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.
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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), 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.
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.
