\DOC match
\TYPE {Compat.match : term -> term -> ((term*term) list *
(hol_type*hol_type) list)}
\SYNOPSIS
Finds instantiations to match one term to another.
\DESCRIBE
When applied to two terms, {match_term} attempts to find a set of type
and term
instantiations for the first term (only) to make it equal the second. If
it
succeeds, it returns the instantiations in the form of a pair containing
a
term substitution and a type substitution. If the first term represents
the
conclusion of a theorem, the returned instantiations are of the
appropriate
form to be passed to {INST_TY_TERM}.
\FAILURE
Fails if the term cannot be matched by one-way instantiation. It is also
not
apt to be useful unless {Old_syntax} is open, since the substitutions
that
{match} produces are not of the right type for the hol90 routines that
use
substitutions, like {subst} for instance.
\EXAMPLE
The following shows how {match_term} could be used to match the
conclusion of a
theorem to a term.
{
- val th = REFL (--`x:'a`--);
th = |- x = x
- match (concl th) (--`1 = 1`--);
val it = ([((--`1`--),(--`x`--))],
[((==`:num`==),(==`:'a`==))])
: term subst * hol_type subst
- INST_TY_TERM it th;
|- 1 = 1
}
\COMMENTS
Note that there is no guarantee that the returned instantiations will be
possible for {INST_TY_TERM} to achieve, because some of the variables
(term or
type) which need to be instantiated may be free in the assumptions, eg:
{
- (show_types := true; show_assums := true);
() : unit
- val th = ASSUME (--`x:'a = x`--);
val th = [(x :'a) = (x :'a)] |- (x :'a) = (x :'a) : thm
- match_term (concl th) (--`1 = 1`--);
val it = ([((--`1`--),(--`x`--))],
[((==`:num`==),(==`:'a`==))])
: term subst * hol_type subst
- Old_syntax.INST_TY_TERM it th handle e => Raise e;
Exception raised at Thm.INST_TYPE:
type variable(s) in assumptions would be instantiated in concl
}
In fact, for instantiating a theorem, {PART_MATCH} is usually easier.
Why is {match} in Compat? Because {match} is not provided in hol90;
the more accurate name {match_term} is used. Also, hol90 provides
{match_type}.
\SEEALSO
INST_TY_TERM, PART_MATCH.
\ENDDOC