TITLE: Types versus kinds and sorts
QUESTION [6 upvotes]: In the context of logic, especially Higher‑Order‑Logic and Calculus‑of‑Construction, what is a kind and how does it relates to and differs from a type?
My raw guess if that a kind is the higher level type of a type. Is that it? If not, so what's a kind? If yes, is this as simple as it looks or are there more elaborated things to know about the relation between both?
Update: same question with sorts (or may be they are synonymous?).

REPLY [3 votes]: Yes, your guess about kinds is correct. According to Types and Programming Languages, kinds are "the types of types". 
From the same source:

[...] we introduce a system of kinds that classify type expressions
  according to their arity, just as arrow types tell us about the arities of terms. Kinds, then, are “the types of types.” In essence, the system of kinds is a copy
  of the simply typed lambda-calculus, “one level up.”