[stack] language hierarchy

Going along with the discussion trying to pin down a definition of  
concatenative and/or develop a new term, I propose this hierarchy with  
the hope that it might be partially correct and/or useful:

A functional programming language is one that treats computation as  
the evaluation of mathematical functions and avoids state and mutable  
data.
Examples: Scheme, ML, Haskell

A function-level programming language is a variable-free functional  
programming language in which all functions are unary and new  
functions are created in terms of existing functions through the use  
of functional forms.
Examples: FP, FL, APL (?), J (?)

A compositional programming language is a function-level programming  
language in which composition is the only functional form.
Examples: Joy, Cat, etc

A concatenative programming language is a compositional programming  
language in which the concatenation of functions denotes composition.
Examples: Joy, Cat, etc

- - -

Side note: Given that the term compositional programming is taken,  
what about calling them composable programming languages? You'd have  
the following definition (roughly):

"A programming language is composable if it is a variable-free, all  
functions are unary, and new functions are created only by composing  
existing functions."

In addition to it not yet having a meaning, I find the term  
"composable programming language" somewhat more playful and to-the- 
point. It also highlights the composable/factorable nature of such  
programs nicely.

- John