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  freesl,   free_in,   thm_frees