Curry: An Integrated Functional Logic Language

A.5 Constraint Solving and Concurrent Programming
In this example we demonstrate how Curry’s concurrent features can be used to solve constraint
problems with finite domains more efficiently than a simple generate-and-test solver. We want to
solve the classical map coloring problem. Consider the following simple map:
Country 1
Country 2
Country 3
Country 4
The problem is to assign to each of the four countries a color (red, green, yellow, or blue) such that
countries with a common border have different colors.
To solve this problem, we have to specify that some countries have different colors. For this
purpose, we define the following constraint which checks to elements for incompatibility:
diff :: a -> a -> Success
diff x y = (x==y)=:=False
For instance, diff t1 t2 is satisfied if t1 and t2 are different constants. If one of the arguments is a
variable, the evaluation of the function is delayed by definition of ==.
Now there is a straightforward solution of the map coloring problem. We define a constraint
coloring specifying the valid colors for each country and a constraint correct specifying which
countries must have different colors:
data Color = Red | Green | Yellow | Blue
isColor :: Color -> Success
isColor Red = success
isColor Yellow = success
isColor Green = success
isColor Blue = success
coloring :: Color -> Color -> Color -> Color -> Success
coloring l1 l2 l3 l4 = isColor l1 & isColor l2 & isColor l3 & isColor l4
correct :: Color -> Color -> Color -> Color -> Success
correct l1 l2 l3 l4 =
diff l1 l2 & diff l1 l3 & diff l2 l3 & diff l2 l4 & diff l3 l4
In classical logic programming, we can compute the solutions to the map coloring problem by
enumerating all potential solutions followed by a check whether a potential solution is a correct
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