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Authoring Lambda Calculus Content

This article is intended for kata authors and translators who would like to create new content in Lambda Calculus. It attempts to explain how to create and organize things in a way conforming to authoring guidelines, shows the most common pitfalls and how to avoid them.

This article is not a standalone tutorial on creating kata or translations. It's meant to be a complementary, Lambda Calculus-specific part of a more general set of HOWTOs and guidelines related to content authoring. If you are going to create a Lambda Calculus translation, or a new Lambda Calculus kata from scratch, please make yourself familiar with the aforementioned documents related to authoring in general first.

General info​

Any technical information related to the Lambda Calculus setup on Codewars can be found on the Lambda Calculus reference page (language versions, available libraries, and setup of the code runner).

For further information about Lambda Calculus as a language, and for a collection of extensive authoring, syntax and style guides, see The Lambda Calculus Documentation Wiki.

Description​

Lambda Calculus code blocks can be inserted with Lambda Calculus-specific part in sequential code blocks:

```lambdacalc

...your code here...

```
```lambdacalc

...your code here...

```

Lambda Calculus-specific paragraphs can be inserted with language conditional rendering:

~~~if:lambdacalc

...text visible only for Lambda Calculus description...

~~~

~~~if-not:lambdacalc

...text not visible in Lambda Calculus description...

~~~
~~~if:lambdacalc

...text visible only for Lambda Calculus description...

~~~

~~~if-not:lambdacalc

...text not visible in Lambda Calculus description...

~~~

Tests​

lc-test​

Lambda Calculus kata use lc-test to implement and execute tests.

Setup​

Lambda Calculus is heavily dependant upon what encodings are chosen to represent various data types. All Lambda Calculus kata should declare in the description which Purity and which numEncoding (if any) are going to be used in the kata. Additionally, any required encodings, such as for inputs and outputs, should be specified by their constructors and deconstructors, allowing the actual implementation to remain free to the solver.

What is in what language, what syntax, what encoding?​

The Preloaded section, example Solution, and solver Solution code are Strings in Lambda Calculus syntax. The sample and submission tests are written and run in Javascript.

LC.compile compiles Lambda Calculus code to JavaScript Functions. There is a one-to-one correspondence between Lambda Calculus syntax and JavaScript syntax, and everything that comes out of compile is JavaScript, and is a callable Function. It can be applied with native JavaScript Functions, with compiled Lambda Calculus terms ( thus JavaScript Functions ), or with other JavaScript values, which will pass uncompiled. Thus, everything that happens in testing happens in JavaScript.

The only way to arrive at JavaScript values from compiled Lambda Calculus code is passing its compiled form a JavaScript value in testing; there is no way to embed JavaScript values in Lambda Calculus code - not even passing it Numbers, which will be transparently encoded ( or generate an EvalError, when numEncoding = None ).

Note that there are no Strings in Lambda Calculus syntax, though you can pass and manipulate Strings in testing ( i.e. in JavaScript ).

Also note that all passed Numbers will be transparently encoded, which will generate a RangeError for negative numbers in most numEncodings.

Leave solvers free to use encodings​

numEncoding is designed to set a particular numeral encoding for the kata, and provide support for testing with that. Other encodings however should be as free for solvers as possible. Use constructors and deconstructors in wrappers for testing, and allow solvers to export their own (de)constructors for datatypes other than numbers.

For booleans, ask for False, True and some if then else ( TBD ). For 2-tuples, ask for Pair and fst, snd. For lists, ask for nil, cons and foldr. For option types, ask for none, some and option.

Refer to the Encodings Reference for naming conventions.

Example test suite​

Below you can find an example test suite, showing how the components of lc-test are used to compile and test a Lambda Calculus Kata.

import { assert, LC, getSolution } from "./lc-test.js";

LC.configure({ purity: "LetRec", numEncoding: "Church", verbosity: "Concise" });
const { multiply } = LC.compile(getSolution());

describe("Multiply",()=>{

  it("example tests",()=>{
    assert.equal( multiply(7)(7), 49 );
    assert.equal( multiply(11)(11), 121 );
  });

  it("random tests",()=>{
    const rnd = (m,n=0) => Math.random() * (n-m) + m | 0 ;
    for ( let i=1; i<=100; i++ ) {
      const m = rnd(i), n = rnd(i);
      assert.equal( multiply(m)(n), m*n );
    }
  });
});
import { assert, LC, getSolution } from "./lc-test.js";

LC.configure({ purity: "LetRec", numEncoding: "Church", verbosity: "Concise" });
const { multiply } = LC.compile(getSolution());

describe("Multiply",()=>{

  it("example tests",()=>{
    assert.equal( multiply(7)(7), 49 );
    assert.equal( multiply(11)(11), 121 );
  });

  it("random tests",()=>{
    const rnd = (m,n=0) => Math.random() * (n-m) + m | 0 ;
    for ( let i=1; i<=100; i++ ) {
      const m = rnd(i), n = rnd(i);
      assert.equal( multiply(m)(n), m*n );
    }
  });
});