REAL_INT_REDUCE_CONV : conv

SYNOPSIS

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

DESCRIPTION

When applied to a term, REAL_INT_REDUCE_CONV performs a recursive bottom-up evaluation by proof of subterms built from integer 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 integer literals are of the form &n or -- &n for numeral n, nonzero in the negative case.

FAILURE CONDITIONS

Never fails, but may have no effect.

EXAMPLE

  # REAL_INT_REDUCE_CONV
     `if &5 pow 4 < &4 pow 5 then (&2 pow 3 - &1) pow 2 + &1 else &99`;;
  val it : thm =
    |- (if &5 pow 4 < &4 pow 5 then (&2 pow 3 - &1) pow 2 + &1 else &99) = &50

COMMENTS

The corresponding INT_REDUCE_CONV works for the type of integers. The more general function REAL_RAT_REDUCE_CONV works similarly over :real but for arbitrary rational literals.