Cost of Substitution. (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} )
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1 Cost of Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} 1
2 Cost of Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (interp {with {y 2} {+ 100 {+ 99 { {+ y 1}}}}} 2
3 Cost of Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (interp {with {y 2} {+ 100 {+ 99 { {+ y 1}}}}} (interp {+ 100 {+ 99 { {+ 2 1}}}} 3
4 Cost of Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (interp {with {y 2} {+ 100 {+ 99 { {+ y 1}}}}} (interp {+ 100 {+ 99 { {+ 2 1}}}} With n variables, evaluation will take O(n 2 time 4
5 Deferring Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} 5
6 Deferring Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} x = 1 (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} 6
7 Deferring Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} x = 1 (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} y = 2 x = 1 (interp {+ 100 {+ 99 { {+ y x}}}} 7
8 Deferring Substitution (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} x = 1 (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} y = 2 x = 1 (interp {+ 100 {+ 99 { {+ y x}}}}... (interp y y = 2 x = 1 8
9 Deferring Substitution with the Same Identifier (interp {with {x 1} {with {x 2} x}} 9
10 Deferring Substitution with the Same Identifier (interp {with {x 1} {with {x 2} x}} (interp {with {x 2} x} x = 1 10
11 Deferring Substitution with the Same Identifier (interp {with {x 1} {with {x 2} x}} (interp {with {x 2} x} x = 1 (interp x x = 2 x = 1 11
12 Deferring Substitution with the Same Identifier (interp {with {x 1} {with {x 2} x}} (interp {with {x 2} x} x = 1 (interp x x = 2 x = 1 Always add to start, then always check from start 12
13 Deferring Substitution with the Same Identifier (interp {with {x 1} {+ {with {x 2} x} x}} 13
14 Deferring Substitution with the Same Identifier (interp {with {x 1} {+ {with {x 2} x} x}} x = 1 (interp {+ {with {x 2} x} x} 14
15 Deferring Substitution with the Same Identifier (interp {with {x 1} {+ {with {x 2} x} x}} x = 1 (interp {+ {with {x 2} x} x} x = 1 (+ (interp {with {x 2} x} (interp x x = 1 15
16 Deferring Substitution with the Same Identifier (interp {with {x 1} {+ {with {x 2} x} x}} x = 1 (interp {+ {with {x 2} x} x} x = 1 (+ (interp {with {x 2} x} (interp x x = 1 (+ (interp x x = 2 x = 1 (interp x x = 1 16
17 Deferring Substitution with the Same Identifier (interp {with {x 1} {+ {with {x 2} x} x}} x = 1 (interp {+ {with {x 2} x} x} x = 1 (+ (interp {with {x 2} x} (interp x x = 1 (+ (interp x (+ 2 1 x = 2 x = 1 (interp x x = 1 17
18 Representing Deferred Substitution Change ; interp : WAE -> num to ; interp : WAE DefrdSub -> num 18
19 Representing Deferred Substitution Change ; interp : WAE -> num to ; interp : WAE DefrdSub -> num (define-type DefrdSub [mtsub] [asub (name symbol? (value number? (rest DefrdSub?] 19
20 Interp with DefrdSub (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (mtsub 20
21 Interp with DefrdSub (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (mtsub (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} (asub 'x 1 (mtsub 21
22 Interp with DefrdSub (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (mtsub (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} (asub 'x 1 (mtsub (interp {+ 100 {+ 99 { {+ y x}}}} (asub 'y 2 (asub 'x 1 (mtsub 22
23 Interp with DefrdSub (interp {with {x 1} {with {y 2} {+ 100 {+ 99 { {+ y x}}}}}} (mtsub (interp {with {y 2} {+ 100 {+ 99 { {+ y x}}}}} (asub 'x 1 (mtsub (interp {+ 100 {+ 99 { {+ y x}}}}... (asub 'y 2 (asub 'x 1 (mtsub (interp y (asub 'y 2 (asub 'x 1 (mtsub 23
24 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr...] [id (name...] 24
25 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr...] [id (name (lookup name ds] 25
26 WAE Interpreter with Deferred Substitutions ; lookup : symbol DefrdSub -> num (define (lookup name ds (type-case DefrdSub ds [mtsub ( (error 'lookup "free variable"] [asub (sub-name num rest-ds (if (symbol=? sub-name name num (lookup name rest-ds] 26
27 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr...] [id (name (lookup name ds] 27
28 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr... (interp named-expr ds...] [id (name (lookup name ds] 28
29 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr... (asub bound-id (interp named-expr ds ds...] [id (name (lookup name ds] 29
30 WAE Interpreter with Deferred Substitutions ; interp : WAE DefrdSub -> num (define (interp a-wae ds (type-case WAE a-wae [num (n n] [add (l r (+ (interp l ds (interp r ds] [sub (l r (- (interp l ds (interp r ds] [with (bound-id named-expr body-expr (interp body-expr (asub bound-id (interp named-expr ds ds] [id (name (lookup name ds] 30
31 {deffun {f x} {+ 1 x}} Function Calls (interp {with {y 2} {f 10}} 31
32 {deffun {f x} {+ 1 x}} Function Calls (interp {with {y 2} {f 10}} (interp {f 10} y = 2 32
33 {deffun {f x} {+ 1 x}} Function Calls (interp {with {y 2} {f 10}} (interp {f 10} (interp {+ 1 x} y =
34 {deffun {f x} {+ 1 x}} Function Calls (interp {with {y 2} {f 10}} (interp {f 10} (interp {+ 1 x} y = 2 x = 10 Interpreting function body starts with only one substitution 34
35 Function Calls What goes wrong if you extend the old substitution? {deffun {f x} {+ y x}} (interp {with {y 2} {f 10}} 35
36 Function Calls What goes wrong if you extend the old substitution? {deffun {f x} {+ y x}} (interp {with {y 2} {f 10}} (interp {f 10} y = 2 36
37 Function Calls What goes wrong if you extend the old substitution? {deffun {f x} {+ y x}} (interp {with {y 2} {f 10}} (interp {f 10} (interp {+ y x} 12 wrong y = 2 x = 10 y = 2 37
38 Function Calls What goes wrong if you extend the old substitution? {deffun {f x} {+ y x}} (interp {with {y 2} {f 10}} (interp {f 10} (interp {+ y x} "free var: y" y = 2 x = 10 38
39 F1WAE Interpreter with Deferred Substitutions ; interp : F1WAE list-of-fundef DefrdSub -> num (define (interp a-f1wae fundefs ds (type-case F1WAE a-f1wae... [app (name arg-expr...] 39
40 F1WAE Interpreter with Deferred Substitutions ; interp : F1WAE list-of-fundef DefrdSub -> num (define (interp a-f1wae fundefs ds (type-case F1WAE a-f1wae... [app (name arg-expr (local [(define a-fundef (lookup-fundef name fundefs] (interp (fundef-body a-fundef fundefs... (interp arg-expr fundefs ds...] 40
41 F1WAE Interpreter with Deferred Substitutions ; interp : F1WAE list-of-fundef DefrdSub -> num (define (interp a-f1wae fundefs ds (type-case F1WAE a-f1wae... [app (name arg-expr (local [(define a-fundef (lookup-fundef name fundefs] (interp (fundef-body a-fundef fundefs (asub (fundef-arg-name a-fundef (interp arg-expr fundefs ds (mtsub] 41
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