BlooP and FlooP
simple programming languages
BlooP and FlooP (Bounded loop and Free loop) are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book Gödel, Escher, Bach. BlooP is a Turing-incomplete programming language whose main control flow structure is a bounded loop (i.e. recursion is not permitted). All programs in the language must terminate, and this language can only express primitive recursive functions.
FlooP is identical to BlooP except that it supports unbounded loops; it is a Turing-complete language and can express all computable functions. For example, it can express the Ackermann function, which (not being primitive recursive) cannot be written in BlooP. Borrowing from standard terminology in mathematical logic, Hofstadter calls FlooP's unbounded loops MU-loops. Like all Turing-complete programming languages, FlooP suffers from the halting problem: programs might not terminate, and it is not possible, in general, to decide which programs do.
BlooP and FlooP can be regarded as models of computation, and have sometimes been used in teaching computability.
BlooP examples
The only variables are OUTPUT (the return value of the procedure) and CELL(i) (an unbounded sequence of natural-number variables, indexed by constants, as in the Unlimited Register Machine). The only operators are ⇐ (assignment), + (addition), × (multiplication), < (less-than), > (greater-than) and = (equals).
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