Lecture 3 Of Lists and Slippery Slopes CS

Lecture 3: Of Lists and Slippery Slopes CS 655: Programming Languages University of Virginia 25 Jan David Evans http: //www. cs. virginia. edu/~evans CS 655: Lecture 3 1

Menu • Language Features and the Inevitability of Language Decay • Lists • Higher Order Procedures 25 Jan CS 655: Lecture 3 2

Recap: Last Time • Primitives – Numerals, Booleans, Functions • Means of Combination – Application – lambda for making procedures – Special forms: if • Means of Abstraction – define for giving expressions names 25 Jan CS 655: Lecture 3 3

What Else? • We can probably write all possible programs with just this (but no one has proven it yet, Challenge #1) • But, it will be easier to write and understand them, and make them perform efficiently if we have more stuff in the language • Another Means of Abstraction – compound data 25 Jan CS 655: Lecture 3 4

Lists • LISP = LISt Processing • Could we define pair functions using Mini-Scheme? (make-pair 3 4) (first (make-pair 3 4)) (second (make-pair 3 4)) 25 Jan CS 655: Lecture 3 pair <3, 4> 3 4 5

Defining Pair (define make-pair (lambda (x) (lambda (y) (+ x (* 10000 y))) (define (pair-first p) (if (> p 10000) p (pair-first (+ p -10000))))) (define (pair-second p) (mod p 10000)) Only works for pair elements from 0 – 10000. But could do something more complicated to make it work for all numbers. 25 Jan CS 655: Lecture 3 6

Too Painful. . . Provide new Primitives • We can always make particular programs easier to write by adding primitives to our language • This is a very slippery slope! – C++: spec is 680 pages, 223 unresolved issues, 50 operators with 16 precedence levels, etc. 25 Jan CS 655: Lecture 3 7

The Slippery Slope • Everything you add to a language makes it harder to implement, harder to reason about, harder to understand programs in, harder to learn, more expensive to buy manuals for, etc. . . • Everything you add to a language interacts with everything else in complex and often unexpected ways 25 Jan CS 655: Lecture 3 8

Java on the Slope • Java in 1994: “Write once, run anywhere” – Language spec and tutorial and Hot. Java description: ~40 pages • Java in 2001: “Write once, test everywhere” – Java Standard (J 2 SE), Java Enterprise (J 2 EE), Java Micro (J 2 ME), Personal. Java, Embedded. Java, Java. Card, (all from Sun) – J 2 EE Spec Book: 800 pages, 7 authors – J 2 SE Language Spec: 544 pages – AP Computer Science (transitioning to Java by 2003? ) – needs 35 points to define Java subset Java. Phone, Java. TV, etc. 25 Jan CS 655: Lecture 3 9

Java is on the slope now, about to crash! 25 Jan CS 655: Lecture 3 (Duke suicide picture by Gary Mc. Graw. ) 10

Feature-itis • Every possible new feature makes some program better • Every programmer will clamor for their favorite feature • There is no cure: Mistakes never go away, they just get “deprecated” 25 Jan CS 655: Lecture 3 11

Committees Feature-itis • Languages designed and/or evolved by committees* and marketing departments (not passionate creators) quickly become morasses of complexity * Unless the committee has at least 3 eventual Turing award winners Algol 60: Backus, Mc. Carthy, Perlis Algol 68: Dijkstra, Hoare, Mc. Carthy, Wirth 25 Jan CS 655: Lecture 3 12

“A final hint: listen carefully to what language users say they really want, until you have an understanding of what they really want. Then find some way of achieving the latter at a small fraction of the cost of the former. ” C. A. R. Hoare, Hints on Programming Language Design, 1973. 25 Jan CS 655: Lecture 3 13

So. . . When programmers say they want pairs, lists, binary trees, red-black trees, hash tables, network streams, 3 D graphics, complex numbers, etc. we should give them a way to glue two values together. 25 Jan CS 655: Lecture 3 14

Enough (for now) on language complexity. . . Next: how do we provide that glue 25 Jan CS 655: Lecture 3 15

List Primitives in Scheme cons: , List (“construct”) , ( . ) Procedure that takes something of any type, and returns something a List. (cons 3 4) (3. 4) (cons 3 (cons 4 5) (3. (4. 5)) shown as (3 4. 5) 25 Jan CS 655: Lecture 3 16

cdr, sdr • car – ( . ) Takes a cons pair and returns the first element. Contents of the Address part of the Register • cdr – ( . ) Takes a cons pair and returns the second element. Contents of the Decrement part of the Register • They sdr called cdr “tail”, and car, “head” but historical names too entrenched in LISP to change. 25 Jan CS 655: Lecture 3 17

Examples (car (cons 3 4)) 3 (cdr (cons 3 4)) 4 (cdr (cons 3 (cons 4 5))) (4. 5) (car (cdr (cons 3 (cons 4 5)))) 4 25 Jan CS 655: Lecture 3 18

Lists • ‘() is a special constant known as nil. • We call zero or more cons’s ending with ‘() a “List” (nil is a list). (cons 3 ‘()) (3) 25 Jan CS 655: Lecture 3 19

Creating Lists • list is short for using a lot of cons’s (list) () (list 1 2 3 4) = (cons 1 (cons 2 (cons 3 (cons 4 ‘()) (1 2 3 4) • ‘ (quote) is even shorter (but has more special meanings) (quote (1 2 3)) ‘(1 2 3) 25 Jan (1 2 3) CS 655: Lecture 3 20

Examples (cdr (cons 3 4)) 4 (cdr (list 3 4)) (4) (cdr ‘(3 4)) (4) (car ‘((3 4) (5 4 6) 7)) (3 4) 25 Jan CS 655: Lecture 3 21

List Predicates: null? : boolean (not really a type in Scheme) #f is applied to something that is not nil. (null? (cdr (cons 3 4))) #f Scheme 7. 5 gives (), means the same thing. (null? (cdr (list 3))) #t 25 Jan CS 655: Lecture 3 22

List Predicates: list? : boolean #f if applied to something that is not a list. (list? (cons 3 4)) #f (list? (cons 3 ‘()) #t 25 Jan CS 655: Lecture 3 23

Manipulating Cons Cells set-car!: ( . ), Takes a cons cell and value of any type. Replaces first element of cons with value. (define pair 1 (cons 1 2)) (1. 2) (set-car! pair 1 3) no value pair 1 (3. 2) 25 Jan CS 655: Lecture 3 24

Manipulating Cons Cells set-cdr!: ( . ), Takes a cons cell and value of any type. Replaces second element of cons with value. pair 1 (3. 2) (set-cdr! pair 1 3) no value pair 1 (3. 3) 25 Jan CS 655: Lecture 3 25

Can we make an infinite list? (define little '(1)) little (1) (set-cdr! little) Unspecified return value little (1 1 1 1 1 1 1 111111111111111111111111111111 11111111111111111111111111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1. . . 25 Jan CS 655: Lecture 3 26

Bang! • set-car! and set-cdr! change state • All Scheme (primitive) procedures that change state end with ! (pronounced “bang”) • Without them, Scheme is a pure functional language. 25 Jan CS 655: Lecture 3 27

Functions • Mathematical Abstraction: same inputs always give same outputs +, , max, <, etc. are all functions • If f is a function and x contains only functions and literals, we can always replace (+ (f x)) with (define result (f x)) (+ result)) 25 Jan CS 655: Lecture 3 28

Referential Transparency • This is called referenential transparency • It doesn’t matter what order or how often you do things if everything is a function • Once you have procedures that change state, it does matter, and language implementers much be much more careful! • Much more on this later in the course. . . 25 Jan CS 655: Lecture 3 29

Forget the last 7 slides • For the next two+ weeks, we will concentrate only on the purely functional subset of Scheme • Adding set-car! and set-cdr! is an example of how a small language change has a big impact • You should not use any nonfunctional things in PS 1. 25 Jan CS 655: Lecture 3 30

Higher Order Procedures • Last time – procedure that returns procedure (define (make-adder x) (lambda (y) (+ x y))) • Now – procedures that use procedures are parameters 25 Jan CS 655: Lecture 3 31

Maximum of a List (define (max x y) (if (> x y))) (define (max-worker arg val) (if (null? arg) val (max-worker (cdr arg) (max (car arg) val)))) (define (max-list arg) (max-worker arg 0)) 25 Jan CS 655: Lecture 3 32

Sum of a List (define (sum-worker arg val) (if (null? arg) val (sum-worker (cdr arg) (+ (car arg) val)))) (define (sum-list arg) (sum-worker arg 0)) 25 Jan CS 655: Lecture 3 33

Can we abstract this? (define (sum-worker arg val) (define (max-worker arg val) (if (null? arg) val (sum-worker (max-worker (cdr arg) (+ (car arg) val)))) (max (car arg) val)))) 25 Jan CS 655: Lecture 3 34

Sure. . . (define (hard-worker arg val func) (if (null? arg) val (hard-worker (cdr arg) (func (car arg) val) func))) (define (max-list arg) (hard-worker arg 0 max)) (define (sum-list arg) (hard-worker arg 0 +)) 25 Jan CS 655: Lecture 3 35

Average (define (average-list arg) (/ (sum-list arg) (hard-worker arg 0 (lambda (x y) (+ y 1))))) 25 Jan CS 655: Lecture 3 length 36

Even harder worker. . . (define (harder-worker arg end-val func) (if (null? arg) end-val (func (car arg) (harder-worker (cdr arg) end-val func)))) (harder-worker '(1 2 3) '() (lambda (el ls) (cons el ls))) (1 2 3) 25 Jan CS 655: Lecture 3 37

More examples. . . (harder-worker ‘(1 2 3) ‘() (lambda (el ls) (append ls (list el)))) (3 2 1) (harder-worker ‘(1 2 3) 0 (lambda (x y) (+ x y))) 6 25 Jan CS 655: Lecture 3 38

Even more convoluted/powerful example ((harder-worker '(1 2 4) (lambda (x y) (* x y)) (lambda (el f) (lambda (x y) (f el (f x y))))) 1 2) 2048 25 Jan = 211 CS 655: Lecture 3 39

Charge • Problem Set 1 due Thursday – Office hours, Monday 3 -5 • Not on the problem set, but do for fun: – Obfuscated Scheme contest: try to come up with a convoluted use of higher-order procedures for your problem set partner to figure out. • Next time: Metalinguistic Abstraction (Ch 4) 25 Jan CS 655: Lecture 3 40