unwindLib.PRUNE_ONE

STRUCTURE

SYNOPSIS

Prunes a specified hidden variable.

LIBRARY

unwind

DESCRIPTION

PRUNE_ONE_CONV `lj` when applied to the term:

   "?l1 ... lj ... lr. t1 /\ ... /\ ti /\ eq /\ t(i+1) /\ ... /\ tp"

returns a theorem of the form:

   |- (?l1 ... lj ... lr. t1 /\ ... /\ ti /\ eq /\ t(i+1) /\ ... /\ tp) =
      (?l1 ... l(j-1) l(j+1) ... lr. t1 /\ ... /\ ti /\ t(i+1) /\ ... /\ tp)

where eq has the form "!y1 ... ym. lj x1 ... xn = b" and lj does not appear free in the ti’s or in b. The conversion works if eq is not present, that is if lj is not free in any of the conjuncts, but does not work if lj appears free in more than one of the conjuncts. Each of m, n and p may be zero.

If there is more than one line with the specified name (but with different types), the one that appears outermost in the existential quantifications is pruned.

FAILURE

Fails if the argument term is not of the specified form or if lj is free in more than one of the conjuncts or if the equation for lj is recursive. The function also fails if the specified line is not one of the existentially quantified lines.

EXAMPLE

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

#PRUNE_ONE_CONV `l1` "?l2 l1. (!(x:num). l1 x = F) /\ (!x. l2 x = ~(l1 x))";; 
evaluation failed     PRUNE_ONE_CONV

SEEALSO

PRUNE_ONCE_CONV, PRUNE_SOME_CONV, PRUNE_CONV, PRUNE_SOME_RIGHT_RULE, PRUNE_RIGHT_RULE