Editing All About Monads (section)

=== Transformer versions of standard monads ===

The standard monads of the monad template library all have transformer versions which are defined consistently with their non-transformer versions. However, it is not the case the all monad transformers apply the same transformation. We have seen that the <code>ContT</code> transformer turns continuations of the form <code>(a->r)->r</code> into continuations of the form <code>(a->m r)->m r</code>. The <code>StateT</code> transformer is different. It turns state transformer functions of the form <code>s->(a,s)</code> into state transformer functions of the form <code>s->m (a,s)</code>. In general, there is no magic formula to create a transformer version of a monad — the form of each transformer depends on what makes sense in the context of its non-transformer type.

<table>
<tr class="header">
<th align="left">Standard Monad</th>
<th align="left">Transformer Version</th>
<th align="left">Original Type</th>
<th align="left">Combined Type</th>
</tr>
<tr class="odd">
<td align="left">[[errormonad.html|Error]]</td>
<td align="left">[https://www.haskell.org/ghc/docs/latest/html/base/Control.Monad.Error.html#ErrorT ErrorT]</td>
<td align="left"><code>Either e a</code></td>
<td align="left"><code>m (Either e a)</code></td>
</tr>
<tr class="even">
<td align="left">[[statemonad.html|State]]</td>
<td align="left">[https://www.haskell.org/ghc/docs/latest/html/base/Control.Monad.State.html#StateT StateT]</td>
<td align="left"><code>s -> (a,s)</code></td>
<td align="left"><code>s -> m (a,s)</code></td>
</tr>
<tr class="odd">
<td align="left">[[readermonad.html|Reader]]</td>
<td align="left">[https://www.stackage.org/haddock/lts-16.22/mtl-2.2.2/Control-Monad-Reader.html#g:3 ReaderT]</td>
<td align="left"><code>r -> a</code></td>
<td align="left"><code>r -> m a</code></td>
</tr>
<tr class="even">
<td align="left">[[writermonad.html|Writer]]</td>
<td align="left">[https://www.haskell.org/ghc/docs/latest/html/base/Control.Monad.Writer.html#WriterT WriterT]</td>
<td align="left"><code>(a,w)</code></td>
<td align="left"><code>m (a,w)</code></td>
</tr>
<tr class="odd">
<td align="left">[[contmonad.html|Cont]]</td>
<td align="left">[https://www.haskell.org/ghc/docs/latest/html/base/Control.Monad.Cont.html#ContT ContT]</td>
<td align="left"><code>(a -> r) -> r</code></td>
<td align="left"><code>(a -> m r) -> m r</code></td>
</tr>
</table>

[[Image:info.png]] Order is important when combining monads. <code>StateT s (Error e)</code> is different than <code>ErrorT e (State s)</code>. The first produces a combined type of <code>s -> Error e (a,s)</code>, in which the computation can either return a new state or generate an error. The second combination produces a combined type of <code>s -> (Error e a,s)</code>, in which the computation always returns a new state, and the value can be an error or a normal value.<br />