F UNCTIONAL P ROGRAMMING 05 Functions

F UNCTIONS - G LOBAL F UNCTIONS fboundp Tells whether there is a function with a given symbol as its name > (fboundp ‘+) T > (symbol-function ‘+) # (setf (symbol-function ‘add2) #’(lambda (x) (+ x 2))) > (add2 1) 3

F UNCTIONS - G LOBAL F UNCTIONS (setf func_name) (defun primo (lst) (car lst)) (defun (setf primo) (val lst) (setf (car lst) val)) > (let ((x (list ‘a ‘b ‘c))) (setf (primo x) 480) x) (480 B C) The first parameter : new value The remaining parameters : the arguments of this setf function

F UNCTIONS - G LOBAL F UNCTIONS Documentation string If you make a string the first expression in the body of a function defined with defun, then this string will become the function’s documentation string (defun foo (x) “Implements an enhanced paradigm of diversity.” x) > (documentation ‘foo ‘function) “Implements an enhanced paradigm of diversity.”

F UNCTIONS - L OCAL F UNCTIONS Functions defined via defun or setf of symbol-function are global functions You can access global functions anywhere Local functions can be defined with labels, which is a kind of let for functions (labels ((add10 (x) (+ x 10)) (consa (x) (cons ‘a x))) (consa (add10 3))) (A. 13)

F UNCTIONS - L OCAL F UNCTIONS > (labels ((len (lst) (if (null lst) 0 (+ (len (cdr lst)) 1)))) (len ‘(a b c))) 3

F UNCTIONS - P ARAMETER L ISTS &rest Insert &rest before the last variable in the parameter list of a function This variable will be set to a list of all the remaining arguments (defun our-funcall (fn &rest args) (apply fn args))

F UNCTIONS - P ARAMETER L ISTS &optional All the arguments after it could be omitted (defun philosoph (thing &optional property) (list thing ‘is property)) > (philosoph ‘death) (DEATH IS NIL) The explicit default of the optional parameter (defun philosoph (thing &optional (property ‘fun)) (list thing ‘is property)) > (philosoph ‘death) (DEATH IS FUN)

F UNCTIONS - P ARAMETER L ISTS &key A keyword parameter is a more flexible kind of optional parameter These parameters will be identified not by their position, but by symbolic tags that precede them > (defun keylist (a &key x y z) (list a x y z)) KEYLIST > (keylist 1 :y 2) (1 NIL 2 NIL) > (keylist 1 :y 3 :x 2) (1 2 3 NIL)

F UNCTIONS – E XAMPLE : U TILITIES > (single? ‘(a)) T → returns true when its argument is a list of one element > (append1 ‘(a b c) ‘d) (A B C D) → adds an element to the end of the list > (map-int #’identify 10) ( ) → returns a list of the results of calling the function on the integers from 0 to n-1

F UNCTIONS – E XAMPLE : U TILITIES > (map-int #’(lambda (x) (random 100)) 10) ( ) > (filter #’(lambda (x) (and (evenp x) (+ x 10))) ‘( ) ( ) → returns all the non-nil values returned by the function as it is applied to the elements of the list > (most #’length ‘((a b) (a b c) (a))) (A B C) → returns the element of a list with 3 the highest score, according to some scoring function

F UNCTIONS – E XAMPLE : U TILITIES (defun single? (lst) (and (consp 1st) (null (cdr lst)))) (defun appendl (1st obj) (append 1st (list obj))) (defun map-int (fn n) (let ((acc nil)) (dotimes (i n) (push (funcall fn i) acc)) (nreverse acc))) (defun filter (fn lst) (let ((acc nil)) (dolist (x lst) (let ((val (funcall fn x))) (if val (push val acc)))) (nreverse acc)))

F UNCTIONS – E XAMPLE : U TILITIES (defun most (fn 1st) (if (null 1st) (values nil nil) (let* ((wins (car lst)) (max (funcall fn wins))) (dolist (obj (cdr lst)) (let ((score (funcall fn obj))) (when (> score max) (setf wins obj max score)))) (values wins max))))

F UNCTIONS – C LOSURES (defun combiner (x) (typecase x (number #’+) (list #’append) (t #’list))) (defun combine (&rest args) (apply (combiner (car args)) args)) > (combine 2 3) 5 > (combine ‘(a b) ‘(c d)) (A B C D)

F UNCTIONS – C LOSURES When a function refers to a variable defined outside it, it is called a free variable Closure A function that refers to a free variable (defun add-to-list (num lst) (mapcar #’(lambda (x) (+ x num)) lst)) num is free (defun make-adder (n) #’(lambda (x) (+ x n))) → returns a function n is free

F UNCTIONS – C LOSURES (setf add3 (make-adder 3)) # > (funcall add3 2) 5 (setf add27 (make-adder 27)) # > (funcall add27 2) 29

F UNCTIONS – C LOSURES Make several closures share variables (let ((counter 0)) (defun reset ( ) (setf counter 0)) (defun stamp ( ) (setf counter (+ counter 1)))) > (list (stamp) (stamp) (reset) (stamp)) ( ) You can do the same thing which a global counter, but this way the counter is protected from unintended references

F UNCTIONS – E XAMPLE : F UNCTION B UILDERS (defun disjoin (fn &rest fns) (if (null fns) fn (let ((disj (apply #’disjoin fns))) #’(lambda (&rest args) (or (apply fn args) (apply disj args))))))

F UNCTIONS – E XAMPLE : F UNCTION B UILDERS (defun conjoin (fn &rest fns) (if (null fns) fn (let ((conj (apply #’conjoin fns))) #’(lambda (&rest args) (and (apply fn args) (apply conj args)))))) (defun curry (fn &rest args) #’(lambda (&rest args2) (apply fn (append args args2)))) (defun rcurry (fn &rest args) #’(lambda (&rest args2) (apply fn (append args2 args)))) (defun always (x) #’(lambda (&rest args) x))

F UNCTIONS – E XAMPLE : F UNCTION B UILDERS > (mapcar (disjoin #’integerp #’symbolp) ‘(a “a” 2 3)) (T NIL T T) > (mapcar (conjoin #’integerp #’oddp) ‘(a “a” 2 3)) (NIL NIL NIL T) > (funcall (curry #’- 3) 2) 1 > (funcall (rcurry #’- 3) 2) -1

F UNCTIONS – R ECURSION Recursion plays a greater role in Lisp than in most other languages Functional programming Recursive algorithms are less likely to involve side-effects Recursive data structure Lisp’s implicit use of pointers makes it easy to have recursively defined data structures The most common is the list: a list is either nil, or a cons whose cdr is a list Elegance Lisp programmers care a great deal about the beauty of their programs Recursive algorithms are often more elegant than their iterative counterparts

F UNCTIONS – R ECURSION To solve a problem using recursion, you have to Show how to solve the problem in the general case by breaking it down into a finite number of similar, but smaller, problems Show how to solve the smallest version of the problem - the base case - by some finite number of operations Finding the length of a proper list In the general case, the length of a proper list is the length of its cdr plus 1 The length of an empty list is 0

F UNCTIONS – R ECURSION member Something is a member of a list if it is the first element, or a member of the cdr Nothing is a member of the empty list copy-tree The copy-tree of a cons is a cons made of the copy-tree of its car, and the copy-tree of its cdr The copy-tree of an atom is itself

F UNCTIONS – R ECURSION The obvious recursive algorithm is not always the most efficient E.g. Fibonacci function 1. Fib(0)=Fib(1)=1 2. Fib(n)=Fib(n-1)+Fib(n-2) (defun fib (n) (if (<= n 1) 1 (+ (fib (- n 1)) (fib (- n 2))))) The recursive version is appallingly inefficient The same computations are done over and over

F UNCTIONS – R ECURSION (defun fib (n) (do ((i n (- i 1)) (f1 1 (+ f1 f2)) (f2 1 f1)) ((<= i 1) f1))) The iterative version is not as clear, but it is far more efficient However, this kind of thing happen very rarely in practice

F UNCTIONS Homework (Due April 14) Use the lambda function and closures to write a function called our-complement that takes a predicate and returns the opposite predicate. For example: > (mapcar (our-complement #’oddp) ‘( )) (NIL T NIL T NIL T)