Boolean variables

The Mosel module mmxprs defines the entity type boolvar for representing a pseudo boolean decision variable. This type supports the operators and, or and not for building logical expressions and can be combined with ordinary Boolean variables (type boolean). A logical constraint is specified either by associating a pseudo boolean variable to a logical expression or by forcing the truth value (i.e. true or false) of an expression as shown in the code example below. When a logical expression is used on its own as a statement it is implicitly turned into a constraint (forced to true) and added to the constraint store.

 uses "mmxprs"

 public declarations
   R=1..5
   bv: array(R) of boolvar
   LC1, LC2: logctr
 end-declarations

! Simple clause, same as:  bv(1) and not bv(5) = true
 bv(1) and not bv(5)

! Association of clauses
 bv(3)=(not bv(4))

! The opposite of 'bv(1) or bv(3)' must be false
 (not (bv(1) or bv(3)))=false

! Defining a logic expression (not recorded in the constraint store)
 LC1:= and(i in 1..3) bv(i) or and(i in 4..5) not bv(i)

! Turn expression into a constraint
 LC1:= LC1=true

! A named logic expression (this defines a constraint)
 LC2:= (or(i in 1..3) not bv(i)) = false

! Solve as feasibility (SAT) problem
 maximise(0)
 if getprobstat=XPRS_OPT then
   writeln("Problem is feasible")
 else
   writeln("Problem is unsatisfiable")
 end-if