ORDERED_REWR_CONV : (term -> term -> bool) -> thm -> term -> thm

SYNOPSIS

Basic rewriting conversion restricted by term order.

DESCRIPTION

Given an ordering relation ord, an equational theorem A |- !x1...xn. s = t that expresses a rewrite rule, the conversion ORDERED_REWR_CONV gives a conversion that applied to any term s' will attempt to match the left-hand side of the equation s = t to s', and return the corresponding theorem A |- s' = t', but only if ord `s'` `t'`, i.e. if the left-hand side is ``greater'' in the ordering than the right-hand side, after instantiation. If the ordering condition is violated, it will fail, even if the match is fine.

FAILURE CONDITIONS

Fails if the theorem is not of the right form or the two terms cannot be matched, for example because the variables that need to be instantiated are free in the hypotheses A, or if the ordering requirement fails.

EXAMPLE

We apply the permutative rewrite:

  # ADD_SYM;;
  val it : thm = |- !m n. m + n = n + m

with the default term ordering term_order designed for this kind of application. Note that it applies in one direction:

  # ORDERED_REWR_CONV term_order ADD_SYM `1 + 2`;;
  val it : thm = |- 1 + 2 = 2 + 1

but not the other:

  # ORDERED_REWR_CONV term_order ADD_SYM `2 + 1`;;
  Exception: Failure "ORDERED_REWR_CONV: wrong orientation".

USES

Applying conditional rewrite rules that are permutative and would loop without some restriction. Thanks to the fact that higher-level rewriting operations like REWRITE_CONV and REWRITE_TAC have ordering built in for permutative rewrite rules, rewriting with theorem like ADD_AC will effectively normalize terms.