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Sixian Li

Binding & Closure

Functional Programming

Binding & Closure

Binding created a (name, value) pair. Here, values can also be functions.

Declarations create bindings.

  • let: declaration
  • in: scope
  • NOTE: Do not confuse this with assignment.

3 components of closure

  1. parameters
  2. body
  3. pointer to the environment when it is defined (static binding, lexical scoping)

NOTE: Environment can only be added, so there are layers. The pointer is pointing to the correct environment. A layer will be swept by garbage collection when there is no pointer points to it.

Side note: static binding and dynamic binding in Java:

  • Static binding

    …So whenever a binding of static, private and final methods happen, type of the class is determined by the compiler at compile time (not determined by type of the object) and the binding happens then and there.

  • Dynamic binding

    The type of the object is determined at the runtime(by the new someconstructor() keyword).

  • Overload and Override

    The binding of overloaded methods is static and the binding of overridden methods is dynamic.


Binding vs. Assignment

In an imperative language, like Java, when we assign a value to a variable, we make an analogy between our variable and box. A variable itself is a container, and it holds some value. However, when we bind a name to a variable, we are attaching a label on that value.

Consider the code snippet below.

y = x + 1 is not closed on the name x. It is closed on the value 3 which was bound to x. So y will never change with x.

A really good explanation from stack overflow:

You can think of binding as a label on a suitcase, and assignment as a suitcase.

Now, let’s look at this example:

Layers

x | 99

f | (3 components) parameter: x | body: x | pointer to x = 3

x | 3

When we evaluate f x:

  1. f is a closure, should be a function
  2. Now its parameter is x! Let’s look for x
  3. Ok, x is 99. Let’s evaluate. At this point, the layer x | 99 will go along with the pointer to the layer x | 3. IMPORTANT: 3 is masked because 99 is on the top layer.

When you evaluate this, x is not built-in. It is stored in a structure called environment. So the compiler will look for what is x.

x | 3 ---> base environment

x + 2 to be evaluated. x is found in the top layer.

Layers

x | 2

y | 4

x | 3

|||BASE ENV|||

NOTE: Never put bindings in the value part. It looks for x in the environment, and put the value of x in x+1.

Here, x-3 is masked, but it is still there. During the evaluation, it picks the x in the top layer.