(Posted at mathematica.SE, as it might be better there)
I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica:
f[xx_, a_, b_] := 3*xx /. {a -> b}
(* f[3*a*b, a, d] gives 9 b d *)
or
g[exp_] := exp /. {a_[n_] -> a[-n + 2]}
(* g[3 b[3 + m]^2] gives 3 b[-1 - m]^2 *)
Is there a mathematical symbol and term to describe such transformations (which is denoted as /. + a substituation list with { someA -> someB } in Mathematica)?
PS: I see that there are two things I use here. First, the mathematica-functions f[xx_, a_, b_] and g[exp_] seem to be functionals (their arguments are functions). And then, there are those symbolic replacement operations denoted by /. { someA -> someB}. I am interested in the mathematically correct name for the second part. Thanks!
I assume you mean assigning a new value to some variable? In that case, $:=$ is often used, especially in computer science. The symbol $\leftarrow$ is also often used, and is perhaps more intuitively understandable, as the value on the right-hand side is "put into" the variable on the left-hand side.
Closely related, := is also sometimes used as the symbol for defining a variable, so that $$a := 5x$$ means that $a$ is equal to $5x$ by definition. Other notations for this include $\stackrel{def}{=}$, $\stackrel{\Delta}{=}$, and $\equiv$.