Syntax and Semantics of Prolog

1
Syntax and Semantics of Prolog

• Syntax Terminologies
• Data Types
• Search Tree (Proof Tree)
• Unification
• Backtracking

2
Prolog Program consists of

• Facts - unconditional statement
• boy_names(john, 1700, 1).
• likes(rong, prolog).
• Rules - conditional statement
• likes(rong,X)- likes(X,prolog).
  grandparent(X,Y)- parent(X,Z), parent(Z,Y).
• Queries - something need to be proved (or goal
  needs to be solved)

3
Some Funny Terminologies

• Head
• Body
• Neck
• Tail
• gp(X,Y) - p(X,Z), p(Z,Y).
• Clause
• Goal

4
Data Objects in Prolog

• Variable - represents unknown object
• Constant - represents simple instance
• atom
• number
• Nested Structure
• list represents a sequence of objects
• structure - represents compound objects
• (all data objects are called terms)

5
Syntax - Data Objects

• Variable - strings starting with a capital letter
• strings starting with a _
• Constant
• atom - strings starting with a lower-case
  letter, and any strings enclosed in single quotes
• number same as numbers in Java
• Nested Structure
• list - term, term, term
• structure - atom(term, term, )

6
Syntax Prolog Program

• A Prolog program consists of either
• goal. or
• goal - goal, goal, , goal.
• A goal can be either
• atom (i.e. a name without arguments) or
• atom(term, term, )
• A term can be either
• variable, constant, or nested structure

7
Can You Spot Any Syntax Errors?

• Student_id(adam, 04971111)
• done - do1, do2 do3.
• done(Job - design(Job), imp(Job), test(Job),
• likes(tom marry).

8
How Does a Prolog Program Work - by example

• program
• father(john,ben).
• father(john,steve).
• father(steve,chris).
• father(chris,adam).
• father(steve,tom).
• grandfather(X,Z) -
• father(X,Y), father(Y,Z).

• ?- father(steve,X).

9
How Does a Prolog Program Work - by example

• program
• father(john,ben).
• father(john,steve).
• father(steve,chris).
• father(chris,adam).
• father(steve,tom).
• grandfather(X,Z) -
• father(X,Y), father(Y,Z).

• ?- grandfather(X,chris).
• ?- f(X,Y),f(Y,chris).

10
Unification

• There is a matching operation between the
• goal and the head of clause. This matching
• operation is called unification.
• Rules of unification
• a variable can unify with any term
• two constants (i.e. number or atom) can be
  unified if they are same
• two structures can be unified if they have same
  name and all arguments can be unified.

11
An ExampleSimplify an Arithmetic Expression

• Problem given an expression like 3x0, we want
  to change it to 3x, i.e. remove redundant 0s.
• What are the rewriting rules?
• simplify E0 to E
• simplify 0E to E
• keep E1E2 unchanged
• if both E1 and E2 are not 0.

12
A Prolog Program to Simplify Arithmetic
Expressions

• rules_for_plus(X, 0, X).
• rules_for_plus(0, X, X).
• rules_for_plus(X, Y, XY)- X \ 0, Y \ 0.
• simp(X,X)- atomic(X).
• simp(XY, NewXY)-
• simp(X, NewX), simp(Y, NewY),
• rules_for_plus(NewX, NewY, NewXY).