BlooP, FlooP, and GlooP
BlooP, FlooP, and GlooP are programming languages introduced for instructional purposes in chapter XIII of Gödel, 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.
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 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 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.