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6.001 SICP Environment model

6.001 SICP Environment model. ; Can you figure out why this code works?

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6.001 SICP Environment model

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  1. 6.001 SICPEnvironment model ; Can you figure out why this code works? (define make-counter (lambda (n) (lambda () (set! n (+ n 1)) n )))(define ca (make-counter 0))(ca) ==> 1(ca) ==> 2(define cb (make-counter 0))(cb) ==> 1(ca) ==> 3 ; ca and cb are independent

  2. What the EM is: • A precise, completely mechanical description of: • name-rule looking up the value of a variable • define-rule creating a new definition of a var • set!-rule changing the value of a variable • lambda-rule creating a procedure • application applying a procedure • Enables analyzing arbitrary scheme code: • Example: make-counter • Basis for implementing a scheme interpreter • for now: draw EM state with boxes and pointers • later on: implement with code

  3. A shift in viewpoint • As we introduce the environment model, we are going to shift our viewpoint on computation • Variable: • OLD – name for value • NEW – place into which one can store things • Procedure: • OLD – functional description • NEW – object with inherited context • Expressions • Now only have meaning with respect to an environment

  4. A x: 15 y: 1 2 Frame: a table of bindings • Binding: a pairing of a name and a value Example: x is bound to 15 in frame Ay is bound to (1 2) in frame A the value of the variable x in frame A is 15

  5. B z: 10 E2 A x: 15 E1 y: 1 2 Environment: a sequence of frames • Environment E1 consists of frames A and B • Environment E2 consists of frame B only • A frame may be shared by multiple environments this arrow is calledthe enclosingenvironment pointer

  6. Evaluation in the environment model • All evaluation occurs in an environment • The current environment changes when theinterpreter applies a procedure • The top environment is called the global environment (GE) • Only the GE has no enclosing environment • To evaluate a combination • Evaluate the subexpressions in the current environment • Apply the value of the first to the values of the rest

  7. In E1, the binding of x in frame A shadows the binding of x in B B • x | GE ==> 3 z: 10x: 3 GE A x: 15 E1 y: 1 2 Name-rule • A name X evaluated in environment E givesthe value of X in the first frame of E where X is bound • z | GE ==> 10 z | E1 ==> 10 x | E1 ==> 15

  8. B z: 10 x: 3 GE z: 20 A x: 15 y: E1 1 2 Define-rule • A define special form evaluated in environment Ecreates or replaces a binding in the first frame of E (define z 25) | E1 (define z 20) | GE z: 25

  9. B z: 10 x: 3 GE 20 25 A x: 15 y: E1 1 2 Set!-rule • A set! of variable X evaluated in environment E changes the binding of X in the first frame of E where X is bound (set! z 20) | GE (set! z 25) | E1

  10. 11 1 2 Your turn: evaluate the following in order 11 (+ z 1) | E1 ==> (set! z (+ z 1)) | E1 (modify EM) (define z (+ z 1)) | E1 (modify EM) (set! y (+ z 1)) | GE (modify EM) Error:unbound variable: y B z: 10x: 3 GE A x: 15 z: 12 E1 y:

  11. (lambda (x) (* x x)) print Environmentpointer #[compound-...] evallambda-rule A compound procthat squares itsargument Code pointer parameters: xbody: (* x x) Double bubble: how to draw a procedure

  12. B z: 10x: 3 A x: 15 E1 square: Evaluating a lambda actually returns a pointer to the procedure object parameters: xbody: (* x x) Lambda-rule • A lambda special form evaluated in environment Ecreates a procedure whose environment pointer is E (define square (lambda (x) (* x x)))| E1 environment pointerpoints to frame Abecause the lambdawas evaluated in E1and E1  A

  13. To apply a compound procedure P to arguments: 1. Create a new frame A 2. Make A into an environment E: A's enclosing environment pointer goes to the same frame as the environment pointer of P 3. In A, bind the parameters of P to the argument values 4. Evaluate the body of P with E as the current environment You mustmemorize thesefour steps

  14. A E1 (square 4) | GE (* x x) | E1 x: 10 *: #[prim] GE square: parameters: xbody: (* x x) x: 4 square | GE ==> #[proc] ==> 16 x | E1 ==> 4 * |E1 ==> #[prim]

  15. Example: inc-square (define square (lambda (x) (* x x))) | GE (define inc-square (lambda (y) (+ 1 (square y))) | GE inc-square: GE square: p: xb: (* x x) p: yb: (+ 1 (square y))

  16. inc-square: GE square: E1 p: xb: (* x x) p: yb: (+ 1 (square y)) Example cont'd: (inc-square 4) | GE y: 4 inc-square | GE ==> #[compound-proc ...] (+ 1 (square y)) | E1 + |E1 ==> #[prim] (square y) | E1

  17. inc-square: GE square: E2 E1 y: 4 p: xb: (* x x) p: yb: (+ 1 (square y)) Example cont'd: (square y) | E1 x: 4 square | E1 ==> #[compound] y | E1 ==> 4 (* x x) | E2 (+ 1 16) ==> 17 ==> 16 * |E2 ==> #[prim] x | E2 ==> 4

  18. Lessons from the inc-square example • EM doesn't show the complete state of the interpreter • missing the stack of pending operations • The GE contains all standard bindings (*, cons, etc) • omitted from EM drawings • Useful to link environment pointer of each frame to the procedure that created it

  19. Example: make-counter • Counter: something which counts up from a number (define make-counter (lambda (n) (lambda () (set! n (+ n 1)) n ))) (define ca (make-counter 0))(ca) ==> 1(ca) ==> 2(define cb (make-counter 0))(cb) ==> 1(ca) ==> 3(cb) ==> 2 ; ca and cb are independent

  20. make-counter: GE ca: E1 p: nb:(lambda () (set! n (+ n 1)) n) p: b:(set! n (+ n 1)) n (define ca (make-counter 0)) | GE n: 0 environment pointerpoints to E1because the lambdawas evaluated in E1 (lambda () (set! n (+ n 1)) n) | E1

  21. make-counter: GE ca: E1 1 n: 0 p: nb:(lambda () (set! n (+ n 1)) n) E2 p: b:(set! n (+ n 1)) n (ca) | GE ==> 1 empty (set! n (+ n 1)) | E2 n | E2 ==> 1

  22. make-counter: GE ca: E1 1 n: 0 p: nb:(lambda () (set! n (+ n 1)) n) 2 E3 p: b:(set! n (+ n 1)) n (ca) | GE ==> 2 empty (set! n (+ n 1)) | E3 n | E3 ==> 2

  23. make-counter: GE cb: ca: E1 E4 n: 2 p: nb:(lambda () (set! n (+ n 1)) n) E3 p: b:(set! n (+ n 1)) n p: b:(set! n (+ n 1)) n (define cb (make-counter 0)) | GE n: 0 (lambda () (set! n (+ n 1)) n) | E4

  24. make-counter: GE ca: cb: E1 E4 n: 2 n: 0 p: nb:(lambda () (set! n (+ n 1)) n) 1 E2 E5 p: b:(set! n (+ n 1)) n p: b:(set! n (+ n 1)) n (cb) | GE ==> 1

  25. make-counter: GE ca: cb: E1 E4 n: 2 n: 1 p: nb:(lambda () (set! n (+ n 1)) n) E2 p: b:(set! n (+ n 1)) n p: b:(set! n (+ n 1)) n Capturing state in local frames & procedures

  26. Lessons from the make-counter example • Environment diagrams get complicated very quickly • Rules are meant for the computer to follow, not to help humans • A lambda inside a procedure body captures theframe that was active when the lambda was evaluated • this effect can be used to store local state

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