# tuple-append

## Usage

The package defines five typeclasses: `TupleAddL`

, `TupleAddR`

, `TupleAppend`

, `SequenceTuple`

, and `FoldTuple`

. These are defined in the `Data.Tuple.Append.Class`

module and re-exported in the `Data.Tuple.Append`

module. These typeclasses define the functions `(<++) ∷ x → (v₁, v₂, …, vₙ) → (x, v₁, v₂, …, vₙ)`

, `(++>) ∷ (v₁, v₂, …, vₙ) → x → (v₁, v₂, …, vₙ, x)`

, `(+++) ∷ (u₁, u₂, …, uₘ) → (v₁, v₂, …, vₙ) → (u₁, u₂, …, uₘ, v₁, v₂, …, vₙ)`

, `sequenceTupleA ∷ Applicative f ⇒ (f v₁, f v₂, …, f vₙ) → f (v₁, v₂, …, vₙ)`

, `sequenceTupleA_ ∷ Applicative f ⇒ (f v₁, f v₂, …, f vₙ) → f ()`

, `foldlTuple ∷ (a → v → a) → a -> (v₁, v₂, …, vₙ) → a`

, `foldrTuple ∷ (v → a → a) → a -> (v₁, v₂, …, vₙ) → a`

, and `foldMapTuple ∷ Monoid m ⇒ (a → m) → (v₁, v₂, …, vₙ) → m`

respectively. Functions that thus add an element to the left side or the right side of tuple; append two tuples together into a new tuple; sequence or fold a tuple. The `Data.Tuple.Append`

module creates instances for these typeclasses.

Usually appending, sequencing and folding tuples is not a good idea. So if you use this package, it is definitely something is not done very elegantly in your own software. There might however be some rare cases where these operations are indeed useful.

## Standard instances

For `TupleAddL`

and `TupleAddR`

the `Data.Tuple.Append`

module defines instances for `(<++) ∷ x → (v₁, v₂, …, vₙ) → (x, v₁, v₂, …, vₙ)`

and `(++>) ∷ (v₁, v₂, …, vₙ) → x → (v₁, v₂, …, vₙ, x)`

for *0 ≤ n ≤ 61*. These will construct *n+1*-tuples so it can construct at most a 62-tuple, which is the maximum number of elements that can be stored in a tuple in GHC. This thus means that there are 62 instances for the `TupleAddL`

and `TupleAddR`

typeclasses for tuples.

For the `(+++) ∷ (u₁, u₂, …, uₘ) → (v₁, v₂, …, vₙ) → (u₁, u₂, …, uₘ, v₁, v₂, …, vₙ)`

function, the module defines instances for *0 ≤ m, n ≤ 19* with *0 ≤ m+n ≤ 19*, it thus can append all possible tuples up to a 19-tuple. This is the maximum size that is defined for the `Control.Lens.Tuple`

module in the `lens`

package on tuple items. We think this is reasonable: for the constructed *k*-tuple, there are *k+1* instances, which means that 210 instances are defined in total.

The `SequenceTuple`

has instances for `sequenceTupleA ∷ Applicative f ⇒ (f v₁, f v₂, …, f vₙ) → f (v₁, v₂, …, vₙ)`

and `sequenceTupleA_ ∷ Applicative f ⇒ (f v₁, f v₂, …, f vₙ) → f ()`

for *1 le; n ≤ 62*. This can thus sequence any tuple that is allowed in GHC, since a 62-tuple is the largest tuple allowed.

The `FoldTuple`

has instances for `foldlTuple ∷ (a → v → a) → a -> (v₁, v₂, …, vₙ) → a`

, `foldrTuple ∷ (v → a → a) → a -> (v₁, v₂, …, vₙ) → a`

, and `foldMapTuple ∷ Monoid m ⇒ (a → m) → (v₁, v₂, …, vₙ) → m`

for *1≤n≤62*. We thus can fold any non-empty tuple that is allowed in GHC, since a 62-tuple is the largest tuple allowed. Folding an empty tuple is not possible since then there the functional dependencies do not hold.

Besides tuples `(<++) ∷ x → [x] → [x]`

, `(++>) ∷ [x] → x → [x]`

, `(+++) ∷ [u] → [u] → [u]`

, `sequenceTupleA ∷ Applicative f ⇒ [f u] → f [u]`

, `sequenceTupleA_ ∷ Applicative f ⇒ [f u] → f ()`

, `foldlTuple ∷ (a → v → a) → a -> (v₁, v₂, …, vₙ) → a`

, `foldrTuple ∷ (v → a → a) → a -> (v₁, v₂, …, vₙ) → a`

, and `foldMapTuple ∷ Monoid m ⇒ (a → m) → (v₁, v₂, …, vₙ) → m`

are also defined on lists and `NonEmpty`

objects, to make the functions more reusable. One can also define these on other collections like `Text`

, `Vector`

s, etc. For that, one can use the `tuple-append-instances`

package.

For builds where one makes use of `ghc-prim`

prior to version `ghc-prim-0.7.0`

, the `Solo`

data type (a tuple with one element) is not available. For these builds, it will thus not make instances with singleton tuples, and thus there are only 61 instances for `TupleAddL`

and `TupleAddR`

and 173 instances for `TupleAppend`

that work with tuples. Whether the "*unit type*" `()`

is a tuple with no elements, and the `Solo`

type is a tuple with exactly one element is debatable, but regardless, this package implemented instances for these.

## Generating (extra) functions and instances

One can create extra functions and typeclass instances to prepend and append tuples. While we think that the number of instances for *boxed* tuples is likely sufficient for all practical use cases, this might be more useful when one aims to construct such functions for example for *unboxed* tuples, or for boxed tuples for specific types to make it more clear what the function is doing. Such unboxed types can not be specified through a type *parameter*. Since there are several unboxed types, exhaustively creating functions for all such types would result in millions of functions, which would likely exhaust the memory of the compiler.

One can however make use of these functions to generate such functions such that it is unlikely to make mistakes, for example by swapping two variables that have the same type. For these one can make use of the `makeBoxedTupleAppendFun`

, `makeUnboxedTupleAppendFun`

, `makeBoxedAddLFun`

, `makeUnboxedAddLFun`

, `makeBoxedAddRFun`

, and `makeUnboxedAddRFun`

functions. These functions can be used when working with *template* Haskell to generate Haskell code. See for example the following example:

```
{-# LANGUAGE MagicHash, TemplateHaskell, UnboxedTuples #-}
{-# OPTIONS_GHC -fobject-code #-}
module Data.Tuple.Append.Example where
import Data.Tuple.Append.TemplateHaskell(makeBoxedTupleAppendFun, makeUnboxedTupleAppendFun)
import GHC.Exts(Float#, Int#)
import Language.Haskell.TH.Syntax(Type(ConT, VarT), mkName)
makeBoxedTupleAppendFun (mkName "append_if_f") [ ConT ''Int, ConT ''Float ] [ ConT ''Float ]
makeUnboxedTupleAppendFun (mkName "uappend_ix_f") [ ConT ''Int#, VarT (mkName "a")] [ConT ''Float# ]
```

This will create a function named `append_if_f ∷ (Int, Float) → Solo Float → (Int, Float, Float)`

that appends a 2-tuple with an `Int`

and a `Float`

to a singleton tuple with a `Float`

to a 3-tuple with an `Int`

, a `Float`

and another `Float`

. Furthermore it creates a function named `uappend_ix_f ∷ (# Int#, a #) → (# Float# #) → (# Int#, a, Float# #)`

that will append an unboxed tuple `(# Int#, a #)`

with an `Int#`

a type variable `a`

and an unboxed tuple `(# Float# #)`

with a `Float#`

to an unboxed tuple `(# Int#, a, Float# #)`

. This example can be found in the hidden `Data.Tuple.Append.Example`

module.

## Laziness

The prepend and append functions are implemented with *irrefutable* patterns for the tuples. So an append function is implemented as:

```
~(u₁, u₂, …, uₘ) +++ ~(v₁, v₂, …, vₙ) = (u₁, u₂, …, uₘ, v₁, v₂, …, vₙ)
```

These tildes will prevent evaluating the tuples to *weak head normal-form (WHNF)* if this is not necessary. For example if one would use:

```
ghci> let (_, _, x, _) = undefined +++ (4, 2) in x
4
```

then this will return `4`

, whereas if we would not use an irrefutable pattern, then this would error, since it will first try to evaluete the first and second parameters to WHNF, and if one of these fails, will thus raise an error.

This is *not* the case for *unboxed* tuples, since then the parameters will not be the result of an evaluation, but are already passed without the tuple.

## Package structure

The package contains three modules:

`Data.Tuple.Append`

that re-exports the `TupleAddL`

, `TupleAddR`

and `TupleAppend`

typeclasses together with instances a large number of tuple types;
`Data.Tuple.Append.Class`

that defines the `TupleAddL`

, `TupleAddR`

and `TupleAppend`

typeclasses together with instances for lists; and
`Data.Tuple.Append.TemplateHaskell`

that creates template Haskell expressions for function defintions and typeclass instances for boxed and unboxed tuples.

`tuple-append`

is *safe* Haskell

The package contains a module `Data.Tuple.Append.TemplateHaskell`

that defines routines to construct the instances for a large number of tuples. These are then used with *quasiquotation* to define instances in a safe module. All modules in the package are safe, except the `Data.Tuple.Append.Example`

module, which is not exported.

## Contribute

You can contribute by making a pull request on the *GitHub repository*.

You can contact the package maintainer by sending a mail to `hapytexeu+gh@gmail.com`

.