# BlooP, FlooP, and GlooP

**BlooP, FlooP, and GlooP** are programming languages introduced for instructional purposes in chapter XIII of *GĂ¶del, Escher, Bach: An Eternal Golden Braid* (ISBN 978-0-465-02656-2, ISBN 0-14-017997-6), by Douglas R. Hofstader. They are defined with strictly limited built-in capabilities in order to explore what sorts of computations are theoretically possible given a particular set of language capabilities.

Each of these languages has only addition and multiplication as built-in functions, so other functions such as subtraction need to be defined in terms of these. Variables can only be natural numbers, integers zero or higher.

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## BlooP

BlooP supports program loops, but only with a specified maximum number of iterations (as either a constant or a variable, so the bounds can be computed; however, this computation must be done before the loop starts, so that the iteration limit can't be changed once the loop starts), meaning that all programs are guaranteed to terminate.

## FlooP

FlooP has the capabilities of BlooP, but allowing unbounded loops, which exit only when a test is passed, so an infinite loop could occur if the test never passes. Hence, programs do not necessarily terminate. This language can be shown to be Turing-complete, meaning that it can compute anything that any other Turing-complete programming language (a category which includes all general-purpose programming languages in actual use) can do.

## GlooP

GlooP is a hypothetical language that is even more unbounded than FlooP, and thus able to compute things that are logically uncomputable in the (Turing-complete) FlooP language, but it is believed that no such language is actually possible.