Restricted Computations and Parameters in Type-Theory of Acyclic Recursion

• Loukanova, Roussanka ^[1]
  1. [1] Institute of Mathematics and Informatics

     Institute of Mathematics and Informatics

     Bulgaria

     
• Localización: ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, ISSN-e 2255-2863, Vol. 12, Nº. 1, 2023
• Idioma: inglés
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• Resumen

  • The paper extends the formal language and the reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative restrictions. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The extended type-theory of restricted recursion (TTRR) provides computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages.

    The reduction calculi of TTRR provides a mathematical foundation of the work of compilers for reducing recursive programs to iterative ones. The type-theory of acyclic recursion (TTAR) has a special importance to syntax-semantics interfaces in computational grammars.