METIS_TAC : thm list -> tactic
Automated first-order proof search tactic using Metis algorithm.
A call to METIS_TAC[theorems] will attempt to establish the current goal
using pure first-order reasoning, taking theorems as the starting-point. (It
does not take the assumptions of the goal into account, but the similar
function ASM_METIS_TAC does.) It will usually either solve the goal
completely or run for an infeasibly long time, but it may sometimes fail
This tactic is closely related to MESON_TAC, and many of the same general
comments apply. Generally speaking, METIS_TAC is capable of solving more
challenging problems than MESON_TAC, though the latter is often faster where
it succeeds. Like MESON_TAC, it will exploit no special properties of the
constants in the goal, other than equality and logical primitives. Any
properties that are needed must be supplied explicitly in the theorem list,
e.g. LE_REFL to tell it that <= on natural numbers is reflexive, or
REAL_ADD_SYM to tell it that addition on real numbers is symmetric.
Sometimes the similar MESON_TAC tactic is faster, especially on simpler
- FAILURE CONDITIONS
Fails if the goal is unprovable within the search bounds.
Here is a simple `group theory' type property about a binary function m:
It is solved in a fraction of a second by:
# g `(!x y z. m(x, m(y,z)) = m(m(x,y), z) /\ m(x,y) = m(y,x))
==> m(a, m(b, m(c, m(d, m(e, f))))) = m(f, m(e, m(d, m(c, m(b, a)))))`;;
This is an example where METIS_TAC substantially outperforms MESON_TAC,
which does not seem to be able to solve that problem in a reasonable time.
val it : goalstack = No subgoals
- SEE ALSO
ASM_METIS_TAC, MESON_TAC, METIS.