**Documentation and Walkthrough**

**Introductory Blog Post**

## Beautiful Mutable Values

**Mutability can be awesome!**

Take back the power of **mutable objects** with all the **safety** and explicit
state of Haskell. Associate and generate "piecewise-mutable" versions for your
composite data types in a composable and automatic way. Think of it like a
"generalized `MVector`

for all ADTs". It also leverages GHC Generics to make
working with piecewise mutability as simple as possible.

Making piecewise updates on your giant composite data types (like artificial
neural networks or game states in your game loop) got you down because they
require re-allocating the entire value? Tired of requiring a full deep copy
every time you make a small change, and want to be able to build mutable
versions of your types automatically in composable ways? This is the package
for you.

Useful for a situation where you have a record with many fields (or many nested
records) that you want to use for efficient mutable in-place algorithms. This
library lets you do efficient "piecewise" mutations (operations that only edit
one field), and also efficient entire-datatype copies/updates, as well, in many
cases.

Check out the documentation home page, haddock reference,
introductory blog post on insights and lessons learned, or read below
for motivation and high-level descriptions.

## Motivation

### Piecewise-Mutable

For a simple motivating example where in-place piecewise mutations might be
better, consider a large vector.

Let's say you only want to edit the first item in a vector, multiple times.
This is extremely inefficient with a pure vector:

```
addFirst :: Vector Double -> Vector Double
addFirst xs = iterate incr xs !! 1000000
where
incr v = v V.// [(0, (v V.! 0) + 1)]
```

That's because `addFirst`

will copy over the entire vector for every step
--- every single item, even if not modified, will be copied one million times.
It is `O(n*l)`

in memory updates --- it is very bad for long vectors or large
matrices.

However, this is extremely efficient with a mutable vector:

```
addFirst :: Vector Double -> Vector Double
addFirst xs = runST $ do
v <- V.thaw xs
replicateM_ 1000000 $ do
MV.modify v 0 (+ 1)
V.freeze v
```

This is because all of the other items in the vector are kept the same and not
copied-over over the course of one million updates. It is `O(n+l)`

in memory
updates. It is very good even for long vectors or large matrices.

(Of course, this situation is somewhat contrived, but it isolates a problem that
many programs face. A more common situation might be that you have two
functions that each modify different items in a vector in sequence, and you
want to run them many times interleaved, or one after the other.)

### Composite Datatype

That all works for `MVector`

, but let's say you have a simple composite data
type that is two vectors:

```
data TwoVec = TV { tv1 :: Vector Double
, tv2 :: Vector Double
}
deriving Generic
```

Is there a nice "piecewise-mutable" version of this? You *could* break up
`TwoVec`

manually into its pieces and treat each piece independently, but that method
isn't composable. If only there was some equivalent of `MVector`

for
`TwoVec`

...and some equivalent of `MV.modify`

.

That's where this library comes in.

```
instance PrimMonad m => Mutable m TwoVec where
type Ref m TwoVec = GRef m TwoVec
```

This gives us `thawRef :: TwoVec -> m (GRef m TwoVec)`

, where `GRef m TwoVec`

is a mutable version of `TwoVec`

, like how `MVector s Double`

is a mutable
version of `Vector Double`

. It stores each field `tv1`

and `tv2`

as a seaprate
`MVector`

in memory that can be modified independently.

Now we can write:

```
addFirst :: TwoVec -> TwoVec
addFirst xs = runST $ do
v <- thawRef xs
replicateM_ 1000000 $ do
withField #tv1 v $ \u ->
MV.modify u 0 (+ 1)
freezeRef v
```

This will in-place edit only the first item in the `tv1`

field one million
times, without ever needing to copy over the contents `tv2`

. Basically, it
gives you a version of `TwoVec`

that you can modify in-place piecewise. You
can compose two functions that each work piecewise on `TwoVec`

:

```
mut1 :: PrimMonad m => Ref m TwoVec -> m ()
mut1 v = do
withField #tv1 v $ \u ->
MV.modify u 0 (+ 1)
MV.modify u 1 (+ 2)
withField #tv2 v $ \u ->
MV.modify u 2 (+ 3)
MV.modify u 3 (+ 4)
mut2 :: PrimMonad m => Ref m TwoVec -> m ()
mut2 v = do
withField #tv1 v $ \u ->
MV.modify u 4 (+ 1)
MV.modify u 5 (+ 2)
withField #tv2 v $ \u ->
MV.modify u 6 (+ 3)
MV.modify u 7 (+ 4)
doAMillion :: TwoVec -> TwoVec
doAMillion xs = runST $ do
v <- thawRef xs
replicateM_ 1000000 $ do
mut1 v
mut2 v
freezeRef v
```

This is a type of composition and interleaving that cannot be achieved by
simply breaking down `TwoVec`

and running functions that work purely on each of
the two vectors individually.

## Mutable Sum Types

There is also support for mutable sum types, as well. Here is the automatic
definition of a *mutable linked list*:

```
data List a = Nil | Cons a (List a)
deriving (Show, Generic)
infixr 5 `Cons`
instance (Mutable m a, PrimMonad m) => Mutable m (List a) where
type Ref m (List a) = GRef m (List a)
```

We can write a function to "pop" out the top value and shift the rest of the
list up:

```
popStack
:: (PrimMonad m, Mutable m a)
=> Ref m (List a)
-> m (Maybe a)
popStack xs = do
c <- projectBranch (constrMB #_Cons) xs
forM c $ \(y, ys) -> do
o <- freezeRef y
moveRef xs ys
pure o
```

```
ghci> runST $ do
r <- thawRef $ 1 `Cons` 2 `Cons` 3 `Cons` Nil
y <- popStack r
(y,) <$> freezeRef r
-- => (Just 1, 2 `Cons` 3 `Cons` Nil)
```

## Show me the numbers

Here are some benchmark cases --- only bars of the same color are comparable,
and shorter bars are better (performance-wise).

There are four situations here, compared and contrasted between pure and
mutable versions

A large ADT with 256 fields, generated by repeated nestings of ```
data V4 a =
V4 !a !a !a !a
```

- Updating only a single part (one field out of 256)
- Updating the entire ADT (all 256 fields)

A composite data type of four `Vector`

s of 500k elements each, so 2 million
elements total.

- Updating only a single part (one item out of 2 million)
- Updating all elements of all four vectors (all 2 million items)

We can see four conclusions:

- For a large ADT, updating a single field (or multiple fields, interleaved)
is going to be faster with
*mutable*. This speedup is between x4 and x5,
suggesting it is a speedup arising from the fact that the top-level type
has four fields.
- For a large ADT, updating the whole ADT (so just replacing the entire
thing, no actual copies) is faster just as a pure value by a large factor
(which is a big testament to GHC).
- For a small ADT with huge vectors, updating a single field is
*much* faster
with *mutable*.
- For a small ADT with huge vectors, updating the entire value (so, the
entire vectors and entire ADT) is actually faster with
*mutable* as well.

Interestingly, the "update entire structure" case (which should be the
worst-case for *mutable* and the best-case for pure values) actually becomes
faster with *mutable* when you get to the region of *many* values... somewhere
between 256 and 2 million, apparently. However, this may just be from the
efficiency of modifying vectors sequentially.