1 Functional languages (e.g. Scheme, ML) Scheme is a functional language. Scheme is based on lambda calculus. lambda abstraction = function definition In Scheme, a function is defined using the keyword lambda: (lambda ( ) ) Syntax of Scheme is very simple: primitive expressions numbers, such as 17 symbols, such as ’fred names, such as fred complex expressions function applications, such as (+ 3 2) or (addOne x), consist of a function and arguments for the function. special forms, such as (define x y), are evaluated in special ways. ML is a functional language. ML is based on lambda calculus. lambda abstraction = function definition In ML, a function is (typically) defined using the fun keyword: fun = Syntax of ML is familiar: block-structured syntax infix operators for +, *, etc function names appear before argument lists, not inside parentheses

2 Evaluation (Scheme and ML share model – focus on Scheme) Numbers are interpreted in base 10. Names are looked up in an environment, starting with the current environment, following static links, until the name is found. If it is not found, an error occurs. (define ) is evaluated by first evaluating, and binding, in the current environment, the name to that value. (lambda …) is evaluated by creating an appropriate closure (sometimes called a procedure). The closure’s environment link refers to the environment which was active when the closure was created. All members of an application are evaluated, after which the first is applied to the rest. A procedure application is evaluated by creating an environment to bind the parameters of the procedure to its arguments, and then evaluating the body relative to this new environment. The static link of the environment refers to the same environment as the closure, whereas the dynamic link refers to the environment that was active when the procedure was applied.

3 Examples > > (define x 12) > x 12 > (define addOne (lambda (x) (+ x 1))) > (addOne x) 13 > (define add (lambda (x y) (+ x y))) > (add 3 x) 15 > (define adder (lambda (x) (lambda (y) (+ x y)))) > (define add3 (adder 3)) > (add3 x) 15 > (define add7 (adder 7)) > (add7 x) val it=12:int - val x=12; val x=12:int - x val it=12:int - fun addOne x = x+1; val addOne=fn:int->int - addOne x val it=13:int - fun add (x,y) = x+y; val add=fn:int*int->int; - add(3,x); val it=15:int - fun adder x y = x+y; val adder=fn:int->int->int - val add3 = adder 3; val add3=fn:int->int - add3 x; val it=15:int; - val add7 = adder 7; val add7=fn:int->int - add7 x; val it=19:int;

4 Scheme Although Scheme is syntactically a simple language, it supports sophisticated modeling: higher-order functions are a powerful tool in describing problems. Many ideas in design patterns have their roots in functional programming (e.g. strategy allows us to treat methods as first-class, a decorator acts like a function which maps a function to a function – think of the stream decorators in Java). With mutation (the ability to change a name-value binding in an environment) sophisticated systems can be built quite compactly.

5 Review of evaluation model Numbers evaluation to “themselves” (a character string representing a number evaluates to its base 10 numeric representation). For example: > 213 if you ask Scheme to evaluate a number 213 you get the number as a result

6 Evaluating names A name is evaluated by looking it up. Lookup starts in the current environment, and continues along the chain of statically-linked environments until either a binding is found (in which case the corresponding value is returned) or it isn’t (in which case an error occurs). For example (assuming no binding for x exists yet): > x Error: reference to undefined identifier: x > (define x 12) > x 12 >

7 Primitives Primitives, such as + and -, are ordinary names with name-value bindings established at start-up in the primitive environment, the base environment for evaluation (base in the sense that it’s static link is null). We can use + wherever we need a function. For example: > (define applyOperator (lambda (op) (op 3 4))) > (applyOperator +) 7 > (applyOperator -) > We can also rebind the names of primitives (not a good idea in general, but this shows that primitives are not treated differently from other names in the language). > (+ 3 4) name “+” refers to addition function 7 > (define + -) name “+” now refers to subtraction function > (+ 3 4)

8 lambda forms A lambda form (lambda abstraction) defines a function in Scheme. Informally, the syntax is: (lambda ( ) ) When a lambda form is evaluated a closure results (which is printed as # ). For example: > (define addOne (lambda (p) (+ p 1))) > addOne # >

9 Function applications A function application is evaluated by first evaluating each expression inside the application, then applying the function to its arguments. This is accomplished by first creating a new environment in which the function’s parameters are bound to its arguments, and then evaluating the function’s body with respect to the new environment (which is now the current environment).

10 Evaluating (addOne 4) + addOne primitive env user env - cons … p (+ p 1) p4

11 Local bindings In a language like C or Java we can create local bindings inside a function/method by defining local variables: int mystery(int x, int y, int z) { int a = func1(x,y); int b = func2(y,z); } Local bindings can be created using a let-form: (define mystery (lambda (x y z) (let ((a (func1 x y)) (b (func2 y z))) ) Let-form is just syntactic sugar for a procedure application; the above let-form is equivalent to: ((lambda (a b) ) (func1 x y) (func2 y z))

12 Evaluating (define foo (let ((a 1) (b 2)) (lambda (c) (+ a b c)))) + addOne foo primitive env user env - cons … a b (lambda (c) (+ a b c)) a1 b2 (lambda (c) (+ a b c)) c (+ a b c)

13 Mutation set! allows an existing name-value binding to be changed.

14 Structuring data So far we’ve seen two types of values that we can bind to names: –numbers –functions two others are: –symbols –pairs

15 Symbols A symbol is an unevaluated name. Consider the following interaction: > (define x 12) > x 12 The x in the define is not evaluated. It is a symbol. The x in the second line is evaluated by looking up the value it is bound to in the current environment.

16 Using symbols We can bind a name to a symbolic value by quoting the symbol – quoting prevents evaluation: > (define fifi 'poodle) > fifi poodle The quote mark (') is syntactic sugar for the form (quote …); the above is equivalent to: > (define fifi (quote poodle))

17 Pairs cons is a primitive function which builds a pair. A pair has two members. (cons 'a 'b) builds a pair –whose first member is the symbol a –whose second member is the symbol b cons is therefore a pair constructor. Graphically: ba

18 accessors car returns the first member of a pair cdr returns the second member of a pair > (define myPair (cons 'a 'b)) > (car myPair) a > (cdr myPair) b

19 How is a pair displayed? > (define myPair (cons 'a 'b)) > myPair (a. b) Pairs are printed with a dot (.) separating the first (left) and second (right) components.

20 The REPL When interacting with a Scheme system, a Read-Eval-Print Loop (REPL) reads what you type, evaluates it, prints the resulting value, and loops back to repeat. The reader and printer parts of the REPL handle syntactic sugar (like converting 'a into (quote a)) and also printing things like lists.

21 Lists What is a list? A recursive definition: –the empty list () is a list –a pair whose cdr is a list is a list We can build a list using cons and (): > (define myList (cons 'a '())) > myList (a)

22 Wait a minute!! > (define myPair (cons 'a 'b)) > myPair (a. b) > (define myList (cons 'a '()) > myList (a)

23 What's going on? Why did myList print as (a) rather than as (a. ())? In fact, they are entirely equivalent: the REPL strikes again. The printer formats pairs which cdr is a pair in a special way to make lists easier to read.

24 Printing lists (a. (b. (c. (d. ())))) is printed as (a b c d) Graphically the structure is: This structure can be built in a variety of ways, some of which are shown on the next slide. abcd

25 Choices…choices (cons 'a (cons 'b (cons 'c (cons 'd '())))) (list 'a 'b 'c 'd) '(a b c d) '(a. (b c d)) (cons 'a (list 'b 'c 'd)) and so on!

26 Association lists An association list is a list of pairs. Used to implement a look-up table of key- value pairs. The primitive assoc is used to search an association list, given a key. Example on next slide.

27 > (define aList '((fifi. poodle) (fido. bulldog) (clifford. bigRed) (lassie. collie))) > (assoc 'fido aList) (fido. bulldog) > (assoc 'rufus aList) #f

28 Mutating pair components set-car! mutates the value of the car of a pair set-cdr! mutates the value of the cdr of a pair > (define myPair (cons 'a 'b)) > myPair (a. b) > (set-car! myPair 'fred) > myPair (fred. b) > (set-cdr! myPair 'wilma) > myPair (fred. wilma)

29 Lists in other languages Lists in ML Lists in Prolog

30 Homework issues What is basic algorithm?

31 Homework issues What is basic algorithm? –while file is not empty read in a line if the line is an odd line, –then write line to output file –else don’t