Abstract
In this paper, we intend to establish the theory of multi-type recursive functions (MTRF). The aim is to present a theoretical prototype of functional language to be implemented on computer. MTRF functions are computable, whose domain and range include: natural numbers, Boolean values, words on nite alphabet, context free languages, and parse trees of context free grammars. It is indicated that the natural number recursive functions and the MTRF functions are equivalent. Finally, an MTRF function eval is constructed, which is an evaluator to compute arbitrary MTRF functions, and can be implemented on the computer.
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