Online Unlambda Interpreter Features
Combinatory Logic Fundamentals
- Only three basic combinators—S (substitution), K (constant), I (identity) build all computation
- No variables ever—functions manipulate other functions without naming them
- Application is everything—` (backtick) applies one function to another: ``skk is K applied to result of s(k)
- Turing-complete minimalism—proves you can compute anything with just three operations
S, K, I Combinators
- S combinator: ```sxyz reduces to ``xz`yz—distributes z over x and y, then applies results
- K combinator: ``kxy reduces to x—creates constant function that ignores second argument
- I combinator: `ix reduces to x—identity function, can be built from S and K: ``skk ≡ i
- Composition creates logic—conditionals, numbers, recursion all from S, K, I combinations
Church Encoding
- Numbers as functions—0 is ``ki, 1 is i, higher numbers through function composition
- Booleans as choice—true is k (selects first), false is ``ki (selects second)
- Pairs for data structures—encode multiple values using function currying
- No primitive types—everything constructed from pure function application
Theoretical Exploration
- Study lambda calculus foundations—Unlambda proves computation without lambda abstraction
- Minimal language design—understand what is truly necessary for universal computation
- Esoteric programming challenge—pushing functional programming to philosophical extremes
- Computer science education—visualize computational theory with concrete, runnable examples
Unlambda Keyboard Shortcuts
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Get started freeFrequently Asked Questions
What is Unlambda?
Unlambda is a minimalist functional esoteric programming language based on combinatory logic. Programs use only S, K, I combinators and function application—no variables, no lambda abstraction. It is Turing-complete despite extreme simplicity.
Why would I use Unlambda?
Unlambda is educational, not practical. It teaches combinatory logic, lambda calculus fundamentals, and theoretical computer science. Perfect for understanding what is essential in functional programming and exploring computational theory limits.
How do S, K, and I combinators work?
S applies two functions to the same argument: ```sxyz → ``xz`yz. K creates constant functions: ``kxy → x. I is identity: `ix → x. These three combinators can express any computable function through composition.
How do I write Hello World in Unlambda?
Use .x to output character x. Hello World is: .H.e.l.l.o.,. .W.o.r.l.d.!i (ending with i to satisfy evaluation). Unlambda focuses on computation theory, not practical programming—output is secondary.
Can I write useful programs in Unlambda?
Technically yes (it is Turing-complete), practically no. Unlambda is an esoteric language for exploring theoretical concepts, not building applications. Even simple programs become extremely complex due to no variables or structured syntax.
What is the backtick character?
Backtick ` is function application operator. ``abc applies function a to b, then applies result to c. Think of it like Haskell's $ or parentheses in Lisp. Applications read right-to-left.
How does Unlambda relate to lambda calculus?
Lambda calculus uses lambda abstraction to create functions. Unlambda achieves equivalent expressive power using only combinators—no lambda needed. It is a different formulation of the same computational foundation, proving variables are not essential.
Is Unlambda the simplest programming language?
One of them! Unlambda reduces computation to just function application with S, K, I combinators. Other minimal languages include Iota (single combinator) and Jot (binary encoding). All prove how little is needed for universal computation.
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