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

Contents (PDF format)

Bibliography

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