The environment model Frame A substitution from variables to values ie every variable in a frame has a single value Environment A finite sequence of frames where the last frame is ID: 274403
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Slide1
Practice session #9:
The environment modelSlide2
Frame: A substitution from variables to values (i.e., every variable in a frame has a single value).
Environment:
A finite sequence of frames, where the last frame is the global environment.The global environment: A single-frame environment, the only environment that statically exists.Enclosing environment: For an environment E, the enclosing environment is E, excluding its first frame.
GE
I
x:3y:5
IIz:6x:7
IIIn:1y:2
E1
E2
E
1
=<II,I>, E2=<III,I>, GE=<I>
Enclosing-env (E1) = GEEnclosing-env (E2) = GE
Environments:
Environment Model:
IntroductionSlide3
GE
I
x:3
y:5
II
z:6x:7
IIIn:1y:2
E1
E2
E
1=<II,I>, E2=<III,I>, GE=<I>
Enclosing-env
(E1) = GEEnclosing-env
(E2) = GEThe value of variable in an environment:The value of x in the environment E is its values in the first frame in which it is define.Environments:
Environment Model:
IntroductionSlide4
A procedure value (closure) is a data structure with:(1)
Procedure parameters.
(2) Procedure body.(3) The environment in which it has been created.Procedures:> (define square (lambda (x
) (*
x x)))
GEsquare:
p:(x(b
1:(* x x(
p:(y(
b
2:y
> (lambda (y) y)
b1b2
Environment Model:
IntroductionSlide5
Procedure application:(1)
Create new frame, mapping the procedure params to application values.(2) The new frame extends the environment associated with the procedure.(3) Evaluate the body of the procedure in the new environment.Procedures:
GE
square:
p:(x(
b1:(* x x(
GE
E1
B
1
x:5
> (define square (lambda (x) (* x x)))
> (square 5)b1
Environment Model:
IntroductionSlide6
GE
sq
:
sum-of-squares:
f:
p: (x)
b
1: (* x x)
p:
(
x y(b2: (+ (sq x) (sq y))
p: (a)
b3: (sum-of-squares (+ a 1) (* a 2))
Environment Model:
Definition and ApplicationSlide7
B
3
E
1
a:5
GE136
B2
E2x:6y:10
B
1
E
3
x:6
B1
x:10
E
2
100E1136GE
sq
:
sum-of-squares:
f:
p: (x)
b
1
: (* x x)
p:
(
x y(
b
2
: (+ (sq x)
(sq y))
p: (a)
b
3
: (sum-of-squares
(+ a 1)
(* a 2))
Environment Model:
Definition and Application
E
2
36
E
4Slide8
Environment Model:
Definition and Let
GE
a:8
b:5
c:8
f:
b
1
E
1
x:8
y:8
GE
16
p: (x y)
b
1: (+ x y)Slide9
GE
53
b
2
E
1a:8b:5
c:3
p: (a b c)b2: (let…)E1
53
b
3
E2
d:13e:40
E253
b1
E
3
x:40y:13f:
p: (x y)b1: (+ x y)
p:
p: (d e)
b
3
: (f e d)
Environment Model:
Definition and Let
GE
a:8
b:5
c:8Slide10
GE
p:(n)
b:(if…)
fact:
b
E
1
n:3GE
6
b
E
2
n:2
E12
b
E
3
n:1E21
b
E
4
n:0
E
3
1
Environment Model:
RecursionSlide11
GE
p:(x y)
b
1
:(lambda(
sel)…)
make-pair:P1:
p:(sel)b2:(sel x y)b
1
E
1
x:5
y:10GE
Environment Model:
Pair
ADT, Lazy implementationSlide12
GE
b
2
E
2
sel:
b3
E3a:5
b:10
E
2
5
GE
p:(x y)b1:(lambda(
sel)…)
make-pair:
P1:
p:(sel)b2:(sel x y)b1E1
x:5
y:10
GE
p:(a b)
b
3
:a
> (p1 (lambda (a b) a))
5
Environment Model:
Pair
ADT, Lazy implementationSlide13
GE
b
2
E
2
sel:
b3
E3a:5
b:10
E
2
5
GE
p:(x y)b1:(lambda(
sel)…)
make-pair:
P1:
p:(sel)b2:(sel x y)b1E1
x:5
y:10
GE
p:(a b)
b
3
:a
> (p1 (lambda (a b) a))
5
Environment Model:
Pair
ADT, Lazy implementationSlide14
p:(x y)
b
3:(p1(lambda…)
b
3
E2x:1
y:2GE
p:(first second)b4:first
b
1
E
3
E
2sel:
b
4
E
4first:5second:10GE
p:(x y)
b
1
:(lambda(
sel
)…)
make-pair:
P1:
p:(
sel
)
b
2
:(
sel
x y)
b
1
E
1
x:5
y:10
GE
> (let ((x 1)
(y 2))
(p1 (lambda (first second)
first)))
b4
b3
Environment Model:
Pair
ADT, Lazy implementationSlide15
Environment Model:
Lexical (static)
vs
Dynamic
Scoping
Lexical Scoping:
A closure “carries” the environment in which it has been created.
In application of a closure, its carried environment is extended.Dynamic Scoping:A closure does not correspond to any environment.In application of a closure, the calling environment is extended.Simpler implementation (no need to “store” environments).Slide16
GE
p:(x y)
b
1
:(lambda(
sel)…)make-pair:p1:
p:(sel)b2:(sel x y)
b1E1
x:5
y:10
p:(x y)
b
3:(p1(lambda…)
b3E2x:1y:2
p:(first second)
b
4
:firstb2E3sel:
b
4
E
4
first:1
second:2
1
1
1
Environment Model:
Dynamic Scoping - Example
> (let ((x 1)
(y 2))
(p1 (lambda (first second)
first)))
b4
b3Slide17
p:(n c)
b
1:(if…)GE
fact$:
b
1
E1
n:3
GE6
p(fact-3)
b3:(fact-3)
c:
p:(fact-n-1)
b2:(c…)b1
E
2
n:2
E16c:p:(fact-n-1)b
2:(c…)
b
1
E
3
n:1
E
2
6
c:
b
2
E
4
fact-n-1:1
E
3
6
b
2
E
5
fact-n-1:2
E
4
6
b
3
E
6
fact-n-1:6
E
5
6
Environment Model:
CPS