Restricted Computations and Parameters in Type-Theory of Acyclic Recursion

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.