GEN_REWRITE_TAC : (conv -> conv) -> thm list -> tactic
SYNOPSIS
Rewrites a goal, selecting terms according to a user-specified strategy.
DESCRIPTION
Distinct rewriting tactics differ in the search strategies used in finding
subterms on which to apply substitutions, and the built-in theorems used in
rewriting. In the case of REWRITE_TAC, this is a recursive traversal starting
from the body of the goal's conclusion part, while in the case of
ONCE_REWRITE_TAC, for example, the search stops as soon as a term on which a
substitution is possible is found. GEN_REWRITE_TAC allows a user to specify a
more complex strategy for rewriting.
The basis of pattern-matching for rewriting is the notion of conversions,
through the application of REWR_CONV. Conversions are rules for mapping
terms with theorems equating the given terms to other semantically equivalent
ones.
When attempting to rewrite subterms recursively, the use of conversions (and
therefore rewrites) can be automated further by using functions which take a
conversion and search for instances at which they are applicable. Examples of
these functions are ONCE_DEPTH_CONV and RAND_CONV. The first argument to
GEN_REWRITE_TAC is such a function, which specifies a search strategy; i.e.
it specifies how subterms (on which substitutions are allowed) should be
searched for.
The second and third arguments are lists of theorems used for rewriting. The
order in which these are used is not specified. The theorems need not be in
equational form: negated terms, say "~ t", are transformed into the
equivalent equational form "t = F", while other non-equational theorems with
conclusion of form "t" are cast as the corresponding equations "t = T".
Conjunctions are separated into the individual components, which are used as
distinct rewrites.
FAILURE CONDITIONS
GEN_REWRITE_TAC fails if the search strategy fails. It may also cause a
non-terminating sequence of rewrites, depending on the search strategy used.
The resulting tactic is invalid when a theorem which matches the goal (and
which is thus used for rewriting it with) has a hypothesis which is not
alpha-convertible to any of the assumptions of the goal. Applying such an
invalid tactic may result in a proof of a theorem which does not correspond to
the original goal.
USES
Detailed control of rewriting strategy, allowing a user to specify a search
strategy.
EXAMPLE
Given a goal such as:
?- a - (b + c) = a - (c + b)
we may want to rewrite only one side of it with a theorem,
say ADD_SYM. Rewriting tactics which operate recursively result in
divergence; the tactic ONCE_REWRITE_TAC [ADD_SYM] rewrites on both
sides to produce the following goal:
?- a - (c + b) = a - (b + c)
as ADD_SYM matches at two positions. To rewrite on
only one side of the equation, the following tactic can be used:
GEN_REWRITE_TAC (RAND_CONV o ONCE_DEPTH_CONV) [ADD_SYM]