6.001, Spring 2006—Recitation 15 — 4/7/2006 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.001—Structure and Interpretation of Computer ProgramsSpring 2006Recitation 15 — 4/7/2006Environment ModelEval• name - Look up name in the current environment, if found return value, otherwise lookup inenclosing (parent) environment.• (lambda (params) body) - Create double bubble with code ptr to params and body and envptr to current environment.• (define name value) - Evaluate value and then create/replace binding for name with theresult.• (set! name value) - Evaluate value and then replace the first binding for name in the chainof environments, starting with the current env.• (proc args ... ) - Evaluate proc and args in the current environment, then a¯pply.• Otherwise – Follow the correct rule (numbers, if, cond, begin, quote, etc.)Apply• Step 1 - Drop a new frame• Step 2 - Link frame pointer of new frame to environment pointed to by env pointer of doublebubble being applied.• Step 3 - Bind params of double bubble in the new frame.• Step 4 - E¯val the body in the new frame.6.001, Spring 2006—Recitation 15 — 4/7/2006 2ProblemsProblem 1(define (square x)(* x x))(define (sum-of-squares x y)(+ (square x) (square y)))(sum-of-squares 2 3)Problem 2(define x 3)((lambda (x y) (+ (x 1) y))(lambda (z) (+ x 2))3)6.001, Spring 2006—Recitation 15 — 4/7/2006 3Problem 3(define (fact n)(if (= n 0)1(* n (fact (- n 1)))))(fact 2)Problem 4(define x 1)(let ((x 5)(y (+ x 5)))(+ x y))6.001, Spring 2006—Recitation 15 — 4/7/2006 4Problem 5(define (previous f)(let ((old #f))(lambda (x)(let ((return old))(set! old (f x))return))))(define echo (previous (lambda (y) y)))(echo
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