News

• PA 7 is out, due Fri 6/8

PA5, 6 Issues

• Bear with us, but let us know of anomalies

Final

• Tuesday 6/12/2012 from 7-10pm

• CENTER 105

• Stay tuned for review session

Logic Programming

Traditional Languages

• Program = Algorithm + Data Structures

• Execute

Prolog

• Program = Facts + Rules

• Queried

Logic Programming

• 

Prolog History

• 1970s: Logic + Automated Theorem Proving

• Developed for Artificial Intelligence

Prolog : Original Vision “Expert Systems”

Collection of Facts

• Carnitas is Mexican

Collection of Rules

• Mexican food is delicious

Queries

• What is a delicious food ?

Deductions

• Carnitas!

Declarative Programming

• Specify what you want

• Specify desired properties of result

• Not how to obtain result

Declarative Programming

Ideal for Searching Large Space of Results

Philosophy

• It is often hard to specify search algorithm

• But easy to specify the characteristics of the solution.

Declarative Programming: Application Orbitz/Expedia/etc.

Collection of Facts

• Airports
• Flights
• Times
• Durations
• Costs

Collection of Rules

If

• travel from A to B with price (P1), duration …
• travel from B to C with price (P2), duration …

Then

• travel from A to C with price (P1 + P2), duration …

Queries

• What is cheapest flight from SAN to JFK with duration < 6 Hrs ?

Declarative Programming: “Operations Research”

Specifically Linear Programming (CSE 101)

Collection of Facts

• El Cuervo makes two products
  • CA Burrito (profit = $2)
  • Fish Taco (profit = $1)

Collection of Rules

• Burrito Capacity < 200
• Taco Capacity < 500
• Total Capacity < 400

Queries

• How many burritos and tacos to maximize profit?

max     2.x + 1.y       /* profit           */
s.t.    x   < 200       /* burrito capacity */
        y   < 400       /* taco    capacity */
        x+y < 300       /* total   capacity */
          0 < x, y      /* must produce!    */  

Declarative Programming

Used heavily in many domains (together with statistical methods)

• Scheduling
  • Travel, Sports, …

• Rule-based Anomaly detection
  • Credit card fraud!

• SQL (and similar DB Query Languages)
  • Find all pairs of stocks, with same price on same day,
  • More than 50 times last year

• Many of these are inspired-by / subsets of Prolog …

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Language: Terms

Prolog Program

• Facts
• Rules

… but facts and rules about what ?

• Terms

Terms are Prolog’s way of representing Data

“Tree-like” values, similar to Ocaml ADTs

Four Kinds of Terms

1. Constants

2. Atoms

3. Variables

4. Compound Terms

Prolog Terms: Constants

Constants the simplest term, representing primitive values

• Basic types like integers, reals

• Examples: 1, 92, 4.4

Prolog Terms: Atoms

Atom: any identifier starting with lower-case

• x, alice, taco, giraffe, appleSauce

Prolog Terms: Atoms

Atom: any identifier starting with lower-case

• x, alice, taco, giraffe, appleSauce

Atoms are not variables

• Elements of a single mega enum type
• Similar to tags used in ML types (except ML tags are uppercase)
  • type atoms = x | alice | taco | giraffe | appleSauce | ...

Prolog Terms: Atoms

Atom: any identifier starting with lower-case

• x, alice, taco, giraffe, appleSauce

Atoms are Uninterpreted Constants (Names)

• Prolog knows NOTHING about the tags, they are just names

• Each tag is equal to itself (more later…)
  • alice = alice
  • taco = taco

• Each tag is disequal to every other tag
  • alice = taco never holds in Prolog
  • never
  • ever

Prolog Terms: Variables

Variables: any identifier starting with upper-case

• X, Y, Z, Head, Tail, Taco, Burrito, Alice, Bob

• _ is the wildcard variable, similar to ML

Variables are quite special …

• Even though x = a makes no sense to Prolog …

• … X = a does have a meaning but not what you might think!

Prolog Terms: Compound Terms

Compound terms are of form atom(term1, term2, term3, ...)

Where each term is one-of

• constant
• atom
• variable
• compound term

Prolog Terms: Compound Terms

Compound terms are of form atom(term1, term2, term3, ...)

Where each term is one-of

• constant
• atom
• variable
• compound term

Examples

x(y, z)              % y, z       are atoms
parent(alice, bob)   % alice, bob are atoms
parent(alice, Child) % alice is an atom, Child is a variable

Prolog Compound Terms

• Terms are NOT Function Calls!

• More like trees

• 

Prolog Terms: Compound Terms

Compound terms are of form atom(term1, term2, term3, ...)

Each term is one-of - constant - atom - variable - compound term

An Ocaml Type For Prolog Terms

type term = Constant of int
          | Atom     of string 
          | Variable of string 
	      | Compound of string * term list

QUIZ: An Ocaml Type For Prolog Terms

type term = Constant of int
          | Atom     of string 
          | Variable of string 
	      | Compound of string * term list

(Hint: atom = lowercase, variable = uppercase)

What Ocaml value of type term represents Prolog term parent(alice, bob) ?

A. parent ("alice", "bob")

B. parent (Atom "alice", Atom "bob")

C. [Atom "parent"; Atom "alice"; Atom "bob"]

D. Compound ("parent", [Atom "alice"; Atom "bob"])

E. Compound (Atom "parent", [Atom "alice"; Atom "bob"])

Prolog Compound Terms

Prolog term parent(alice, Charlie) is represented by:

Ocaml Value

Compound (Atom "parent", [Atom "alice"; Var "Charlie"])

Tree

QUIZ: An Ocaml Type For Prolog Terms

type term = Constant of int
          | Atom     of string 
          | Variable of string 
	      | Compound of string * term list

(Hint: atom = lowercase, variable = uppercase)

What Ocaml value of type term represents Prolog term factorial(5) ?

A. factorial(5)

B. factorial(Atom 5)

C. 120

D. Constant 120

E. Compound ("factorial", [Constant 5])

Prolog Terms

Prolog term factorial(5) is simply the tree

• The term is just a box containing 5 labeled factorial

Prolog Terms

Prolog term factorial(5) is simply the tree

• The term is just a box containing 5 labeled factorial

Function Symbols

• factorial just a label called a function symbol

• Prolog has no idea about implementation of function …

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Language: Facts

Example

The following facts specify a list of parent-child relationships

parent(kim, holly).  
parent(margaret, kim).  
parent(herbert, margaret). 
parent(john, kim).
parent(felix, john).  
parent(albert, felix).

• Note kim, holly, margaret etc. are all atoms

• Facts are just terms (typically without variables.)

• Specified by term followed by .

Language: Facts

The following facts specify a list of parent-child relationships

parent(kim, holly).  
parent(margaret, kim).  
parent(herbert, margaret). 
parent(john, kim).
parent(felix, john).  
parent(albert, felix).

Prolog maintains a Database of facts

• You can make up and add new facts to the collection

• We will be able to ask Prolog queries over these facts

Language: Facts

The following facts specify a list of parent-child relationships

parent(kim, holly).  
parent(margaret, kim).  
parent(herbert, margaret). 
parent(john, kim).
parent(felix, john).  
parent(albert, felix).

Predicates = Function Symbols Used For Facts

• Represent functions that evaluate to a boolean

• e.g. parent is a predicate of arity 2 (that takes 2 arguments)

Language: Facts

The following facts specify a list of parent-child relationships

parent(kim, holly).  
parent(margaret, kim).  
parent(herbert, margaret). 
parent(john, kim).
parent(felix, john).  
parent(albert, felix).

Predicates Are Just Names: No Meaning Or Implementation

• parent is a predicate of arity 2 (that takes two arguments)

• Programmer mentally notes that:
  • parent(kim, holly) means kim is a “parent-of” holly
  • parent(margaret, kim) means margaret is a “parent-of” kim
  • etc.

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Language: Queries

TBD

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Unification

TBD

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Language: Rules

TBD

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Programs = Facts + Rules

TBD

Plan

Language

1. Terms
2. Facts
3. Queries (Implementation: Unification)
4. Rules
5. Programs (Implementation: Backtracking Search)

Programming

• Numeric Computation
• Data Structures
• Puzzle Solving

Implementation: Backtracking Search

TBD