Functional Programming: Lisp MacLennan Chapter 10

2 Control Structures Atoms are the only primitives: since they are the only constructs that do not alter the control flow. –Literals (represent themselves) Numbers Quoted atoms lists –Unquoted atoms are bound to Functions (if they have expr property) Data values (if they have apval property) Control-structure constructors –Conditional expression –Recursive application of a function to its arguments

3 In LISP we have conditional expression. While in Fortran and Pascal we have to drop from expression level to instruction level to make a choice.

4 The logical connectives are evaluated conditionally (or x y) = (if x t y) (or (eq (car L) ‘key) (null L) ) What happen if L is null? (or (null L) (eq(car L) ‘key) ) Does this work? (if (null L) t (eq (car L) ‘key))

5 Iteration is done by recursive (defun getprop (p x) (if (eq (car x) p) ( cadr x) (getprop p (cddr x)) ))

6 Reduction : reducing a list to one value (defun plus-red (a) (if (null a) 0 (plus (car a) (plus-red (cdr a)) )) ) (plus-red ‘( )) >> 15

7 Mapping: mapping a list into another list of the same size (defun add1-map (a) (if (null a) nil (cons (add1 (car a)) (add1-map (cdr a)) )) ) (add1-map ‘( )) >>( )

8 Filtering: forming a sublist containing all the elements that satisfy some property (defun minus-fil (a) (cond ((null a) nil) (( minusp (car a)) (cons (car a) minusp-fil (cdr a)) )) (t (minusp-fil (cdr a)) )) )

9 Some thing like Cartesian product, which needs two nested loop For example: (All-pairs ‘(a b c) ‘(x y z)) >>((a x) (a y) (a z) (b x) (b y) (b z) (c x) (c y) (c z)) We use distl (distribute from left) (distl ‘b ‘(x y z)) >>((b x) (b y) (b z))

10 (defun all-pairs (M N) (if (null M) nil (append (distl (car M) N) (all-pairs (cdr M) N)) )) (defun distl (x N) (if (null N) nil (cons (list x) (car N)) (distl x (cdr N)) )) ) (the list function makes a list out of its argument)

11 Recursion for Hierarchical structures (defun equal (x y) ( or (and (atom x) (atom y) (eq x y)) (and (not (atom x)) (not (atom y)) (equal (car x) (car y)) (equal (cdr x) (cdr y)) )) )

12 Recursion and Iteration are theoretically equivalent

13 Functional arguments allow abstraction mapcar: a function which applies a given function to each element of a list and returns a list of the results. (defun mapcar (f x) (if (null x) nil (cons (f (car x)) (mapcar f (cdr x)) )) ) (mapcar ‘add1 ‘( )) >> ( ) (mapcar ‘zerop ‘( )) >> (nil nil t nil nil t nil) (mapcar ‘not (mapcar ‘zerop ‘( ))) >> (t t nil t t nil t)

14 Functional arguments allow programs to be combined They simplify the combination of already implemented programs.

15 Lambda expressions are anonymous functions Instead of defining a name for a function (defun twotimes (x) (times x 2) (mapcar ‘twotimes L) We may write: (mapcar ‘(lambda (x) (times x 2)) L)

16 Name Structures The primitive name structures are the individual bindings of names (atoms) to their values. Bindings are established through –Property lists By pseudo-functions –set (like declaring a variable) –Defun (like declaring a procedure) –Actual-formal correspondence

17 Application binds Formals to Actuals

18 Temporary bindings are a simple, syntactic extension (with let )

19 Dynamics scoping is the constructor Dynamic scoping complicates functional arguments