A theory of unicode

Given

• CP: a set of codepoints
• GLP: a subset of CP+ (non-empty sequences)

With the property:

(1) if x in GLP then x+y not in GLP (for all x,y in CP+)

Define:

STR: smallest subset of CP* such that

• empty in STR
• if s in STR and x in GLP then x+s in STR

Theorem: If s in STR then there exist unique n, and x1, ..., xn in GLP such that s = x1 + ... + xn. We call n the length of s.

In-place Udate:

If s1 + x1 + ... + xn + s2 in STR and |y1 + ... + ym| = |x1 + ... + xn| then s1 + y1 + ... + ym + s2 in STR. (for s1, s2 in S and x1, ..., xn and y1, ..., ym in GLP).