REAL_RAT_REDUCE_CONV : conv

SYNOPSIS

Evaluate subexpressions built up from rational literals of type :real, by proof.

DESCRIPTION

When applied to a term, REAL_RAT_REDUCE_CONV performs a recursive bottom-up evaluation by proof of subterms built from rational literals of type :real using the unary operators `--', `inv' and `abs', and the binary arithmetic (`+', `-', `*', `/', `pow') and relational (`<', `<=', `>', `>=', `=') operators, as well as propagating literals through logical operations, e.g. T /\ x <=> x, returning a theorem that the original and reduced terms are equal. The permissible rational literals are integer literals (&n or -- &n), ratios (&p / &q or -- &p / &q), or decimals (#DDD.DDDD or #DDD.DDDDeNN). Any numeric result is always put in the form &p / &q or -- &p / &q with q > 1 and p and q sharing no common factor, or simply &p or -- &p when that is impossible.

FAILURE CONDITIONS

Never fails, but may have no effect.

EXAMPLE

  # REAL_RAT_REDUCE_CONV
     `#3.1415926535 < &355 / &113 /\ &355 / &113 < &3 + &1 / &7`;;
  val it : thm =
    |- #3.1415926535 < &355 / &113 /\ &355 / &113 < &3 + &1 / &7 <=> T