Closures

Today: Scopes

Where are we now?

• IMP
• Heaps
• Types
• Closures
• Scopes (Stacks)
• Long-lived scopes (Linked Stacks)
• Functions

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What is a Closure?

f = lambda x, y : x + y

var f = function(x, y) {

return x + y;

}

var f = (x, y) => {

return x + y;

}

auto f = [](int x, int y) {

return x + y;

};

BinaryOperator<int> f = (int x, int y) -> {

return x + y;

};

Python

C++

Java

Javascript

What is a Closure?

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• A function and a scope (in which to run the function)
• First-class: a closure is a value
• Higher-Order: functions may take closures as arguments

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var f = fun(x) {

print(x);

};

f(1)

var x = 1;

var f = fun() {

print(x);

};

f();

Output: 1

var x = 1;

var f = fun() {

x = 2;

};

print(x)

var g = fun(h) {

h();

}

print(x)

g(f);

print(x);

Output: 1

Outputs: �1�1�2

Why?

Callbacks

Anonymous helper functions

What is a Closure?

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​

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​

• A function and a scope (in which to run the function)
• First-class: a closure is a value
• Higher-Order: functions may take closures as arguments

​

var f = fun(x) {

print(x);

};

f(1)

var x = 1;

var f = fun() {

print(x);

};

f();

Output: 1

var x = 1;

var f = fun() {

x = 2;

};

print(x)

var g = fun(h) {

h();

}

print(x)

g(f);

print(x);

Output: 1

Outputs: �1�1�2

Scoping

• Which variables do the references to x and y refer to?

class Test

{

void foo()

{

int x = 1;

​

int y = x;

}

}

...

y = x;

...

class Test

{

void foo(int x)

{

int y = x;

}

}

class Test

{

void foo(int x, int y)

{

{

int y = x;

}

print(y);

}

}

Scoping

• Which variables do the references to x and y refer to?

class Test

{

static int y = 1;

​

void foo(int x)

{

y = x;

}

}

class Test

{

int y = 1;

​

void foo(int x)

{

y = x;

}

}

Block Scopes for IMP (MITScript is different)

• Scope: a defined context that holds a set of variables
• Block Scope: introduce a new local frame (i.e., scope) via braces
• var declares a new variable in frame

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• Enables user-controllable scoping
• Is also a basic building block for other program constructs (next slide)

var x = 1;

{

var x = 2;

print(x);

}

print(x)

var x = 1;

{

x = 2;

print(x);

}

print(x)

output:

2

1

output:

2

2

Scoped For Loop Translation

{

int i = 0;

while (i < n) {

...

++i;

}

}

​

{

i = 0;

while (i < n) {

...

++i;

}

}

for (int i = 0; i < n; ++i) {

...

}

​

for (i = 0; i < n; ++i) {

...

}

Add Block Scopes: Grammar

Add Block Scopes: Grammar

Block Scopes: Semantic Meaning

• Introduce a new local frame
• var introduces new variable in frame

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• Multiple representation options: multiple bindings for each variable or multiple frames. Trick, determine which x to update
• Solution: keep stack of frames.

var x = 1;

{

var x = 2;

print(x);

}

print(x)

var x = 1;

{

x = 2;

print(x);

}

print(x)

Add x = 1 to scope

Modify x in scope

Add x = 1 to scope

Add x = 2 to scope

Frames, Heaps, and Stacks

Evaluation Relations (old)

• Define the semantics of each term in our language (E, B, and S) with an evaluation relation:

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• Meaning: given a frame and heap, the term evaluates to a result

Evaluation Relations (with heaps and stacks)

• Define the semantics of each term in our language (E, B, and S) with an evaluation relation:

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• Meaning: given a stack, and heap, the term evaluates to a result

Statements: Inference Rules

Expressions: Inference Rules

Integer

Constant

Variable

Reference

Unary

Minus

Lookup

Expressions: Inference Rules

Integer

Constant

Variable

Reference

Unary

Minus

Statements: Inference Rules

{

var x = 1;

var x = 2;

}

Statements: Inference Rules

Update

Managing Scopes (Example)

1: var f = 0;

2: {

3: var x = 1;

4: f = 5;

5: }