\DOC frees
\TYPE {hol88Lib.frees : term -> term list}
\SYNOPSIS
Returns a list of the variables which are free in a term.
\DESCRIBE
Found in the hol88 library. When applied to a term, {frees} returns a
list of the free variables in that term. There are no repetitions in the
list produced even if there are multiple free instances of some
variables.
\FAILURE
Never fails.
\EXAMPLE
Clearly in the following term, {x} and {y} are free, whereas {z} is
bound:
{
- frees (--`(x=1) /\ (y=2) /\ (!z. z >= 0)`--);
> val it = [(--`x`--),(--`y`--)] : term list
}
\COMMENTS
The function {frees} is not in the standard hol98 kernel; the function
{free_vars} is used instead. WARNING: the order of the list returned
by {frees} and {free_vars} is different.
{
- val tm = (--`x (y:num):bool`--);
> val tm = (--`x y`--) : term
- free_vars tm
> val it = [(--`y`--),(--`x`--)] : term list
- frees tm;
> val it = [(--`x`--),(--`y`--)] : term list
}
It ought to be the case that the result of a call to {frees}
(or {free_vars}) is treated as a set, that is, the order of the free
variables should be immaterial. This is sometimes not possible; for
example the result of {gen_all} (and hence the results of {GEN_ALL}
and {new_axiom}) necessarily depends on the order of the variables
returned from {frees}. The problem comes when users write code that
depends on the order of quantification. For example, contrary to some
expectations, it is not the case that ({tm} being a closed term already)
{
GEN_ALL (SPEC_ALL tm) = tm
}
where ``{=}'' is interpreted as identity or alpha-convertibility.
\SEEALSO
hol88Lib.freesl, Term.free_in, thm_frees.
\ENDDOC