Practice session #9:
The environment model
Environment Model: Introduction
Environments:
• Frame:
GE
A substitution from variables to values (i.e., every
variable in a frame has a single value).
I
x:3
y:5
• 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.
II
z:6
x:7
III
n:1
y:2
E1
E2
EI<=EG ,>I,III<=2E ,>I,II<=1>
Enclosing-env (E1) = GE
Enclosing-env (E2) = GE
Environment Model: Introduction
Environments:
• The value of variable in an environment:
GE
The value of x in the environment E is its values in the
first frame in which it is define.
I
x:3
y:5
II
z:6
x:7
III
n:1
y:2
E1
E2
EI<=EG ,>I,III<=2E ,>I,II<=1>
Enclosing-env (E1) = GE
Enclosing-env (E2) = GE
Environment Model: Introduction
Procedures:
• A procedure value (closure) is a data structure with:
(1) Procedure parameters.
(2) Procedure body.
(3) The environment in which it has been created.
b1
> (define square (lambda (x) (* x x)))
> (lambda (y) y)
b2
GE
square:
p:(x(
b(x x *(:1
p:(y(
by:2
Environment Model: Introduction
Procedures:
• 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.
b1
> (define square (lambda (x) (* x x)))
> (square 5)
GE
square:
p:(x(
b(x x *(:1
E1
B1
x:5
GE
Environment Model: Definition and Application
GE
sq:
p: (x)
b1: (* x x)
sum-of-squares:
f:
p :(x y(
b2: (+ (sq x)
(sq y))
p: (a)
b3: (sum-of-squares
(+ a 1)
(* a 2))
Environment Model: Definition and Application
GE
sq:
p: (x)
b1: (* x x)
sum-of-squares:
f:
p :(x y(
b2: (+ (sq x)
(sq y))
E1
B3
GE
136
a:5
E2
x:6
y:10
B2
E1
136
p: (a)
b3: (sum-of-squares
(+ a 1)
(* a 2))
E3
x:6
B1
E2
36
E4
x:10
B1
E2
100
Environment Model: Definition and Let
GE
a:8
b:5
c:8
f:
p: (x y)
b1: (+ x y)
E1
x:8
y:8
b1
GE
16
Environment Model: Definition and Let
GE
a:8
b:5
c:8
f:
p: (x y)
b1: (+ x y)
p:
E1
b2
a:8
b:5
c:3
p: (a b c)
b2: (let…)
GE
53
p: (d e)
b3: (f e d)
E2
b3
E1
53
d:13
e:40
E3
b1
x:40
y:13
E2
53
Environment Model: Recursion
GE
fact:
p:(n)
b:(if…)
E1
b
n:3
GE
6
E2
b
n:2
E1
2
E3
b
n:1
E2
1
E4
b
n:0
E3
1
Environment Model: Pair ADT, Lazy implementation
GE
make-pair:
P1:
E1
b1
x:5
y:10
p:(x y)
b1:(lambda(sel)…)
GE
p:(sel)
b2:(sel x y)
Environment Model: Pair ADT, Lazy implementation
GE
make-pair:
P1:
E1
x:5
y:10
p:(a b)
b3:a
E2
sel:
b1
b2
p:(x y)
b1:(lambda(sel)…)
GE
p:(sel)
b2:(sel x y)
GE
5
E3
a:5
b:10
b3
E2
5
> (p1 (lambda (a b) a))
Environment Model: Pair ADT, Lazy implementation
GE
make-pair:
P1:
E1
p:(x y)
b3:(p1(lambda…)
E2
b3
x:1
y:2
b1
x:5
y:10
GE
p:(first second)
b4:first
p:(x y)
b1:(lambda(sel)…)
GE
p:(sel)
b2:(sel x y)
E3
b1
E2
sel:
E4
b4
first:5
second:10
> (let ((x 1)
(y 2))
b3 (p1 (lambda (first second)
first)))
b4
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).
Environment Model: Dynamic Scoping - Example
GE
make-pair:
p1:
E1
p:(x y)
b1:(lambda(sel)…)
b1
p:(sel)
b2:(sel x y)
x:5
y:10
1
1
E2
E3
b3
x:1
y:2
p:(x y)
b3:(p1(lambda…)
b2
sel:
p:(first second)
b4:first
1
E4
b4
first:1
second:2
> (let ((x 1)
(y 2))
b3 (p1 (lambda (first second)
first)))
b4
Environment Model: CPS
GE
fact:$
p:(n c)
b1:(if…)
p(fact-3)
b3:(fact-3)
E1
b1
n:3
c:
E2
GE
6
b1
n:2
c:
p:(fact-n-1)
b2:(c…)
b2
fact-n-1:2
b3
fact-n-1:6
E3
E5
6
b1
n:1
c:
E2
6
E4
p:(fact-n-1)
b2:(c…)
E5
E6
E1
6
b2
fact-n-1:1
E4
6
E3
6