unwindLib.PRUNE

STRUCTURE

SYNOPSIS

Prunes all hidden variables.

LIBRARY

unwind

DESCRIPTION

PRUNE_CONV "?l1 ... lr. t1 /\ ... /\ eqn1 /\ ... /\ eqnr /\ ... /\ tp" returns a theorem of the form:

   |- (?l1 ... lr. t1 /\ ... /\ eqn1 /\ ... /\ eqnr /\ ... /\ tp) =
      (t1 /\ ... /\ tp)

where each eqni has the form "!y1 ... ym. li x1 ... xn = b" and li does not appear free in any of the other conjuncts or in b. The conversion works if one or more of the eqni’s are not present, that is if li is not free in any of the conjuncts, but does not work if li appears free in more than one of the conjuncts. p may be zero, that is, all the conjuncts may be eqni’s. In this case the result will be simply T (true). Also, for each eqni, m and n may be zero.

FAILURE

Fails if the argument term is not of the specified form or if any of the li’s are free in more than one of the conjuncts or if the equation for any li is recursive.

EXAMPLE

#PRUNE_CONV
# "?l2 l1.
#   (!(x:num). l1 x = F) /\ (!x. l2 x = ~(out x)) /\ (!(x:num). out x = T)";;
|- (?l2 l1. (!x. l1 x = F) /\ (!x. l2 x = ~out x) /\ (!x. out x = T)) =
   (!x. out x = T)

SEEALSO

PRUNE_ONCE_CONV, PRUNE_ONE_CONV, PRUNE_SOME_CONV, PRUNE_SOME_RIGHT_RULE, PRUNE_RIGHT_RULE