=== Symmetric Paths ===

A symmetric path is a convenient short hand notation, e.g.:

  and[not]

This is equal to the same expression as an asymmetric path:

  and[not x not -> not]

The benefit of symmetric paths is that the number of arguments do not matter.

Composition rules of symmetric paths is the same as for normal composition:

  f[g][h] <=> f[h . g]

Most of generic path semantics is first defined for symmetric paths,
because the more general case of asymmetric paths is a simple modification.

Many useful laws in mathematics are expressible as symmetric paths:

  and[not] <=> or       or[not] <=> and       DeMorgan's laws
  add[exp] <=> mul      mul[ln] <=> add       Exponentiation and logarithm
  mul_mat[det] <=> mul                        Matrices and determinants
  concat[len] <=> add                         Lists and lengths