Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

## A Scheme for Extensions of Homomorphisms of Many Sorted Algebras

Andrzej Trybulec
Warsaw University, Bialystok

### Summary.

The aim of this work is to provide a bridge between the theory of context-free grammars developed in [10], [6] and universally free manysorted algebras([14]. The third scheme proved in the article allows to prove that two homomorphisms equal on the set of free generators are equal. The first scheme is a slight modification of the scheme in [6] and the second is rather technical, but since it was useful for me, perhaps it might be useful for somebody else. The concept of flattening of a many sorted function $F$ between two manysorted sets $A$ and $B$ (with common set of indices $I$) is introduced for $A$ with mutually disjoint components (pairwise disjoint function - the concept introduced in [13]). This is a function on the union of $A$, that is equal to $F$ on every component of $A$. A trivial many sorted algebra over a signature $S$ is defined with sorts being singletons of corresponding sort symbols. It has mutually disjoint sorts.

#### MML Identifier: MSAFREE1

The terminology and notation used in this paper have been introduced in the following articles [15] [9] [18] [19] [7] [8] [5] [13] [1] [2] [3] [4] [10] [6] [12] [16] [17] [14] [11]

Contents (PDF format)

#### Bibliography

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