LOOP (programming language)

LOOP is a programming language designed by Uwe Schöning, along with GOTO and WHILE. The only operations supported in the language are assignment, addition and looping.

The key property of the LOOP language is that the functions it can compute are exactly the primitive recursive functions.

Each primitive recursive function is LOOP-computable and vice versa.

In contrast to GOTO programs and WHILE programs, LOOP programs always terminate. Therefore, the set of functions computable by LOOP-programs is a proper subset of computable functions (and thus a subset of the computable by WHILE and GOTO program functions).

An example of a total computable function that is not LOOP computable is the Ackermann function.

LOOP-programs consist of the symbols LOOP, DO, END, :=, +, - and ; as well as any number of variables and constants. LOOP-programs have the following syntax in modified Backus–Naur form:

Here, ${\displaystyle Var:=\{x_{0},x_{1},...\}}$ are variable names and ${\displaystyle c\in \mathbb {N} }$ are constants.

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