# Lambda Abstraction

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Summary: *Lambda abstractions are always leaky, but some are leakier
than others. Clojure programmers recommend keeping most of your
functions pure and containing the leaks as much as possible.*

Lambda abstraction refers to something we do all of the time. Let's say I have some code:

```
(+ 1 2)
```

I'm adding the number 2 to a number, in this case, 1. I could abstract
that into a *lambda*:

```
(defn add2 [x] (+ x 2))
```

Now it's a function, which I can apply to 1. `(add2 1)`

. I can apply it
to any number I want. The actual thing I am adding 2 to is abstracted
away and replaced by the variable `x`

. **Lambda abstractions are just
functions.**

Functional programming is at its best when lambda abstractions are
referentially transparent. That means that given the same arguments, a
function will always return the same value. Being referentially
transparent makes a **software function more like a mathematical
function**. And that lets you reason about your code.

But there's a very real difference between software functions and
mathematical functions: **mathematical functions take no time or energy
to "compute"**. They are defined abstractly, with no notion of
computation. In contrast, software functions always take some time to
compute. Sometimes the clearest way to write a function takes enough
time that the illusion of mathematical functions is shattered. **The
abstraction is leaky.**

So software functions are already a leaky abstraction, even if they are
referentially transparent. Clojure (like most programming languages)
opens the leak even further: **you can put stuff that's not
referentially transparent right in your function**. For instance, you
can write a "function" that reads from the disk or makes a web request.
Making the same request twice can obviously return different values.

What most people programming Clojure recommend is to program *mostly*
with pure functions (that means
referentially transparent). You still have to deal with time, but that's
way easier than dealing with the chaos of the world outside. That leaves
a small bit of your code to deal with mutation, input/output, and the
disk. It's still a lambda abstraction (function) but **it's just
leakier**. Clojure simply leaves the decision up to you where to draw
the line. Clojure tries to make pure functions easy, even when not
everything fits into pure functions.

The takeaway of functional programming is the same recommendation:
**write most of your code as referentially transparent functions**.
The degree to which a language helps you do that is how "functional" the
language is.

If you'd like to learn more about Clojure and pure functions, check out LispCast Introduction to Clojure. It's 2.5 hours of high quality video. You probably haven't seen anything like this! There's animations, exercises, characters, and screencasts. It takes you from no knowledge to a deep experience, all while having fun!