Oettinger's shape language(ID:7226/)Form based programmign calculus References: The geometry of symbols is concerned with written languages or notations as spatial displays of characters. Study of this subject is said to be in fragmentary condition, so that its problems and their appropriate solution techniques are best illustrated by example. First considered is the problem of syntactic symmetry, which appears to be the study of permutations of constants, functors, etc., which leave an axiom system invariant and thus transform theorems into theorems. Examples would be the permutation of a/ -- I and -- ~ -- 1, which leaves the laws of complex arithmetic invariant, or the permutation of the Boolean constants and functors with their duals. Second is the linear representation of trees in the Polish prefix notation. A two-dimensional representation of formulas containing a fourth-degree functor which is mentioned in passing is in fact ambiguous; Figure 3 has 120 possible interpretations. Third is an algorithm, apparently chosen to demonstrate pushdown lists and an early form of Iverson's programming language, which generates all possible selections of a specified number of letters from a specified alphabet. It is not clear to this reviewer that the examples presented have enough in common to justify their treatment as fragments of a single geometry. in ACM Computing Reviews 4(06) November-December 1963 view details |