Imperative programming
languages
• Design based on Von Neumann machine
• Computations performed through the
execution of assignment statements
• Examples: C, C++, Java, Fortran, Pascal,
Ada, Cobol
Sections 16.1, 16.2,16.3, 16.4
1
Functional programming
languages
• Design based on mathematical functions
• Computations performed through the
execution of function calls
• Fundamental characteristics: no variables or
assignment statements, no iteration
(recursion instead), referential transparency
• Examples: Lisp, Haskell, Scheme, ML
Sections 16.1, 16.2,16.3, 16.4
2
Logic programming languages
• Design based on predicate calculus (more
precisely first-order predicate calculus)
• Program is expressed in a form of symbolic logic
• Logical inferencing process is used to produce
results
– (x) (mother(x)  haschild(x))
– mother(cindy).
• Also called declarative programming because
program consists of a specification of results
(declarations) rather than detailed procedures for
producing results
Sections 16.1, 16.2,16.3, 16.4
3
Logic Programming Languages
• Provide:
– syntax for expressing propositions (logic
statement)
– syntax for expressing relationship between
propositions
– interpreter that can infer new propositions from
existing ones
Sections 16.1, 16.2,16.3, 16.4
4
Brief intro to predicate calculus
• First, what is a proposition?
– logical statement that may or may not be true
• Predicate calculus
1) provides a syntax for expressing collections of
propositions
2) plus, provides a method for determining
whether any facts can be inferred from the
propositions
Sections 16.1, 16.2,16.3, 16.4
5
First, the syntax for stating
propositions
• Two types of propositions
– Atomic propositions – consist of a single
compound term (definition on next slide)
– Compound propositions - atomic propositions
joined by connectives
Sections 16.1, 16.2,16.3, 16.4
6
Compound Term
• Looks like a mathematical function
• Two parts:
– Functor – function symbol that names a relation
– Ordered list of parameters where a parameter is
either a constant or a variable
• Examples
• motherof(cindy, baron)
• isfather(jay)
Sections 16.1, 16.2,16.3, 16.4
7
Connectives
•
•
•
•
•
Negation:  or
And:  or 
Or:  or 
Equivalence: or 
Implication:  or 
Sections 16.1, 16.2,16.3, 16.4
8
Examples
• professor(cindy)  mother(cindy)
• goes(cindy, work)  goes(cindy, home)
• (likes(cindy, chocolate)  typeof(chocolate,
godiva))  likes(cindy, godiva)
• (likes(cindy, person)  typeof(person, jay)) 
likes(cindy, jay)
• student(jon)
• The last one is an atomic proposition; the rest are
compound propositions
Sections 16.1, 16.2,16.3, 16.4
9
Quantifiers
• Allows us to express a general position and
include variables
– professor(cindy)  workshard(cindy)
– (x) (professor(x)  workshard(x))
• Universal quantifier - (x) P(x) means that for all
x, P(x) is true
• Existential quantifier – (x) P(x) means that there
exists some value of x for which P(x) is true
Sections 16.1, 16.2,16.3, 16.4
10
Propositions for English
sentences
•
•
•
•
Kim is female and a parent
Someone is a female and a parent
Everyone who is a mother has a child
Given any number you can find another
number which is less than it
Sections 16.1, 16.2,16.3, 16.4
11
Clausal Form
• Proposition is in clausal form if it looks
like:
A1  A2  ..  An  B1  B2  …  Bm
• There are no quantifiers and the only
operators allowed are , , and 
• Example:
likes(bob, fish)  fish(trout)  likes(bob, trout)
Sections 16.1, 16.2,16.3, 16.4
12
Horn clauses
• Clausal form that is appropriate for applying
resolution – a method of inferring new
propositions from existing propositions (the
second thing provided by predicate calculus)
• Clauses in which the right side consists of an
atomic proposition or the right side is empty
• Examples:
likes(bob, fish)  fish(trout)  likes(bob, trout)
likes(bob, fish)
fish(trout)
Sections 16.1, 16.2,16.3, 16.4
13
Method for inferring new
propositions: Resolution
• Inference rule that allows propositions to be
inferred from given propositions
• Example:
P1
P1  P2
P2  P3
From this we can infer P3
• unification and instantiation for the
resolution to succeed
Sections 16.1, 16.2,16.3, 16.4
14
Unification
• Finding values for variables that allow two
propositions to match and the resolution
process to succeed
• Example:
– mother(cindy, baron)
– mother(x, y)  haschild(x)
These two propositions are unified by instantiating x
to cindy and y to baron
Note: value for x must be same on both sides of
inference symbol
Sections 16.1, 16.2,16.3, 16.4
15
Instantiation
• Temporary assignment of a value to a variable
• It is common for an instantiation to occur during resolution
but then nothing gets proved – this requires backtracking
and instantiating the variable to a different value
• Example:
sibling(x, y) ^ sibling(y, z) -> sibling(x, z)
sibling(jay, tricia)
sibling(cindy, mark)
sibling(mark, celeste)
First x is instantiated to jay and y is instantiated to tricia
but then an instantiation can’t be found for z. Back
track and try x = cindy and y = mark
Sections 16.1, 16.2,16.3, 16.4
16
Logic programming languages
• Programmer doesn’t specify how
computation is to be done (no detailed
procedures and specified control flow)
• Programmer provides facts and rules
• User provides queries
• Inferencing engine uses facts and rules to
answer queries
Sections 16.1, 16.2,16.3, 16.4
17
First prolog example
mother(cindy, baron).
mother(ginny, cindy).
parent(X, Y) :- mother(X, Y).
parent(X, Y) :- father(X, Y).
grandmother(X, Y) :- mother(X, Z), mother(Z, Y).
Note: unlike our proposition examples, the
consequent is on the left side.
Sections 16.1, 16.2,16.3, 16.4
18
Declarative semantics
• Can determine meaning of statement just by
looking at statement
• Imperative language
– x = y * foo(x) //meaning depends on types of
x and y and what foo does
• Prolog
– motherof(cindy, baron).
– likes(jay, steak).
Sections 16.1, 16.2,16.3, 16.4
19