1. Logical and Functional Programming
Computational Models
Evolution of Languages
Logical Programming

2. Computational Models
Programming language design amounts to a model, or abstract description, of computation
Most languages based upon computation model where
Arithmetic operations
Variable assignments
Calling procedures, looping, etc.
Three computational models

3. Alan Turing’s Model
Read/write characters on a tape under control of a “program”
Suggests a physical machine
Assignment, control structures
Specify how results computed
What is computed is implicit
Imperative Languages like C++, Fortran, Pascal, Cobol, etc., based on this model.

4. Church’s Model - Equivalent to Turing’s Model
Involves “lambda calculus” and formalizes ideas of mathematical functions
Formal rules govern how to apply a function to its arguments
Repeated use of rules  reduces mathematical expression to its value
Program is one BIG function anyway
Functional Programming Languages like Lisp, SASL based on Church’s model

5. Predicate Calculus Model
OLD
Solution of systems of logical equations
Logical Programming Languages like Prolog based on Predicate Calculus Model
Also known as Declarative Languages
Specify what is to be computed, without the detail of how

6. Evolution of Languages
Ada
PROLOG (70’s France)
Pascal
LISP (60s)
Algol SASL
Fortran
Mercury (95)
Scheme (75)
Haskell (87)

7. Evolution of Languages
Software Engineering drove evolution of imperative languages
Artificial Intelligence drove evolution of non-imperative languages
Aside: 4GLS (non-imperative  imperative)

8. Prolog – Programming in Logic
Prolog is simple
Collection of facts (concrete relations)
And rules (patterns of relations)

9. Simple program dog (fido). --fact spotted (fido). --fact
dalmation (X) :- dog(X), spotted(X). --rule
Semantics of rule: if X is a dog and is spotted, then X is a dalmation

10. Syntax :- (if) , (and) % comment Variables – Uppercase letter to start
Objects – lower case letter to start

11. Prolog is interactive
Program does nothing until programmer adds a question or a query
?- dalmation (fido).
Prolog system answers Yes.
The facts and rules determine substitutions for variables in query (unification)

12. Can add to program Query Response No. leopard (leo). spotted (leo).
?-dalmation (leo).
Response No.

13. Want to know all spotted? That is, “For what X is X spotted?” Query
?-spotted(X).
Answer
X=fido. F8
X=leo. F8
No.

14. Prolog is interpreted Applications Allows flexibility
Can add new facts and rules anytime.
Applications
Knowledge of representation and reasoning
Symbolic manipulation
e.g., validating well-formed prefix expressions

15. Homework Due next Wednesday: Type in fido example and run
Come with questions if NOT working
Turn in program and output, if it is.