...Abel

Theoretical Computer Science , Institute of Computer Science , Ludwigs-Maximilians-University , Oettingenstr. 67, D-80538 Munich, Germany, email: abel@informatik.uni-muenchen.de . I want to thank my supervisor Thorsten Altenkirch and Rolf Backofen for his friendly support in technical questions.

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...foetus

In German foetus is an abbreviation of ``Funktionale - Obgleich Eingeschränkt - Termination Untersuchende Sprache'' ;-). It also expresses that it is derived from MuTTI (this is the German term for Mum).

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...

On the WWW I found the English term ``rig'' for what Germans call a ``Halbring''. This is probably a play of words: Compared to a ``ring'' a ``rig'' misses an ``n'' as well as inverse elements regarding addition. I cite Ross Moore (see http://www.mpce.mq.edu.au/~ross/maths/Quantum/Sect1.html#206 ):

A rig is a set R enriched with two monoid structures, a commutative one written additively and the other written multiplicatively, such that the following equations hold:

a0 = 0 = 0a

a(b + c) = ab + ac,$$\qquad$$(a + b)c = ac + ab

The natural numbers N provide an example of a rig.

A ring is a rig for which the additive monoid is a group. The integers Z provide an example.

A rig is commutative when the multiplicative monoid is commutative.

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