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For example, suppose we want to deal with algebraic formulae represented by ground expressions. In this case, we have to devise a way of representing constants, variables, and formulae formed by applying a binary operator to two smaller formulae. We may choose, for example, the following representation.
Let [p] denote the ground expression that represents the formula p . Then,
numbers may be represented by the corresponding numeric symbols, variables by the
corresponding word symbols, and formulae formed by applying binary operators according to the
following rules:
Thus the formula
The next example is the problem of representing chess positions by ground expressions.
First of all we have to denote the name and color of each piece. For example,