SICP: Inside & Beyond

A brief talk about SICP made on SICPxShanghai 2015.

Transcript

1. SICP: Inside & Beyond DeathKing dk@hit.edu.cn
2. Alan J Perlis If art interprets our dreams, the computer executes them in the guise of programs!
3. SICP as The Book • Structure and Interpretation of Computer Programs • Purple Book • Wizard Book • THE BOOK • 《计算机程序的构造和解释》
4. SICP as The Book • The very first SICP edition. • a.k.a AITR 735 • Draft on 1983.07.31
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   ref: http://sicp.iijlab.net/people.html
7. Inside: • ӱ྽сྶཿ֤ିܔ܂ದૌᄇ؀đ୽غֹಀ܂࠹ෘࠏᆳྛb
   • ቋࠎЧ֥ҋਘѩ҂൞หקӱ྽ഡ࠹ე࿽֥ეمđ҂൞Ⴕི࠹ ෘଖᇕۿି֥ె૳ෘمđ္҂൞ෘم֥ඔ࿐ٳ༅ࠇᆀ࠹ෘ֥ ЧᇉࠎԤđط൞၂ུିܔႨႿ॥ᇅն྘ೈࡱ༢๤֥ᇆ৯گᄖ ྟ࠯ඌb
   • ႋھޓႵϜ໤ֹಀྩڿ၂۱ӱ྽đ๝ൈႻିЌӻჰটቔᆀ֥ ࣚപކڄ۬b
   • o࠹ෘࠏ॓࿐pѩ҂൞၂ᇕ॓࿐đط౏ఃᇗေྟ္ა࠹ෘࠏЧദ ѩ໭෾նܱ༢b
8. Chap 1. Extract Common Pattern • Q: Write a program to compute sum a to b. • A: That’s trivial. (define (sum-integers a b) (if (> a b) 0 (+ a (sum-integers (+ a 1) b))))
9. Chap 1. Extract Common Pattern • Q: Write a program to compute the sum of n2 for all n ∈ [a, b]. • A: Trivial. (define (sum-squares a b) (if (> a b) 0 (+ (* a a) (sum-squares (+ a 1) b))))
10. Chap 1. Extract Common Pattern • Q: Write a program to compute the sequence: • A: Not difficult. (define (pi-sum a b) (if (> a b) 0 (+ (/ 1.0 (* a (+ a 2))) (pi-sum (+ a 4) b))))
11. Chap 1. Extract Common Pattern • Q: Can you figure out the pattern? • A: Of course, it lies there. (define (<name> a b) (if (> a b) 0 (+ (<term> a) (<name> (<next> a) b))))
12. Chap 1. Extract Common Pattern • Q: <term> and <next> are not bounded. • A: We can parameterize them. (define (<name> a b (if (> a b) 0 (+ (<term> a) (<name> (<next> a) b)))) )
13. Chap 1. Extract Common Pattern • Q: <term> and <next> are not bounded. • A: We can parameterize them. (define (<name> a b (if (> a b) 0 (+ (<term> a) (<name> (<next> a) b)))) <term> <next>)
14. Chap 1. Extract Common Pattern • Q: It’s a general sum in some sense? • A: Yes. We could call it gen-sum. (define (gen-sum a b term next) (if (> a b) 0 (+ (term a) (gen-sum (next a) b))))
15. Chap 1. Extract Common Pattern • Q: How could you express π-sum using new pattern. • A: Even easy. π-sum is: (gen-sum a b (λ (x) (/ 1.0 (* x (+ x 2)))) (λ (x) (+ x 4)))
16. Chap 1. Extract Common Pattern • Q: Why it’s better? • A: Because it abstract out the common pattern. Using higher-order procedures to implement the details. • Q: Dose it any good? • A: It gets more reusable. You can perform different action by call it with different procedures.
17. Chap 1. Extract Common Pattern • Q: What’s a higher-order procedure? • A: A higher-order procedure, or, higher-order function, or functor, or functional, is a function which: • either takes at least one function, • or returns a function.
18. Chap 1. Extract Common Pattern Don’t Repeat Yourself! Extract the common pattern. Using higher order procedure to implement the detail for each case.
19. Chap 1. Extract Common Pattern (Beyond) • Q: Can you be more abstract? • A: Of course. (define (gen-sum a b term next) (if (<predicate> a b) 0 (<proc> (term a) (gen-sum (next a) b))))
20. Chap 1. Extract Common Pattern (Beyond) • Q: Then <predicate> and <proc> are free variables! How could we avoid that? (define (gen-sum a b term next) (if (<predicate> a b) 0 (<proc> (term a) (gen-sum (next a) b))))
21. Chap 1. Extract Common Pattern (Beyond) • Q: Then <predicate> and <proc> are free variables! How could we avoid that? (define (gen-sum a b term next predicate proc) (if (predicate a b) 0 (proc (term a) (gen-sum (next a) b)))) • A: By parameterize them!
22. Chap 1. Extract Common Pattern (Beyond) • Q: We got a long parameter list! • A: Currying takes care of it! (define (sum-builder predicate proc) (λ (<para-list>) (gen-sum a b term next predicate proc)))
23. Chap 1. Extract Common Pattern (Beyond) • Q: What is the type of sum-builder? • A: Currying takes care of it! (define (sum-builder predicate proc) (λ (<para-list>) (gen-sum a b term next predicate proc)))
24. Chap 1. Extract Common Pattern (Beyond) • Q: What do we have to fill in the <para-list>? • A: The unbound variables! (define (sum-builder predicate proc) (λ (a b term next) (gen-sum a b term next predicate proc)))
25. Chap 1. Extract Common Pattern (Beyond) • Q: sum-builder is a functional builder in some sense? • A: It seems so. (define f1 (sum-builder (lambda (x y) #t) +) (define f2 (sum-builder < +)) (define f3 (sum-builder vector-cmpare vector+) ......
26. Chap 1. Extract Common Pattern (Beyond) The Functional or Applicative Aspects Describing computation in terms of the definition and application of functions or procedures.
27. Chap 3. Environment • Q: What’s the problem with assignment? • A: Substitution is not suitable for this situation. Which means substitution the value of parameters first, then evaluate it.
28. Chap 3. Environment • Q: What could we do? • A: Introduced the environment. A environment is a map which maps a syntax element Ide to a locale L. And we have another map called save which maps a locale L to a pair (E, T). Identifier Locale Value Save Environment (Lvalue) (Rvalue)
29. Chap 3. Environment • Q: Show me more on implementation. • A: A binding associates a name with a value. and a frame is a table of bindings and a pointer to another frame. identifier value identifier value identifier value identifier value pointer identifier value identifier value pointer
30. Chap 3. Environment • Q: So what is an environment. • A: An environment is a sequence of frames. identifier value identifier value identifier value pointer identifier value identifier value pointer env0 env1
31. Chap 3. Environment • Q: How do we perform a variable lookup? • A: Describe in Scheme: (define (lookup var env) (cond [(null? env) (error)] [(has-binding? var (get-current-frame env)) (get-value var (get-current-frame env))] [else (lookup var (father-env env))]))
32. Chap 3. Environment • Q: How to evaluate the scheme code? • Q: And how about this? (define (make-counter init) (λ (inc) (set! init (+ init inc)) init)) (define my-counter (make-counter 10)) (my-counter 2) ;=> 12 (my-counter 2) ;=> 14
33. Chap 3. Environment • Q: Dose the make-counter acts like a function builder? • A: Yes. We know function builder already. It build a function, then you use that function. Of course, you can build more than one function though the procedure make-counter.
34. Chap 3. Environment • A: Firstly, expand the syntax define. • A: we got: (define (make-counter init) (λ (inc) (set! init (+ init inc)) init)) (define make-counter (λ (init) (λ (inc) (set! init (+ init inc)) init)))
35. Chap 3. Environment • A:Which means: 1. first, evaluate the lambda form 2. then, make counter refer to the evaluation result • A: Let’s try evaluate the lambda form firstly.
36. Chap 3. Environment • LAMBDA: the ultimate closure. • lambda, or, even better, make-closure. • What’s a closure? • A closure is a data structure. • Consists of a pointer to the code. • And a pointer to the environment where the lambda be called.
37. A Closure
38. Chap 3. Environment • A: Evaluate the lambda-form we got: (λ (init) (λ (inc) (set! init (+ init inc)) init)) code env top_env
39. Chap 3. Environment • A: Assign the closure to make-counter. make-counter value pointer * the-code * code env nil
40. Chap 3. Environment • Q: How do we perform a function apply? • A: Evaluate the value of parameter first, save these bindings in a new environment, then evaluate the code under the new environment.
41. Chap 3. Environment • A: Apply, (define my-counter (make-counter 10)). make-counter value pointer * the-code * code env nil (λ (inc) (set! init (+ init inc)) init) code env init 10 pointer my-counter value
42. Chap 3. Environment • A: Go further, (my-counter 2). (λ (inc) (set! init (+ init inc)) init) code env init 10 pointer inc 2 pointer Prepare for Parameter
43. Chap 3. Environment • A: Go further, (my-counter 2). (λ (inc) (set! init (+ init inc)) init) code env init 12 pointer inc 2 pointer Evaluate the body ((set! init (+ init inc) init)
44. Chap 3. Environment • A: You know it all. (λ (inc) (set! init (+ init inc)) init) code env init 12 pointer inc 2 pointer Evaluate the body ((set! init (+ init inc) init)
45. Chap 3. Environment Closure A data structure combine both the code it will call, and the environment when it be called.
46. ୆෮ᆩ֥֡Ⴕܱ࠹ෘ֥ת༆đః෰ದ္׻ି࿐֞bध҂ေಪູ රެӮۿ࠹ෘ֥ᄂӼࣼᅧ໤ᄝ୆֥൭৚b୆෮ᅧ໤֥đ္൞໡ ಪູѩ༐ຬ֥đ္ࣼ൞ᇆ߰ğପᇕु֞ᆃ၂ࠏఖб୆ֻ၂Ցᅟ ᄝ෱૫భൈିቓ֤۷؟֥ି৯đᆃဢ୆Ҍିࡼ෱ཟభ๷ࣉb Alan J Perlis
47. Beyond: What to learn? • Theories of Programming Languages • John C.Raynolds • A wisdom, clear, and gentle textbook on fundamental concept of programming languages with a wide range of topics include denotational semantics and the concurrency.
48. Beyond: What to learn? • Lambda-Calculus, Combinators, and Functional Programming. • G. Revesz, CTiTCS series. • About lambda calculus and the graph reduce theory. A gentle and beginner friendly textbook. Better finished the exercise.