What is a concatenative language?

Michael Nedzelsky — 2007-05-01 18:29:23

Recently I have made some examples in order to better understand the notion of 

a concatenative language. I still do not really understand it, though.



The Joy language is a concatenative language and this language contains two

basic constructors: one binary (concatenation) and one unary (quotation).



But what can be said if language contains for example, three constructors,

one binary and two unary. Is this language a concatenative language?



For example:



Let X be a non-empty set.

Let P denotes the set of all partial functions from X into X,

f_a, f_b are some elements of P,

J and R are some mappings from P into P.



Define the following grammar.



Terminal symbols: a, b, [, ], {, }

Production rules:

S --> e | a | b | S S | [ S ] | { S }



Let L denotes the language which generated by this grammar.



The language L has the following semantics:

let M be mapping from L to P, such that

0) M(e) = identity function on X

1) M(a) = f_a

2) M(b) = f_b

3) (\forall x,y \in L) M(xy) = M(x) M(y) # i.e. composition of the functions 

M(x) M(y)

4) (\forall x \in L) M( [x] ) = J(M(x))

5) (\forall x \in L) M( {x} ) = R(M(x))



I am really don't know, is L a concatenative or not.

If L is not a concatenative, and we drop the {} constructor from the grammar,

will the resulting language be a concatenative?



What do the others think?



Michael Nedzelsky