How to Think about Prolog - 2

Mike’s Prolog Tutorial6 Oct 2011

Recap

• Initial Problem: compute set of fully specified goal states reachable from initial state

• Discovered: counter productive to compute • Reformulated problem: cheaply compute set that

is a close upper bound approximation• Informally verified that this is still correct for our

context• From reformulation, became clear that our

problem can be seen as a CSP

CSP

• Set of variables with their respective domains• Set of constraints on and between variables• CSP = find a set of assignments of values to vars

(from their domains) such that all constraints are satisfied.

• For our problem:– What are the variables?– Their domains?– What are the constraints?

Variables

• For each vehicle we have variables that state – Where its location is (X,Y)– Its orientation– Its length

• For each variable type we have a finite domain

Constraints

• Goal constraint: redCar must be in goal loc

• Consistency constraint: no 2 vehicles can occupy the same location

• Need to refine the notion of vehicles occupying same location

• Refine notion of vehicle occupying a location

Vehicle Occupying a Location• Remember, that at(Vehicle, X, Y) states highest leftmost

X,Y coords of where it is locatedoccupy(Vehicle, X, Y) :-

at(Vehicle, X, Y); at(Vehicle, X-1, Y),

orientation(Vehicle, horizontal); at(Vehicle, X-2, Y), orientation(Vehicle, horizontal), length(Vehicle, 3); ... for vertical direction