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rephrase Free Theorem paragraphs

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Christian Sievers 2015-02-16 14:47:31 +01:00
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006_hindley_milner.md
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@ -134,19 +134,18 @@ $$
A rather remarkably fact of universal quantification is that many properties
about inhabitants of a type are guaranteed by construction, these are the
so-called *free theorems*. For instance the only (nonpathological)
implementation that can inhabit a function of type ``(a, b) -> a`` is an
implementation precisely identical to that of ``fst``.
so-called *free theorems*. For instance any (nonpathological)
inhabitant of the type ``(a, b) -> a`` must be equivalent to ``fst``.
A slightly less trivial example is that of the ``fmap`` function of type
``Functor f => (a -> b) -> f a -> f b``. The second functor law states that.
``Functor f => (a -> b) -> f a -> f b``. The second functor law demands that:
```haskell
forall f g. fmap f . fmap g = fmap (f . g)
```
However it is impossible to write down a (nonpathological) function for ``fmap``
that was well-typed and didn't have this property. We get the theorem for free!
that has the required type and doesn't have this property. We get the theorem for free!
Types
-----