# Unlambda

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**Unlambda** is a minimal, "nearly pure"^{[1]} functional programming language invented by David Madore. It is based on combinatory logic, a version of the lambda calculus that omits the lambda operator. It relies mainly on two built-in functions (*s* and *k*) and an "apply" operator (written *`*, the backquote character). These alone make it Turing-complete, but there are also some I/O functions to make it possible to interact with the user, some shortcut functions and a function for lazy evaluation. There are no variables in the language.

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## Basic principles

As an esoteric programming language, Unlambda is meant as a demonstration of very pure functional programming rather than for practical use. Its main feature is the lack of conventional operators and data types — the only kind of data in the program are one-parameter functions. Data can nevertheless be simulated with appropriate functions as in the lambda calculus. Multi-parameter functions can be represented with the technique of currying.

Unlambda is based around the principle of abstraction elimination, or the elimination of all saved variables, including functions. As a purely-functional language, not only are Unlambda's functions first-class objects, they are the *only* first-class objects.

An implementation of the hello world program in Unlambda follows:

`r```````````.H.e.l.l.o. .w.o.r.l.di

## Original built-in functions

The notation `.`

denotes a function which takes one argument and returns it unchanged, printing the single character *x**x* as a side effect when it is invoked. `i`

represents the version of the identity function that has no such side effect; it is used here as a dummy argument. The program ``.di`

applies the `d`

-printing function to a dummy argument of `i`

, returning `i`

and printing the letter `d`

as a side effect. Similarly, ```.l.di`

first applies `.l`

to `.d`

, printing the letter `l`

and returning `.d`

; this result of `.d`

is then applied to `i`

as in the previous example. The function `r`

is syntactic sugar for the function that prints a newline character.

Other important features provided by Unlambda include the `k`

and `s`

functions. `k`

manufactures constant functions: the result of ``k`

is a function which, when invoked, returns *x**x*. Thus the value of ```k`

is *xy**x* for any *x* and *y*.

`s`

is a generalized evaluation operator. ````s`

evaluates to *xyz*````

for any *xz*`*yz**x*, *y*, and *z*. It is a remarkable fact that `s`

and `k`

are sufficient to perform any calculation; see the SKI combinator calculus article for full details. As a brief example, note that the identity function `i`

can be implemented as ```skk`

, since ````skk`

yields *x**x* for all *x*.

Unlambda's one flow control construction is call with current continuation, denoted `c`

. When an expression of the form ``c`

is evaluated, a special "continuation" object is constructed, representing the state of the interpreter at that moment. Then *x**x* is evaluated, and then the result is given the continuation object as an argument. If the continuation is never applied to an argument, the value of the ``c`

expression is the same as the value of *x**x*. But if the continuation object is applied to a value *y*, execution of *x* is immediately aborted, and the value of the entire ``c`

expression is *x**y*.

Although Unlambda's execution semantics are normally eager, there is a lazy evaluation option, indicated by the use of the `d`

operator. Usually, to evaluate an expression of the form ```

, unlambda first evaluates *xy**x*, then *y*, and then applies *x* to *y*. However, if *x* evaluates to the special value `d`

, then *y* is *not* evaluated; instead, the value of the expression ``d`

is a special "delayed computation" object, which, when applied to an argument *y**z*, evaluates *y*, and then applies its value to *z*. Note that in the absence of side effects, this is exactly the same as ``i`

. The difference is that *y*``i`

executes any side effects in *y**y* immediately, whereas ``d`

defers the side effects until the result is applied to another argument.
*y*

Unlambda's next built-in operator is `v`

, which ignores its argument and returns `v`

. This feature is not strictly necessary, since `v`

could be implemented as ````s``k``sii``s``s`ksk`k``siik`

, but it is supplied as a convenience. (This expression above is simply ``Yk`

, where `Y`

denotes a fixed point combinator.)

## Unlambda 2 built-in functions

Additional built-ins were introduced in version 2 of the Unlambda language. Input in Unlambda is facilitated by operators `@`

and `?`

. When *u*`@`

is applied to a function *x*, a character is read from input, and stored as the "current character"; then *x* is applied to `i`

. However, if no more characters were available on input, the "current character" is left undefined, and *x* is applied to `v`

instead. When a function `?`

is applied to a function *u**x*, the result is the evaluation of ```

if the current character is *x*i*u*, otherwise ```

is evaluated.
*x*v

There is also a "reprint" operator `|`

. When ``|`

is evaluated, the function *x**x* is applied to `.`

if *u**u* is the current character, or to `v`

if there is no current character.

Finally, there is an exit operator `e`

. When `e`

is applied to *x*, the execution of the program is terminated, and *x* is taken as the result of the program (most of the currently existing interpreters ignore the result anyway).

## See also

Similar languages:

## References

- Felix-Hernandez Campos (1 April 2002),
*Lecture 28: More on functional programming*, University of North Carolina COMP144 - 原 悠 (Yutaka Hara) (2008) (in Japanese).
*Rubyで作る奇妙なプログラミング言語*. Tōkyō: Mainichikomyunikēshonzu. p. 205–214. ISBN 4839927847. http://books.google.com/books?id=LlR6__OpAxoC&pg=PA205&dq=Unlambda&cd=2#v=onepage&q=%22Unlambda%22&f=false.