it depends on what you're implementing them in, but in a term-rewriting language all you need is the two lines above. in js you need to implement some kind of term-rewriting. in 02006 i wrote a compiler from λ-calculus (using \ for λ, so you can write for example \x.\y.x for λx.λy.x, which is equivalent to the k combinator) to an augmented sk-combinator language in js that's at http://canonical.org/~kragen/tmp/sk.html

the definitions of s and k in it are

    S: [3, function(f, g, x) { return App(App(f, x), App(g, x)) }],
    K: [2, function(k, _) { return Ind(k) }],

which are used as templates for matching by the 33-line-long sk_reduce function, which i'll spare you here

the λ-calculus parser, the compiler from λ-calculus to sk-combinators, the sk-combinator parser, and the sk-combinator evaluator together are 391 lines of js

if you just want to define the s and k combinators in js they look like this

    s = f => g => x => f(x)(g(x))
    k = a => b => a

but that is depending on the js interpreter to do the actual evaluation

more recently i implemented a term-rewriting language in i386 assembly, it's about 800 bytes and 400 instructions: http://canonical.org/~kragen/sw/dev3/qfitzah.s but i haven't quite figured out how to handle arithmetic, i/o, and variadic lists

i think you could probably implement sk combinatory logic in about half a page of c if you were okay with leaking memory, you don't really need the flexibility of variadic lists and arbitrary identifiers in the sk-combinator language. every term is either a function application (of one function to one argument), s, or k

> it depends on what you're implementing them in, but in a term-rewriting language all you need is the two lines above

Okay, so what do I type those two lines into to implement that? How many lines of code does that involve?

> more recently i implemented a term-rewriting language in i386 assembly, it's about 800 bytes and 400 instructions: http://canonical.org/~kragen/sw/dev3/qfitzah.s but i haven't quite figured out how to handle arithmetic, i/o, and variadic lists

Have you considered having a parameter stack that arithmetic operators pull their arguments from and push their results onto? Oh wait... ;-)

> so what do I type those two lines into to implement that? How many lines of code does that involve?

i just answered that in the comment you are replying to

> Have you considered having a parameter stack

this is a remarkably bad answer to my explanation of how much code i needed to write a self-compiling forth that generates machine code

what is wrong with you

i am sad now