Constraint Logic Programming: A Survey

1
Constraint Logic Programming A Survey

• Joxan Jaffar and Michael J. Maher
• IBM Thomas J. Watson Research Center

Presented by Sharath R. Cholleti
Center for Distributed Object Computing Department
of Computer Science Washington University
2
Introduction

• Constraint Logic Programming (CLP)
• Constraint Solving Logic Programming
• Declarative paradigms
• Example sumto(n, 12..n)
• sumto(0,0).
• sumto(N,S) - Ngt1, NltS, sumto(N-1, S-N).
• ?- Slt3, sumto(N,S)
• Three answers (N0, S0), (N1, S1) (N2,
  S3)

3
Example
4
Key features

• Constraints specify the query as well as answers
• During execution, new variables and constraints
  are created
• Satisfiabilty of the collection of constraints is
  tested

5
Constraint Languages

• SKETCHPAD interactive drawing system
• THINGLAB OO flavor
• JUNO
• CONSTRAINTS
• 2LP c-like
• CHARME
• ILOG C library

6
CLP Languages

• Prolog II
• CLP(R) linear arithmetic constraints
• CHIP
• Prolog III
• LOGIN
• LIFE
• BNR-Prolog
• Computes over 3 domains
• Boolean algebra, finite domains, arithmetic over
  real numbers

7
Top-down Execution

• Operational semantics as a transition system on
  states
• ltA,C,Sgt
• A collection of as-yet-unseen constraints
• C active constraints
• S passive constraints
• Transitions
• ltA U a, C, Sgt ? ltA U B, C, S U (ah)gt
• h ? B is a rule of P

8
Top-down Execution (cont)

• Consistency or satisfiability
• Resolution
• Inference
• Infer(C,S)
• C S ?? C S
• Stronger the collection of active constraints,
  the earlier the failure
• Strong infer function?
• Depth-first search with chronological backtracking

9
Implementation Issues

• Manipulation of constraints
• Top-down systems

10
Incrementality

• Incremental to be practical
• S o1,o2,..,ok-1
• Non-incremental
• cost(S, ok) gt cost(o1,o2,..,ok)
• Incremental
• cost(o1,o2,..,ok-1) cost(S, ok) lt
  cost(o1,o2,..,ok)
• Practical
• cost(o1,o2,..,ok-1) cost(S, ok)
  cost(o1,o2,..,ok) X

11
Satisfiabilty

• Various algorithms
• Gaussian elimination
• Simplex method
• Makanin algorithm
• Davis-Putnam algorithm
• Boolean algebra
• Variable elimination
• Integer programming

12
Backtracking

• Restore the state of the constraint solver
• Trailing of constraints
• Prolog binding of variables
• CLP record changes to constraints
• In CLP an expression might be completely changed
• Value trail each variable is trailed with
  associated expression (constraint)
• Time-stamps same choice point

13
Inference Engine

• Delaying/wakeup of goals constraints
• When passive constraint becomes active
• Pow(x,y,z)
• Pow(1,y,z) awaits grounding of y

14
(No Transcript)
15
Applications

• Two classes
• Query
• Combinatorial
• Analysis and synthesis of analog circuits
• Options trading analysis
• Temporal reasoning
• Cutting stock
• DNA sequencing
• Scheduling