Programming Languages Meeting 10 November 8/9, 2016

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

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.

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));

Primitives first last head tail atom? nil? list?

More Primitives appendr appendl length The arithmetic functions The comparison functions

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

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

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

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

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

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

Theorems about Functions Lengths of lists Equivalent compositions of functions

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

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

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.

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 (1 2 3 4 5)

For next time Complete the Your Turn activities.