Logic Programming Applied to Numerical Integration.
CALIFORNIA UNIV SANTA CRUZ INFORMATION SCIENCES
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This paper uses logic programming to describe numerical integration in a general way. Axioms are added to the basic logic programs to define specific known numerical integration algorithms. Using a slightly different formalization, we construct logic programs for adaptive Romberg integration and for a new algorithm for adaptive integration. The logic programs provide a formal basis for classifying numerical quadrature algorithms recall Rices comment that there are 1,000,000 useful ones. The logic programs are also more understandable than the corresponding programs in conventional programming languages. In terms of logic programming there are several novel points in this paper. The data type, real number, is not definded by a recursive constructor function. Termination is decided by error bounds, rather than by reaching some basis case of the data constructor. The problem itself seems to demand concurrent execution and global variables but in fact is solved in a linear fashion. Author
- Computer Programming and Software