A Numerical Equation Solver in Prolog

The Prolog inference engine can be extended to solve for unknowns in arithmetic equations such as X−1=1/X or X=cos(X), whether or not the equations have analytic solutions. This is done by standard numerical methods, but two features of Prolog make the implementa-tion easy: the ability to treat expressions as data and the ability of the program to extend itself at run time. 1 The problem The Prolog inference engine can solve for any unknown in symbolic queries, but not in arithmetic queries. For example, given the fact father(michael,sharon). one can ask?- father(michael,X). and get the answer sharon, or ask?- father(X,sharon). 1 and get the answer michael. This interchangeability of unknowns extends to complex symbolic manipulations (e.g., append can be used to split a list as well as to concatenate lists), but not to arithmetic. Prolog handles arithmetic the way Fortran did thirty years ago: the unknown can only be a single variable on the left of the operator is, and everything on the right must be known. Thus?- X is 2 + 2. gets the answer 4, but?- X is 1 + 1 / X. fails or raises an error condition. The excuse for this restriction is that Prolog cannot search the set of real numbers the way it searches the symbols in a knowledge base. As far as exhaustive search goes, this is true. However, mathematicians have been using heuristic searches to solve equations since the days of Isaac Newton. The procedures given here implement one such method, making it possible to have dialogues with the computer such as:?- solve ( X = 1 + 1 / X). X = 1.618034?- solve ( X = cos(X))