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Unlambda is a minimal, "nearly pure" functional programming language invented by David Madore. It is based on
combinatory logic Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of comput ...
, an expression system without the lambda operator or free variables. It relies mainly on two built-in functions (s and k) and an apply operator (written `, the
backquote The backtick is a typographical mark used mainly in computing. It is also known as backquote, grave, or grave accent. The character was designed for typewriters to add a grave accent to a (lower-case) base letter, by overtyping it atop that let ...
character). These alone make it Turing-complete, but there are also some input/output (I/O) functions to enable interacting with the user, some shortcut functions, and a lazy evaluation function. Variables are unsupported. Unlambda is
free and open-source software Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source ...
distributed under a GNU General Public License (GPL) 2.0 or later.


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 Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...
. Multi-parameter functions can be represented via the method of
currying In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, currying a function f that ...
. Unlambda is based on the principle of
abstraction elimination Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of comput ...
, or the elimination of all saved variables, including functions. As a purely functional language, Unlambda's functions are first-class objects, and are the ''only'' such objects. Here is an implementation of a hello world program in Unlambda: `r```````````.H.e.l.l.o. .w.o.r.l.di


Original built-in functions

The notation .''x'' denotes a function which takes one argument and returns it unchanged, printing the single character ''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''x'' is a function which, when invoked, returns ''x''. Thus the value of ``k''xy'' is ''x'' for any ''x'' and ''y''. s is a generalized evaluation operator. ```s''xyz'' evaluates to ``''xz''`''yz'' for any ''x'', ''y'', and ''z''. It is a remarkable fact that s and k are sufficient to perform any calculation, as described in SKI combinator calculus. As a brief example, the identity function i can be implemented as ``skk, since ```skk''x'' yields ''x'' for all ''x''. Unlambda's one flow control construct is call with current continuation, denoted c. When an expression of the form `c''x'' is evaluated, a special ''continuation'' object is constructed, representing the state of the interpreter at that moment. Then ''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''x'' expression is the same as the value of ''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''x'' expression is ''y''. Unlambda's execution semantics are normally eager evaluation, but a lazy evaluation option exists, indicated by the use of the d operator. Usually, to evaluate an expression of the form `''xy'', unlambda first evaluates ''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''y'' is a special "delayed computation" object, which, when applied to an argument ''z'', evaluates ''y'', and then applies its value to ''z''. In the absence of side effects, this is exactly the same as `i''y''. The difference is that `i''y'' executes any side effects in ''y'' immediately, whereas `d''y'' defers the side effects until the result is applied to another argument. 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``s``s`kskk`k``s``s`kskk, but it is supplied as a convenience. (This expression above is simply `Yk, where Y denotes a fixed point combinator.)


Version 2 built-in functions

More built-ins were introduced in Unlambda version 2. Input is facilitated by operators @ and ?''u''. When @ 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 ?''u'' is applied to a function ''x'', the result is the evaluation of `''x''i if the current character is ''u'', otherwise `''x''v is evaluated. There is also a "reprint" operator , . When `, ''x'' is evaluated, the function ''x'' is applied to .''u'' if ''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

*
Iota and Jot In formal language theory and computer science, Iota and Jot (from Greek iota ι, Hebrew yodh י, the smallest letters in those two alphabets) are languages, extremely minimalist formal systems, designed to be even simpler than other more popular ...
* SKI combinator calculus


References

* Felix-Hernandez Campos (1 April 2002),
Lecture 28: More on functional programming
', University of North Carolina COMP144 *


External links

*{{Official website, www.madore.org/~david/programs/unlambda
Online Unlambda REPL
Esoteric programming languages Functional languages