## Concept:

# Functions as data

## Headline

The notion of functions being actual data

## Illustration

The notion of "functions as data" is closely related to the notion of higher-order functions. If one wishes to make a difference, then "functions as data" could be meant to focus on the aspect that functions may appear within data structures. The following illustration focuses on this aspect indeed.

Consider the following routine code for evaluating reverse polish notation:

```
-- Evaluation of RPN via stack
eval :: RPN -> Int
eval = loop empty
where
-- Loop over input
loop :: Stack Int -> RPN -> Int
loop s i =
if null i
then if size s == 1
then top s
else rpnError
else
loop (step (head i) s) (tail i)
```

Now let's assume that we want to parametrize this code in the stack *implementation*. Thus, we would need to pass a data structure to the eval function such that this structure essentially lists all the stack operations needed. The corresponding data structure can be set up as a record type like this:

```
data StackImpl s a =
StackImpl {
getEmpty :: s a,
getPush :: a -> s a -> s a,
getPop :: s a -> s a,
getTop :: s a -> a,
getSize :: s a -> Int
}
```

A record for a specific stack implementation can be constructed like this:

```
import qualified SimpleStackADT as Simple
simpleImpl :: StackImpl Simple.Stack a
simpleImpl = StackImpl {
getEmpty = Simple.empty,
getPush = Simple.push,
getPop = Simple.pop,
getTop = Simple.top,
getSize = Simple.size
}
```

The parameterized version of the RPN evaluator looks like this:

```
-- Evaluation of RPN via stack
eval :: forall s. StackImpl s Int -> RPN -> Int
eval si = loop (getEmpty si)
where
-- Loop over input
loop :: s Int -> RPN -> Int
loop s i =
if null i
then if getSize si s == 1
then getTop si s
else rpnError
else
loop (step (head i) s) (tail i)
```

The parametrization boils down to this type:

```
StackImpl s Int
```

That is, the type variable *s* stands for the type constructor used by a specific stack implementation.

We need to pick a stack implementation when invoking the evaluator:

```
main = do
print $ eval simpleImpl sample
```

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