Logic Programming and Prolog

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Logic Programmingand Prolog

• Danielle and Joseph Bennett
• 24 April 2007

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What is Logic Programming?
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What is Logic Programming?

• The use of mathematical logic for computer
  programming. (Wikipedia)
• A declarative, relational style of programming
  based on first-order logic. (Dictionary.com)

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History of Logic Programming

• Came about in 1960s and 1970s due to debates
  about using declarative or procedural
  representations in AI
• Stanford and Edinburgh declarative
• MIT - procedural
• Developed Planner in 1969 (first language in the
  proceduralistic paradigm).

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Systems for Logic Programming

• ALF
• CLP
• ECLiPSe
• Elf
• Fish
• Flang
• Gödel
• KLIC
• LIFE
• MONA
• Oz System
• RELFUN
• SAMPLE
• XSB
• Just to name a few.

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Systems for Logic Programming, cont.

• Prolog is the most common system
• Prolog has many variations
• -Prolog, And-parallel Prolog.
• ACE, And-Or-parallel Prolog.
• Actor Prolog
• Andorra-I, an Or- and (deterministic)
  and-parallel Prolog.
• Aurora, Or-parallel Prolog.
• cu-Prolog, a constraint logic programming
  language
• lambda Prolog
• LeanTaP, a small theorem prover written in
  SICStus Prolog.
• Logtalk, an extension for Object-Oriented
  Programming in Prolog.
• Mixtus, an automatic partial evaluator for full
  Prolog.
• Muse, Or-parallel Prolog.

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All About Prolog
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All About Prolog

• Developed in 1972 by Alain Colmerauer and
  Philippe Roussel
• Name comes from PROgramming in LOGic
• A solution to the debate about which kinds of
  logic to use

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Prolog Structure

• Prolog facts a database of predicates and
  associations.
• Prolog rules define new predicates by using
  Prolog facts.
• Note Prolog considers capital letters to denote
  variables, not predicates.

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Prolog Structure Queries

• A query searches the database for the first fact
  that satisfies its goal.
• If a fact is found it either unifies the variable
  with a constant or returns yes.
• If a fact is not found that meets that condition
  it returns no.

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Prolog Structure Queries, cont.

• Use a semi-colon to request subsequent answers.
• In other words, a semi-colon signifies
  disjunction.
• A comma signifies conjunction.

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Prolog Structure - Unification

• A query resolves by unifying all of its elements.
• A constant unifies with itself and any variable.
• Scope is limited to the rule in which a variable
  occurs.
• When a variable is unified with a constant in a
  rule, all instances of that variable in that rule
  are unified to that constant.

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Prolog Structure - Backtracking

• In more complex examples, Prolog uses
  backtracking to find possible solutions.
• Prolog will attempt to resolve the first fact of
  its rule, unifying any variables with the first
  constant that satisfies that fact
• It then attempts to resolve the rest of that
  rules facts.
• If it is unable to do so under those conditions
  it backs up and tries again with the next
  available unifying constant.

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More Than Just Information

• Prolog rules can also be used write programs that
  do more than find the answers to simple database
  queries.
• append(, L, L).
• append(HT, L, HL1)-append(T, L, L1).
• This will append a list to another list
  recursively.
• A binary tree can be defined as follows
• tree(nil).
• tree(node(_, Left, Right)-tree(left),
  tree(right).

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How Prolog Works

• Example from pages 45-46 of our text
• instructor (bebis, cs365)
• instructor (looney, cs311)
• instructor (yuksel, cs446)
• enrolled (joseph, cs311)
• enrolled (joseph, cs365)
• enrolled (joseph, cs446)
• enrolled (danielle, cs365)
• enrolled (danielle, cs446)
• This is the database of Prolog facts.

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How Prolog Works, cont.

• Prolog rules
• teaches (P,S) - instructor (P,C), enrolled
  (S,C)
• This is to say that an instructor only teaches
  if he teaches a class and students are enrolled
  in that class.

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How Prolog Works, cont.

• Prolog answers queries based off of the database
  that has been given.
• ?enrolled (joseph, cs365)
• yes
• ?enrolled (X, cs365)
• joseph
• danielle
• ?teaches (X, joseph)
• bebis
• looney
• yuksel

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How Prolog Works, cont.

• Imagine what happens if we expand the database
• instructor (bebis, cs365)
• instructor (looney, cs311)
• instructor (yuksel, cs446)
• instructor (helfand, cs493)
• instructor (quint, math486)
• enrolled (ben, cs365)
• enrolled (bill, cs365)
• enrolled (bill, cs446)
• enrolled (brian, cs311)
• enrolled (brian, cs365)
• enrolled (brittney, cs311)
• enrolled (brittney, cs365)
• enrolled (brittney, cs446)
• enrolled (cody, cs311)
• enrolled (cody, cs365)
• enrolled (danielle, cs365)
• enrolled (danielle, cs446)

• enrolled (joel, cs365)
• enrolled (joseph, cs311)
• enrolled (joseph, cs365)
• enrolled (joseph, cs446)
• enrolled (joseph, cs493)
• enrolled (joseph, math486)
• enrolled (kellen, cs365)
• enrolled (matts, cs311)
• enrolled (matts, cs365)
• enrolled (mattw, cs311)
• enrolled (mattw, cs365)
• enrolled (mattw, cs446)
• enrolled (miran, cs365)
• enrolled (ryan, cs365)
• enrolled (samuel, cs365)

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How Prolog Works, cont.

• ?enrolled (X, cs365)
• ben
• bill
• brian
• brittney
• cody
• danielle
• david
• javier
• jeffrey
• joel
• joseph
• kellen
• matts
• mattw
• miran
• ryan
• samuel
• shane

• This list now gives us the entire roster of
  students in CS 365.

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How Prolog Works, cont.

• Queries can be more complicated to compare more
  data
• classmates (S1, S2) - enrolled (S1, C), enrolled
  (S2, C)
• ?classmates (joseph, danielle)
• yes
• ?classmates (joseph, jessica)
• yes
• ?classmates (jessica, danielle)
• no

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How Prolog Works, cont.

• classmates (S1, S2, C) - enrolled (S1, C),
  enrolled (S2, C)
• ?classmates (joseph, danielle, C)
• cs365
• cs446
• cs493
• no
• ?classmates (joseph, jessica, C)
• math
• ?classmates (jessica, danielle, C)
• no

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Free Prolog Access

• SWI-Prolog
• http//www.swi-prolog.org/
• YAProlog
• http//www.ncc.up.pt/vsc/Yap/
• Strawberry Prolog
• http//www.dobrev.com/

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Sources

• http//www.afm.sbu.ac.uk/logic-prog/
• http//en.wikipedia.org/wiki/Logic_programming
• http//dictionary.reference.com/browse/logic20pro
  gramming
• Pages 45-46 of our textbook
• CS 326 lectures on Prolog (written by Dr. Mircea
  Nicolescu)