Abstract
Tree languages which are sets of terms always play a prominent role in the first-order languages and theoretical computer science. In this paper, tree languages induced by terms with fixed variables are considered. Under the applications of an operation on tree languages, we construct the algebra of such languages having many properties of abstract clones. A strong connection with theory of general functions is given through a representation theorem. Additionally, the semigroup of mappings of which their images are tree languages with fixed variables is given.
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