Arith.INSTANCE_T

STRUCTURE

SYNOPSIS

Function which allows a proof procedure to work on substitution instances of terms that are in the domain of the procedure.

DESCRIPTION

This function generalises a conversion that is used to prove formulae true. It does this by first replacing any syntactically unacceptable subterms with variables. It then attempts to prove the resulting generalised formula and if successful it re-instantiates the variables.

The first argument should be a function which computes a list of subterms of a term which are syntactically unacceptable to the proof procedure. This function should include in its result any variables that do not appear in other subterms returned. The second argument is the proof procedure to be generalised; this should be a conversion which when successful returns an equation between the argument formula and T (true).

FAILURE

Fails if either of the applications of the argument functions fail, or if the conversion does not return an equation of the correct form.

EXAMPLE

#FORALL_ARITH_CONV "!f m (n:num). (m < (f n)) ==> (m <= (f n))";;
evaluation failed     FORALL_ARITH_CONV -- formula not in the allowed subset

#INSTANCE_T_CONV non_presburger_subterms FORALL_ARITH_CONV
# "!f m (n:num). (m < (f n)) ==> (m <= (f n))";;
|- (!f m n. m < (f n) ==> m <= (f n)) = T