Prolog 7-Languages

Seven Languages in Seven Months
Language 3: Prolog
Raymond P. de Lacaze
Patch
raymond.delacaze@patch.com
01/30/13

Overview
• Part 1: Introduction to Prolog
Chapter 4 of Seven Languages in Seven Weeks
• Part 2: Advanced Topics
Chapters X-Y of The Art of Prolog
• Part 3: Prolog Today

Prolog Introduction
• Prolog is a declarative language
• Prolog is logic programming language
• Invented in 1972 by Colmerauer & Roussel
– Edinburg Prolog
– Marseilles Prolog
• Initially used for Natural Language Processing
• Programs consist of fact & rules
• Fact is a clause in FOPC
• Rule is an inference: B A1,…,An
• Use queries to run programs and perform retrievals

The Logic Programming Model
• Logic Programming is an abstract model of computation.
• Lambda Calculus is another abstract model of
computation.
• Prolog is a particular implementation of the logic
programming model in much the same way that Clojure
and Haskell are particular implementation of the lambda
calculus.
• OPS5 is another implementation of the logic programming
model.
• The use of mathematical logic to represent and execute
computer programs is also a feature of the lambda
calculus
• Prolog is classified as a functional language (wikipedia)

Logic Programming Paradigm
• A program is logical description of your
problem from which a solution is logically
derivable
• The execution of a program is very much like
the mathematical proof of a theorem
• Where’s my program?
• N! is (N-1)! times N
• 0! is 1

Prolog Facts
• Facts: <predicate>(<arg1>,…,<argN>)
• Example: likes(mary, john)
• Constants must be in lowercase
• Variables must be in uppercase or start with
an underscore.
• Example: eats(mikey, X)
• Example: believes(peter, likes(mary, john))

Basic Inferences & Variables
likes(john, cheese)
likes(mary, cheese)
likes(bob, meat)
similar(X,Y) :- likes(X,Z), likes(Y,Z)
Note: You can use *‘<filename/pathname>’+. to compile and load files
GNU Prolog 1.4.1
By Daniel Diaz
Copyright (C) 1999-2012 Daniel Diaz
| ?- ['C:ProjectsLanguagescodePrologsimilar.pl'].
compiling C:/Projects/Languages/code/Prolog/similar.pl for byte code...
C:/Projects/Languages/code/Prolog/similar.pl compiled, 4 lines read - 935
bytes written,
(16 ms) yes

Filling in the Blanks
| ?- similar(john, mary).
yes
| ?- similar(john, bob).
no
| ?- similar(mary, X).
X = john ?
yes
| ?- similar(X, Y).
X = john
Y = john ? ;
X = john
Y = mary ? ;
X = mary
Y = john ? ;
X = mary
Y = mary ?
Note: can use ; and a to get next or all answers

Map Coloring (1)
different(red, green).
different(red, blue).
different(green, red).
different(green, blue).
different(blue, red).
different(blue, green).
coloring(Alabama, Mississippi, Georgia, Tennessee, Florida) :-
different(Mississippi, Tennessee),
different(Mississippi, Alabama),
different(Alabama, Tennessee),
different(Alabama, Mississippi),
different(Alabama, Georgia),
different(Alabama, Florida),
different(Georgia, Florida),
different(Georgia, Tennessee).

Map Coloring (2)
| ?- ['c:projectslanguagescodeprologmap.pl'].
compiling c:/projects/languages/code/prolog/map.pl for byte code...
c:/projects/languages/code/prolog/map.pl compiled, 16 lines read - 1716 bytes written, 16 ms
yes
| ?- coloring(Alabama, Mississippi, Georgia, Tennessee, Florida).
Alabama = blue
Florida = green
Georgia = red
Mississippi = red
Tennessee = green ?
(16 ms) yes

Unification (1)
• The Unification Algorithm is a famous algorithm
from the field of AI, often used in theorem
proving, game playing, planning, etc…
• It can loosely be thought of as an algorithm that
tries to make to non-grounded terms the same.
• P(X, 2) = P(1, Y)  X=1 & Y=2  P(1, 2)
• P(X, X) = P(Y, 5)  X=5 & Y=5  P (5, 5)
• P(X, Y) = P(2, Z)  X=2 & Y=Z  P (2, Z)
• See Artificial Intelligence (Russell & Norvig)

Prolog Rules
• Rules: <head> :- <body>
• Head: Single clause typically with variables
• Body: Conjunction of goals with variables
• Examples:
ancestor(X,Y) :- parent(X,Y)
ancestor(X,Y) :- parent(X,Z), parent(Z,Y)
ancestor(X,Y) :- parent(X,Z), ancestor(Z,Y)

A Recursive Example(1)
parent(p1, p2).
parent(p2, p3).
parent(p3, p4).
ancestor(X, Y) :- parent(X, Y).
ancestor(X, Y) :- parent(X, Z), ancestor(Z, Y).
| ?- ['c:projectslanguagescodeprologancestor.pl'].
compiling c:/projects/languages/code/prolog/ancestor.pl for byte code...
c:/projects/languages/code/prolog/ancestor.pl compiled, 5 lines read -
818 bytes written, 13 ms
yes

A Recursive Example(2)
| ?- trace.
The debugger will first creep -- showing everything (trace)
yes
{trace}
| ?- ancestor(p1, p4).
1 1 Call: ancestor(p1,p4) ?
2 2 Call: parent(p1,p4) ?
2 2 Fail: parent(p1,p4) ?
2 2 Call: parent(p1,_80) ?
2 2 Exit: parent(p1,p2) ?
4 3 Fail: parent(p2,p4) ?
4 3 Call: parent(p2,_129) ?
5 3 Exit: ancestor(p3,p4) ?
true ?
(63 ms) yes

Using Rules in Both Directions
// Find all ancestors
| ?- ancestor(X, p4).
X = p3 ? ;
X = p1 ? ;
X = p2 ? ;
no
// Find all descendants
| ?- ancestor(p1, X).
X = p2 ? ;
X = p3 ? ;
X = p4 ? ;
no

Lists and Tuples (1)
• List are denoted by comma-separated values in square
brackets. i.e. [1, 2, 3]
• Tuples are denoted by comma-separated values in
parentheses. i.e. (1, 2, 3)
| ?- [1, 2, 3] = [X, Y, Z].
X = 1
Y = 2
Z = 3
yes

Accessing Elements of a List
| ?- [1, 2, 3] = [X | Y].
X = 1
Y = [2,3]
| ?- [1, 2, 3] = [_, X | Y].
X = 2
Y = [3]

Lists and Math (1)
count(0, []).
count(Count, [Head|Tail]) :-
count(TailCount, Tail), Count is TailCount + 1.
sum(0, []).
sum(Total, [Head|Tail]) :-
sum(Sum, Tail), Total is Head + Sum.
average(Average, List) :-
sum(Sum, List),
count(Count, List),
Average is Sum/Count.

Lists and Math (2)
| ?- sum(S, [1,2,3]).
1 1 Call: sum(_17,[1,2,3]) ?
2 2 Call: sum(_92,[2,3]) ?
3 3 Call: sum(_116,[3]) ?
4 4 Call: sum(_140,[]) ?
4 4 Exit: sum(0,[]) ?
5 4 Call: _168 is 3+0 ?
5 4 Exit: 3 is 3+0 ?
3 3 Exit: sum(3,[3]) ?
6 3 Call: _197 is 2+3 ?
6 3 Exit: 5 is 2+3 ?
2 2 Exit: sum(5,[2,3]) ?
7 2 Call: _17 is 1+5 ?
7 2 Exit: 6 is 1+5 ?
1 1 Exit: sum(6,[1,2,3]) ?
S = 6 ?

Solving Sudoku (1)
valid([]).
valid([Head|Tail]) :-
valid(Tail), fd_all_different(Head).
sudoku(S11, S12, S13, S14,
S21, S22, S23, S24,
S31, S32, S33, S34,
S41, S42, S43, S44,
Board) :-
Board = [S11, S12, S13, S14,
S21, S22, S23, S24,
S31, S32, S33, S34,
S41, S42, S43, S44, ],
fd_domain(Board, 1, 4),
Row1 = [S11, S12, S13, S14],
Row2 = [S21, S22, S23, S24],
Row3 = [S31, S32, S33, S34],
Row4 = [S41, S42, S43, S44],
Col1 = [S11, S21, S31, S41],
Col2 = [S12, S22, S32, S42],
Col3 = [S13, S23, S33, S43],
Col4 = [S14, S24, S34, S44],
Square1 = [S11, S12, S21, S22],
Square2 = [S13, S14, S23, S24],
Square3 = [S31, S32, S41, S42,],
Square4 = [S33, S34, S43, S44,],
valid([Row1, Row2, Row3, Row4,]),
valid([Col1, Col2, Col3, Col4, ]),
valid([Square1, Square2, Square3, Square4]).

Solving Sudoku (2)
| ?- sudoku(_, _, 2, 3,
_, _, _, _,
_, _ ,_, _,
3, 4, _, _,
Solution).
Solution = [4, 1, 2, 3,
2, 3, 4, 1,
1, 2, 3, 4,
3, 4, 1, 2]

Solving Sudoku (3)
• Finite Domain variables: A new type of data is introduced: FD
variables which can only take values in their domains. The
initial domain of an FD variable is 0..fd_max_integer where
fd_max_integer represents the greatest value that any FD
variable can take.
• fd_domain(Board, 1, 4).
Used to specify the range of values of each Sudoku cell.
• fd_all_different(X).
Used to specify that all elemts in the list must have distinct values.

Part 2: Advanced Topics
• The Art of Prolog, Sterling and Shapiro, MIT Press, 1986
• Structure Inspection
• Meta-Logical Predicates
• Cuts (and Negation)
• Extra-Logical Predicates

Structure Inspection
| ?- functor(father(tom, harry), P, A).
A = 2
P = father
Yes
| ?- arg(1,father(tom, harry), A1).
A1 = tom
Yes
| ?- arg(2,father(tom, harry), A2).
A2 = harry
yes
| ?- functor(X, father, 2).
X = father(_, _)
Yes
| ?- father(tom, harry) =.. [X, Y, Z].
X = father
Y = tom
Z = harry
yes
| ?- X =.. [father, tom, harry].
X = father(tom, harry)
yes
| ?- X =.. [father, tom, harry], assertz(X).
X = father(tom, harry)
yes
| ?- father(tom, harry).
yes
functor, arg and =..

Meta-Logical Predicates
• Outside scope of first-order logic
• Query and affect the state of the proof
• Treat variables as objects
• Convert data structures to goals
• Type Predicates:
• var(<term>)
• nonvar(<term>)
• Variables as objects: freeze & melt
• Dynamically Affecting the Knowledge Base
• assert(<goal>)
• retract(<goal>)
• The Meta-Variable Facility: call(<goal>)
• Memoization: lemma(<goal>)

Extra-Logical Predicates
• These achieve side-effects as a result of being
logically true
• Three types of extra-logical predicates
• Input / Output
– read & write
• Accessing and manipulating the program
– clause(Head, Body)
– assert (X)
– retract(X)
• Interfacing to the Operating System

Cuts (1)
• Predicate cut or ! affects procedural behavior
• Main purpose is to reduce the search space
• It’s use is controversial: purity vs. efficiency
• Green Cuts: Express determinism
• Consider merging two sorted lists
• Only one of X<Y, X=Y or X>Y can succeed
• Once one succeeds, no need for the others.

Merging with Cuts
merge([X|Xs], [Y|Ys], [X|Zs]) :- X<Y, !, merge(Xs, [Y|Ys], Zs).
merge([X|Xs], [Y|Ys], [X,Y|Zs]) :- X=Y, !, merge(Xs, Ys, Zs).
merge([X|Xs], [Y|Ys], [Y|Zs]) :- X>Y, !, merge([X|Xs], Ys, Zs).
merge(Xs, [], Xs) :- !.
merge([], Ys, Ys) :- !.
?- merge([1,3,5],[2,3], Xs).
Xs = [1,2,3,3,5]
yes

The Effect of Cuts
merge([1,3,4],[2, 5], Xs).
1 1 Call: merge([1,3,4],[2,5],_27) ?
2 2 Call: 1>2 ?
2 2 Fail: 1>2 ?
2 2 Call: 1<2 ?
2 2 Exit: 1<2 ?
3 2 Call: merge([3,4],[2,5],_60) ?
4 3 Call: 3>2 ?
4 3 Exit: 3>2 ?
5 3 Call: merge([3,4],[5],_114) ?
6 4 Call: 3>5 ?
6 4 Fail: 3>5 ?
6 4 Call: 3<5 ?
6 4 Exit: 3<5 ?
7 4 Call: merge([4],[5],_168) ?
8 5 Call: 4>5 ?
8 5 Fail: 4>5 ?
8 5 Call: 4<5 ?
8 5 Exit: 4<5 ?
9 5 Call: merge([],[5],_222) ?
9 5 Exit: merge([],[5],[5]) ?
7 4 Exit: merge([4],[5],[4,5]) ?
5 3 Exit: merge([3,4],[5],[3,4,5]) ?
3 2 Exit: merge([3,4],[2,5],[2,3,4,5]) ?
1 1 Exit: merge([1,3,4],[2,5],[1,2,3,4,5]) ?
Xs = [1,2,3,4,5] ?
| ?- merge([1,3,4],[2, 5], Xs).
1 1 Call: merge([1,3,4],[2,5],_27) ?
2 2 Call: 1>2 ?
2 2 Fail: 1>2 ?
2 2 Call: 1<2 ?
2 2 Exit: 1<2 ?
3 2 Call: merge([3,4],[2,5],_60) ?
4 3 Call: 3>2 ?
4 3 Exit: 3>2 ?
5 3 Call: merge([3,4],[5],_114) ?
6 4 Call: 3>5 ?
6 4 Fail: 3>5 ?
6 4 Call: 3<5 ?
6 4 Exit: 3<5 ?
7 4 Call: merge([4],[5],_168) ?
8 5 Call: 4>5 ?
8 5 Fail: 4>5 ?
8 5 Call: 4<5 ?
8 5 Exit: 4<5 ?
9 5 Call: merge([],[5],_222) ?
9 5 Exit: merge([],[5],[5]) ?
7 4 Exit: merge([4],[5],[4,5]) ?
5 3 Exit: merge([3,4],[5],[3,4,5]) ?
3 2 Exit: merge([3,4],[2,5],[2,3,4,5]) ?
1 1 Exit: merge([1,3,4],[2,5],[1,2,3,4,5]) ?
Xs = [1,2,3,4,5]

Prolog Today
• GNU Prolog Compiler
Full I/O capabilities
Complete Socket programming API
Can be linked to C in both directions
• Approx. 20 existing Prolog implementations
• Some other popular ones: SWI-Prolog & Visual Prolog
• http://en.wikipedia.org/wiki/Comparison_of_Prolog_implementations
• http://orgnet.com/inflow3.html
Software for Social Network Analysis & Organizational Network Analysis

core.logic
• Clojure core.logic (David Nolen)
This is a Clojure implementation of miniKanren. miniKanren is a Logic Programming library
embedded in Scheme based The Reasoned Schemer by Daniel Friedman.
• Another implementation of the Logic Programming Paradigm
• Presented at Strange Loop 2012
• Very well received by the Clojure community
• https://github.com/clojure/core.logic

AllegroGraph (Franz Inc.)
• AllegroGraph is one the leading graph database and application frameworks
for building Semantic Web applications.
• It can store data and meta-data as trillions of triples
• Query these triples through using PROLOG
• Query these triples using SPARQL (the standard W3C query language)
• AllegroGraph includes support for Federation, Social Network Analysis,
Geospatial capabilities and Temporal reasoning
• AllegroGraph is implemented in Common Lisp & CLOS.
• http://www.franz.com/agraph/allegrograph/

References
Seven Languages in Seven Weeks
Bruce A. Tate, Pragmatic Programmers LLC, 2010
The Art of Prolog: Advanced Programming Techniques
Sterling & Shapiro, MIT Press, 1986
GNU Prolog User Manual
Daniel Diaz, November 2012
Artificial Intelligence: A Modern Approach
Russell & Norvig, Prentice Hall, 1995

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