All about binding

1
All about binding
Memory Locations for Variables (ch 12)

• Variables are bound (dynamically) to values
• values must be stored somewhere in the memory.

2
Imperative ??Functional

• Imperative languages
• a 0
• Store a zero in as memory location
• Functional languages
• val a 0
• Bind a to the value zero

• a 0
• a 1
• val a 0
• val a 1

Big deal?
Yes!
3
Function Activations

• Activation of a function
• The lifetime of one execution of the function,
  from call to corresponding return.

If each activation has its own binding for
variables, the variables are called
activation-specific variable (dynamic or
automatic)
most modern languages
4
Block Activations

• A variable might be specific to a particular
  block within a function

fun fact n if (n0) then 1 else let val b
fact (n-1) in nb end
Do we have it in C/JAVA?
5
Other Lifetimes For Variables

• We usually have a way to declare a variable that
  is bound to an independent memory (independent
  from any functions)
• static allocation, the loader does the job of
  allocation

int count 0 int nextcount() count count
1 return count
6
Scope ?? Activation
George Washington
America ?? A.D. 1732-1799
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(lifetime)
Scope ?? Activation
George Washington America ?? A.D. 1732-1799

• In most modern languages, variables with local
  scope have activation-specific lifetimes, by
  default
• some exception

int nextcount() static int count 0 count
count 1 return count
not activation-specific
8
there are other lifetimes for variables
In addition to activation-specific variables

• In OOP, some variables lifetimes are associated
  with object lifetimes
• Some variables may last across multiple
  executions of the program

9
Activation Records

• Each function being executed has an activation
  record

• An activation record contains information about
• Activation-specific variables
• Return address (or pointer to the current
  instructions)
• Link to callers activation record

10
Block Activation Records

• When a block is entered, space must be found for
  the local variables of that block
• Possibile implementations
• Preallocate in the containing functions
  activation record
• Extend the functions activation record when the
  block is entered (and revert when exited)
• Allocate separate block activation records

11
Static Allocation

• The simplest approach allocate one activation
  record for every function, statically
• Older dialects of Fortran and Cobol used this
  system
• Simple and fast, but....(what!)

12
Fortran Example

• Static activation record

FUNCTION AVG (ARR, N) DIMENSION ARR(N)
SUM 0.0 DO 100 I 1, N SUM
SUM ARR(I)100 CONTINUE AVG SUM /
FLOAT(N) RETURN END
13
Drawback

• Each function has one activation record, thus
  There can be only one activation alive at a time

• Modern languages (including modern dialects Cobol
  and Fortran) do not obey this restriction for
• Recursion
• Multithreading

14
Stacks Of Activation Records

• To support recursion, we need to allocate a new
  activation record for each activation
• Dynamic allocation
• allocate ?? deallocate
• A stack of activation records stack frames
• push ?? pop

15
Current Activation Record the one for the
function that is running

• Static location of activation record was
  determined before runtime
• Dynamic location of the current activation
  record is not known until runtime
• A function must know how to find the address of
  its current activation record. A machine register
  is reserved to hold this

16
C Example
The evaluation of fact(3) before the recursive
call
int fact(int n) int result if (nlt2) result
1 else result n fact(n-1) return
result
.... cout ltlt ... ltlt fact(3) ltlt .... .....
somewhere
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int fact(int n) int result if (nlt2) result
1 else result n fact(n-1) return
result
After calling fact(2)
before calling fact(1)
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int fact(int n) int result if (nlt2) result
1 else result n fact(n-1) return
result
Before fact(1)returns
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The second activation is about to return.
int fact(int n) int result if (nlt2) result
1 else result n fact(n-1) return
result
2
1
2
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The first activation is about to return with the
result fact(3) 6.
int fact(int n) int result if (nlt2) result
1 else result n fact(n-1) return
result
21
ML Example
fun halve nil (nil, nil) halve a (a,
nil) halve (abcs) let val
(x, y) halve cs in (ax, by)
end
halve 1,2,3,4
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halve 3,4
This shows the contents of memory just before the
third activation.
fun halve nil (nil, nil) halve a (a,
nil) halve (abcs) let val
(x, y) halve cs in (ax, by)
end
23
halve
This shows the contents of memory just before the
third activation returns.
fun halve nil (nil, nil) halve a (a,
nil) halve (abcs) let val
(x, y) halve cs in (ax, by)
end
24
The second activation is about to return.
fun halve nil (nil, nil) halve a (a,
nil) halve (abcs) let val
(x, y) halve cs in (ax, by)
end
25
The first activation is about to return with the
result halve 1,2,3,4 (1,3,2,4)
fun halve nil (nil, nil) halve a (a,
nil) halve (abcs) let val
(x, y) halve cs in (ax, by)
end
26
Nesting Functions

• Function definitions can be nested inside other
  function definitions
• Inner functions can refer to local variables of
  the outer functions (under the usual block
  scoping rule)
• ML, Ada, Pascal provide such feature
• C, Java dont. (for good reasons)

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The tricky part is the previous activation
record may not help
f() int i 3

• Called by another inner function

g() i
Called by a recursive call.
h() g()
f() int i 3 g()
g() g() i
h()
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Static Scoping and Nesting Link
static scoping
f() int i 3
h() int i 2 f()
g() i
dynamic scoping
g()

• An inner function needs to be able to find the
  address of the most recent activation of the
  outer function (not just the caller function)
• We can keep a nesting link in the activation
  record

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Example
fun quicksort nil nil quicksort
(pivotrest) let fun split(nil)
(nil,nil) split(xxs)
let val (below, above)
split(xs) in if xlt
pivot then (xbelow, above)
else (below, xabove) end
val (below, above) split(rest) in
quicksort below _at_ pivot _at_ quicksort above
end
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time
Current Activation Record
QuickSort()
Split()
Split()
Split()
Return Address
Return Address
Return Address
Return Address
Previous Activation Record
Previous Activation Record
Previous Activation Record
Previous Activation Record
QuickSort local variable pivote, rest,
QuickSort local variable x, xs,
QuickSort local variable x, xs,
QuickSort local variable x, xs,
Cant find pivot here
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time
Current Activation Record
QuickSort()
Split()
Split()
Split()
Return Address
Return Address
Return Address
Return Address
Previous Activation Record
Previous Activation Record
Previous Activation Record
Previous Activation Record
QuickSort local variable pivote, rest,
QuickSort local variable x, xs,
QuickSort local variable x, xs,
QuickSort local variable x, xs,
Nesting link
Nesting link
Nesting link
Nesting link null
3
3
2
1
The rules to setup the nesting links 1, 2, 3
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How to Set Nesting Links

• For one level of nesting
• 1. Calling outer function (non-nesting
  function, e.g. main calls quicksort)
• ? set to null
• 2. Calling from outer to inner (e.g. quicksort
  calls split)
• ? set nesting link same as callers
  activation record
• 3. Calling from inner to inner (e.g. split
  calls split)
• ? set nesting link same as callers nesting
  link

33
Multiple Levels Of Nesting
f() int fi
g() int gi
h() int hi hi, gi, fi

• References n nesting levels away chain back
  through n nesting links

34

• Common methods for referring to non-local
  variables in outer functions
• Nesting links in activation records
• Displays nesting links not in the activation
  records, but collected in a single static array
• Lambda lifting passing all needed variables as
  parameters (i.e., as hidden parameters)

35
Functions As Parameters

• What really gets passed?
• Source code, compiled code, pointer to code, or
  implementation in some other form

macro expanding
OOP objects
Cs way
functional languages
36
Example
fun addXToAll (x,theList) let fun addX y
y x in map addX theList end
5, 2,3,4 ? 7,8,9
where to?
Nesting link
maps activation record?
In the previous example quicksort ?(call) split
Nesting link
addXToAll ? map, map ? addX, addX ? (refers) x
(in addXToAlls activation record)
37

• When map ? addX, what nesting link will addX be
  given?
• Not maps activation record addX is not nested
  inside map
• Not maps nesting link map is not nested inside
  anything
• Therefore, the parameter addX passed to map must
  include the nesting link to use when addX is
  called,

i.e., the nesting link of addx should be prepared
when addToAll tries to pass it as an argument to
map
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Example
fun addXToAll (x,theList) let fun addX y
y x in map addX theList end
Current Activation Record
Right before the call to map. The variable
addX is bound to a function-value including code
and nesting link.
ygtyx Nesting link
39
Not Just For Parameters

• Functional languages allow many more kinds of
  operations on function-values
• passed as parameters,
• returned from functions,
• constructed by expressions, etc.
• Function-values include both code to call, and
  nesting link to use when calling it

40
One More Complication

• What happens if a function created is to be
  returned as a value?

fun funToAddX x let fun addX y y
x in addX end
fun test let val f funToAddX 3 in
f 5 end
return a function that add x
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Current Activation Record
fun test let val f funToAddX 3 in
f 5 end
fun funToAddX x let fun addX y y
x in addX end
ygtyx Nesting link
Before funToAddX returns addx.
42
Current Activation Record
fun test let val f funToAddX 3 in
f 5 end
fun funToAddX x let fun addX y y
x in addX end
ygtyx Nesting link
After funToAddX returns, f is the bound to the
new function-value.
Any Problem ?
43
Problem --

• This will fail if the language system deallocated
  that activation record when the function returned

Solution
keep all activation records (MLs way)
New problem
waste too much memory
Solution
Garbage collection
New problem ??