1. Programming Languages
Meeting 10
November 8/9, 2016

2. Planning Ahead Next week: Short Exam 2 Program functions
Control structures
Parameter passing
Foundations of functional programming
Definitions
Syntax
Semantic specification

3. Reflections on Homework
Program function, II.4, variables in range 0..maxint
What is the value of x when a while loop that has condition x<>b terminates?
If sum(1,25,1,k,A[k]) sums the first 25 elements of the array A, by pattern matching sum( _ , _ , _ , _ , ___ ) sums the first 7 powers of 3.

4. Example 3 (6)
int A,B; A := 3; // Show Env element and Store element B := AV(IV(A)); B := AV(IN(A)); B := AN(IV(A)); B := AN(IN(A));

5. Primitives
first
last
head
tail
atom?
nil?
list?

6. More Primitives appendr appendl length The arithmetic functions
The comparison functions

7. Functional Forms The four Cs constant composition denoted by overbar
depends on one object
composition
denoted by centered small circle
depends on two functions

8. Functional Forms (2) construction conditional denoted by [ ]
depends on n functions
[f]:x <−> <f:x> (n=1)
conditional
denoted using −> and ;
depends on a predicate and two functions

9. Functional Forms (3) apply-to-all insert (also known as reduce)
denoted by αf
depends on one function
works only on lists
insert (also known as reduce)
denoted by /f
depends on one function with a number of properties

10. Exploring reduce Evaluate /f on the list <1,2,3,4,5,6> when f is+ - * / ^
max

11. Exploring apply-to-all
Evaluate αf on the list <0, -1, 1, 2, -2> when f is
sgn, the function that returns 1 if its argument is positive, -1 if its argument is negative, and 0 otherwise.
pow2, where pow2(x) = x^2

12. Enhanced apply-to-all
αf applies f to each element of a list
Called apply-to-all
apply-to-all1 applies a dyadic function (two arguments) to a fixed object and a list of objects
apply-to-all2 applies a dyadic function to a pair of equal length lists

13. Theorems about Functions
Lengths of lists
Equivalent compositions of functions

14. Programming in LISP Our approach; our rules
Functions may only use our primitives and user-defined functions.
Primitives and functionals may use built-in functions
Functions must not use the LISP equivalents of assignment statements or loops
Hints:
Think recursively
Think in parallel
Think with composition

15. Built-In Lisp Functions
car
cdr
reverse
length
cons
append
defun
cond
error
funcall
mapcar
and, or, not
fixp
numberp
zerop, plusp, minusp
equal
atom
null
mod
+, - , *, /
times

16. Your Turn
Create a file using a text editor that contains the LISP definitions of the primitives. Use only the built-in LISP functions listed above.
Load your primitives file and test each function thoroughly
Create a second file using a text editor that contains the LISP definitions of the functionals. Note: You do not have define composition or condition; they are built into the LISP system.

17. Your Turn (2) Test your functionals thoroughly.
Using the primitives and functionals, define concat, a function that concatenates two lists.
Using the primitives and functionals, define IG, the index generator function. (IG n) creates a list of length n containing the first n positive integers. E.g. (IG 5) returns ( )

18. For next time
Complete the Your Turn activities.