, 1, 8, 5]));
const funky = new Function("const funky = (x) => x + 111; return funky",)(); // YES
const funky2 = new Function("const f = function(x) {return x + 222}; return f"); // YES
console.log(funky(3333));
console.log(funky2.call()(3333));
// this works!
// Observe that new Function is called. This is so we can call the function we created directly afterwards
const sumOfArray = new Function("const sumArray = (arr) => arr.reduce((previousValue, currentValue) => previousValue + currentValue); return sumArray",)();
// call the function
console.log(sumOfArray([1, 2, 3, 4])); // 10
/*
console.log(this);
console.log(this.parent());
console.log(this.parent().funk);
if (this.parent().funk) {
console.log("this.parent().funk", this.parent().funk);
const fstr = `const f = ${this.parent().funk}; return f`;
console.log(fstr);
const funkey = new Function(fstr)(); // YES
console.log(funkey(876,1)); // 877
}
*/
//console.log(new Function(`const f = ${this.parent().funk}; return f`)()(981,5)); // 986 or chameleon_0
//console.log(new Function(`return ${this.parent().funk};`)()(982,7)); // 989 or chameleon_0
const args = this.parent().args.split(",").map((item) => isNaN(item) ? item : Number(item), []);
console.log(new Function(`const f = ${this.parent().funk}; return f`)()(...args)); // 986 or chameleon_0
//# sourceURL=FunctionTesterbehavior.js
]]></FunctionTesterbehavior>
<SvgClient><Attribute_String roleName="svgUri"><![CDATA[data:image/svg+xml,
<svg width="100" height="50" xmlns="http://www.w3.org/2000/svg">
<g>
<title>Block</title>
<rect id="PhysicalSystem/Block" fill="#98FB98" height="50" width="50" x="25" y="0"/>
<g>
<title>Lam</title>
<rect id="PhysicalSystem/Lam" fill="#6AB06A" height="50" width="10" x="80" y="0"/>
</g>
</g>
</svg>
]]></Attribute_String><Attribute_String roleName="setup">${MODELNAME_DEFAULT},${SVGURI_DEFAULT}</Attribute_String></SvgClient>
</XholonWorkbook>
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