Show HN: AttaLambda: a language where types and data are made of untyped lambdas

I made a programming language!

I call it AttaLambda.

The idea is this: a usable Lisp-shaped language where all the meaningful computation is done in untyped lambda calculus. Logic, arithmetic, data structures, control flow, even the types — all untyped lambdas. A small, explicit Racket layer sits at the boundary to handle the outside world, plus some macros for syntactic sugar.

This is its story:

A couple years ago, I wanted to play with untyped lambda calculus and go beyond where tutorials usually stop. They show booleans, numbers, arithmetic, maybe the Y-combinator — and then stop. I wanted them to keep going.

So I started a project called All The Lambdas. Using Racket set to lazy, I used only one Racket construct for actual computation — lambda — and built integers, rationals, lists, binary digit-list number encodings, search algorithms, and more.

Then I found Functional Programming Through Lambda Calculus by Greg Michaelson. In it, Michaelson sketches the bones of a language built in untyped lambda calculus, including a type system where typed objects are themselves pair functions containing a type tag and value.

I found that intriguing and implemented and extended the idea, still entirely with untyped lambdas. I don't have a background in programming language theory, so I was figuring it out as I went.

Then I stopped tinkering with it for a while.

Recently I came back and thought: why not turn this into a real usable language with the help of coding agents? I reused most of All The Lambdas as the foundation.

Thus AttaLambda was born.

Some additional details:

* Rat, its number type, uses binary digit-list encodings instead of Church numerals, so numbers scale with their number of binary digits rather than their value

* errors are lambda-encoded values, not Racket exceptions, and propagate through the language like ordinary data

* the Racket host only performs irreducibly external operations; even things like HTTP parsing, routing, and response construction stay in the pure lambda world

* recursion uses lambda-calculus recursion: no loops or true self-reference, just the Y-combinator underneath

* automated purity checks catch accidental cheating, like native computation leaking into the pure parts

* syntax like multi-argument lambdas, let, cond, and list is just macro sugar that reduces to unary lambdas and application

A couple code examples: (short of print, every single thing here reduces to unary untyped lambdas)

Factorial:

  #lang attalambda

  (rec factorial n =
    (cond
      ((eq n 0) 1)
      (else (mult n (factorial (sub n 1))))))

  (print (factorial 10))

Which prints:

  3628800

Or an exact harmonic sum:

  #lang attalambda

  (print
    (reduce add 0
      (map (lambda (n)
             (unwrap-ok (div 1 n)))
           (range 1 8))))

Which prints exactly:

  363/140

As far as I know, no programming language combines all these features: Michaelson-style type tags built from untyped lambdas, exact rationals backed by binary digit lists, errors as lambda values, and real-world programs where almost all computation stays inside the lambda core. None of those pieces are individually new, but I don't know of another language combining them this way.

Download: https://github.com/kserrec/attalambda/releases/tag/v0.7.0

Code: https://github.com/kserrec/attalambda

Original All The Lambdas: https://github.com/kserrec/all_the_lambdas