7/6/2011 1 CS61A Lecture 10 2011-07-06 Colleen Lewis TODAY • Make a calculator program – To better understand how the Scheme interpreter works – STEP 1: calc-apply – STEP 2: list versus quote (Scheme primitives) – STEP 3: read (Scheme primitive) – STEP 4: read-print loop – STEP 5: read-eval-print loop – STEP 6: calc-eval • deep-map STEP 1: calc-apply STk> (calc-apply '+ '(1 2 3)) 6 STk> (calc-apply '* '(2 4 3)) 24 STk> (calc-apply '/ '(10 2)) 5 STk> (calc-apply '- '(9 2 3 1)) 3 (define (calc-apply fn-wd arg-list) (cond ((equal? fn-wd '+) (add-up-stuff-in arg-list)) ((equal? fn-wd '-) (subtract-stuff-in arg-list)) ((equal? fn-wd '*) (multiply-stuff-in arg-list)) ((equal? fn-wd '/) (divide-stuff-in arg-list)) (else (error "Calc: bad op: " fn-wd)))) add-up-stuff-in (define (add-up-stuff-in lst) (accumulate + 0 lst)) STk> (accumulate + 0 '(1 2 4)) .. -> + with args = (4 0) .. <- + returns 4 .. -> + with args = (2 4) .. <- + returns 6 .. -> + with args = (1 6) .. <- + returns 7 7 STEP 2: list versus quote STk> '(1 2 +) (1 2 +) STk> (list 1 2 +) (1 2 #[closure arglist=args 7ff53de8])7/6/2011 2 STEP 3: Demo (read) STk> (read) 45 45 STk> (read) hello hello STk> (read) 'hello (quote hello) I typed this! After I hit return, Scheme printed this I didn’t have to quote words ' is really syntactic sugar for quote (a special form) Demo (read) STk> (define a (read)) hello a STk> a hello STk> Demo (read) STk> (define b (read)) (+ 1 2) b STk> b (+ 1 2) STk> (car b) + STk> (list-ref b 1) 1 Not: #[closure arglist=args 7ff53de8] Demo (read) STk> (define c (read)) (+ 3 (+ 1 2)) c STk> (list-ref c 2) (+ 1 2) STk> (car c) + Woah! read figured out it was a list within a list. Demo (read) STk> (define d (read)) (+ 3 ) d STk> d (+ 3) read waits for me to put necessary close-parens read Summary • Prompts user for input • NOT a function • Whatever the user types it returns – They can type words (without quotes) – They can type numbers – They can type lists • If it looks like a list it waits for you to put necessary close parentheses7/6/2011 3 STEP 4: (read-print) (define (read-print) (display "type here: ") (flush) (print (read)) (read-print)) display prints stuff Make the line above visible Waits for user input print prints stuff on a new line recursive call (infinite loop) STk> (read-print) type here: 4 4 type here: hi hi type here: (+ 1 2) (+ 1 2) type here: (+ (+ 3 4) 2) (+ (+ 3 4) 2) type here: Infinite loop! I’m typing HERE not at STk> (calc) demo STk> (calc) calc: 1 1 calc: (+ 2 3) 5 calc: (+ 2 (* 3 4)) 14 (read-print) Was sort of silly (calc) actually does something STEP 5: Read-Eval-Print Loop (calc) demo – it doesn’t have variables or “real” functions calc: + *** Error: Calc: bad expression: + Current eval stack: STk> (calc) calc: x *** Error: Calc: bad expression: x Current eval stack: (calc) read-eval-print loop (define (calc) (display "calc: ") (flush) (print (calc-eval (read))) (calc)) Representing Math + 2 1 Translating to Scheme (+ 1 2) car: + cdr: (1 2) 2 1 Children7/6/2011 4 Representing Math in Scheme (+ (* 2 4) 5) car: + cdr: ((* 2 4) 5) + 5 * 4 2 Representing Math in Scheme (+ (* 3 (+ 2 1) 4) 5) car: + cdr:((* 3 (+ 2 1) 4) 5) + 5 * 4 + 1 2 3 How many open parens? A) 1 B) 2 C) 3 D) 4 E) 5 Remember the(calc) read-eval-print loop? (define (calc) (display "calc: ") (flush) (print (calc-eval (read))) (calc)) calc-eval base case STk> (calc) calc: 1 1 (define (calc-eval exp) (cond ((number? exp) exp) ((list? exp) _____________ (else (error “Calc: bad exp”)))) calc-eval STk> (calc) calc: (+ 1 2) 3 (define (calc-eval exp) (cond ((number? exp) exp) ((list? exp) (calc-apply (car exp) (map calc-eval (cdr exp)))) (else (error “Calc: bad exp”)))) „+ „(1 2) + 2 1 calc-eval STk> (calc) calc: (+ (* 2 4) 5) 40 (define (calc-eval exp) (cond ((number? exp) exp) ((list? exp) (calc-apply (car exp) (map calc-eval (cdr exp)))) (else (error “Calc: bad exp”)))) „+ „(8 5) + 5 * 4 27/6/2011 5 calc-eval STk> (calc) calc: (+ (* 2 4) 5) 40 (define (calc-eval exp) (cond ((number? exp) exp) ((list? exp) (calc-apply (car exp) (map calc-eval (cdr exp)))) (else (error “Calc: bad exp”)))) + 5 * 4 2 (calc-eval exp) Works for bigger trees! + + 4 5 * 2 2 * 4 2 + 1 + * 3 3 3 (calc-apply (car exp) (map calc-eval (cdr exp)))) deep-map Remember map? Meet deep-map STk> (map square „(1 2 3)) (1 4 9) STk> (deep-map square „(1 2 3)) (1 4 9) STk> (deep-map square „((3 . 4) (5 6))) ((9 . 16) (25 36)) STk> (deep-map square 3) 9 STk> (deep-map square „()) () deep-map base cases STk> (deep-map square 3) 9 STk> (deep-map square „()) () (define (deep-map fn arg) (cond ((null? arg) '()) ((pair? arg) _____________ (else (fn arg)))) Draw ‘((3 . 4) (5 6)) How many pairs? A) 1 B) 2 C) 3 D) 4 E) 57/6/2011 6 (deep-map sq ‘((3 . 4) (5 6)) car cdr car cdr 3 car cdr 4 car cdr 6 car cdr 5 car cdr ? ? (cons (deep-map fn (car arg)) (deep-map fn (cdr arg))) deep-map solution (define (deep-map fn arg) (cond ((null? arg) '()) ((pair? arg) (cons (deep-map fn (car arg)) (deep-map fn (cdr arg)))) (else (fn arg)))) map (define (map fn seq) (if (null? seq) „() (cons (fn (car seq)) (map fn (cdr seq))))) Representing Math in Scheme SOLUTION (+ (* 3 (+ 2 1) 4) 5) car: + cdr:((* 3 (+ 2 1) 4) 5) + 5 * 4 + 1 2 3 How many open parens? A) 1 B) 2 C) 3 D) 4 E) 5 Draw ‘((3 . 4) (5 6)) car cdr car cdr 3 car cdr 4 car cdr 6 car cdr 5
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