Programming Language Theory Leif Grönqvist The national Graduate School of Language Technology (GSLT) MSI

Contents Leif’s three parts of the course: Functional programming Logical programming Similar ways of thinking, but different from the imperative way Formal semantics

Your background Quite good at programming(?) Not familiar to functional/logical programming(?) Which languages do you use?

Functional programming Why? –We want to make programming easier and more effective Some important features/drawbacks compared to imperative programming –Programs are functions –Functions may be data –Modularity, using higher order functions –No side effects

Functional pr. cont. Features/drawbacks –Automatic memory management (Java has it too, but not C/C++) –Not widely used in the industry – still true but for example Erlang is used professionally at Ericsson. Look at Joe Armstrong’s webcasted lecture about Erlang –Inefficiency in execution. Les and less important: Computers get more and more powerful

Performance The compilers are getting better:

The languages C - gcc 3.0, Imperative C++ - g++ 3.0, Imperative and oo Java - Java(TM) 2 Runtime Environment, Standard Edition (build b24), Imperative and oo Mercury - Mercury , Logic SML - MLton , Functional Ocaml - The Objective Caml, v 3.04, Functional and oo GHC - The Glorious Glasgow Haskell Compilation System, version , Purely functional and lazy

The tests Acker - A call to the Ackermann function with arguments 3, 8 Sieve - Calculate primes with Sieve of Eratosthene Hash - Insert and retrieve some values using a hash table Array - Do some array access FileReverse - Reverse i file HeapSort - Sort a list using heap sort NestLoop - Nested loops Rank - Average ranking for all tests

History The first, and most spread, functional language is Lisp (late 50’s) List = LISt Processor Not strongly typed A popular newer dialect is Scheme Many functional enthusiasts do not agree that Lisp is functional, due to things like assignment and other imperative constructions We will not talk more about Lisp/Scheme Take a look at it in the book if you want

Lambda Calculus Published by Alonzo Church 1930 Mathematical formalism expressing computing by functions Same power as a Turing Machine The idea behind the functional languages

Syntax expression -> constant |variable |(expression expression)application | (λ variable. expression)lambda abstraction (λx. + 1 x) 2 -> (+ 1 2) -> 3

Problems (λ x. x x) (λ x. x x) -> … Will not terminate, but (λy.2) ((λ x. x x) (λ x. x x)) will terminate if we use so called ”normal order evaluation” (lazy evaluation) If we use ”applicative evaluation order” it will not terminate

Basic principles Functional programming style possible in many languages In a purely functional language you think functional all the time: –A program is a black box, a function f: X->Y where X is the domain and Y the range –No side effects –Recursion is the only way to make iteration and loops –Strong typing: passing functions as argument is easier and more flexible than in C for example –Higher order functions give modularity Many functional languages look similar, we will use Haskell from now

Haskell First version in the en of the 80’s at Yale and Glasgow Standardized in 1998 Some new things compared to the older Miranda and ML –Monads (solves I/O handling) –Function overloading Purely functional Fully Curried Lazy (gives lazy infinite lists!)

Some small examples fact 0 = 1 fact n = n * fact (n-1) square x = x * x gcd u 0 = u gcd u v = gcd v (u `mod` v) reverse [] = [] reverse (h:t) = reverse t ++ [h]