Term Rewriting Systems
| This section requires expansion. |
A term rewriting system (TRS) is a rewriting system where the objects are terms, or expressions with nested sub-expressions. For example, the system shown under Logic above is a term rewriting system. The terms in this system are composed of binary operators and and the unary operator . Also present in the rules are variables, which are part of the rules themselves rather than the term; these each represent any possible term (though a single variable always represents the same term throughout a single rule).
The term structure in such a system is usually presented using a grammar. In contrast to string rewriting systems, whose objects are flat sequences of symbols, the objects of a term rewriting system form a term algebra, which can be visualized as a tree of symbols, the structure of the tree fixed by the signature used to define the terms.
The system given under Logic above is an example of a term rewriting system.
Read more about this topic: Reduction Systems
Famous quotes containing the words term and/or systems:
“Dead drunk
is the term I think of,
insensible,
neither cool nor warm,
without a head or a foot.
To be drunk is to be intimate with a fool.”
—Anne Sexton (1928–1974)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)