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Commit a9616b68 authored by Maxime Jacquemin's avatar Maxime Jacquemin
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[Kernel] Typos

Credit to Virgile Prevosto
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...@@ -203,7 +203,7 @@ end ...@@ -203,7 +203,7 @@ end
Those functors provide a way to extend a minimal signature into a full Those functors provide a way to extend a minimal signature into a full
monad that satisfies the signatures defined above. This is possible monad that satisfies the signatures defined above. This is possible
because one can defines operations from one monadic definition because one can define operations from one monadic definition
using the operations required by the others. Indeed : using the operations required by the others. Indeed :
1. ∀m:('a t), ∀f:('a -> 'b), [map f m ≣ bind (fun x -> return (f x)) m] 1. ∀m:('a t), ∀f:('a -> 'b), [map f m ≣ bind (fun x -> return (f x)) m]
...@@ -236,7 +236,7 @@ module Make_based_on_map_with_product (M : Based_on_map_with_product) : ...@@ -236,7 +236,7 @@ module Make_based_on_map_with_product (M : Based_on_map_with_product) :
(** {3 Detailled explanations and category theory} (** {3 Detailled explanations and category theory}
To be pedantic, the map based approach defines a monad as a categoric To be pedantic, the map based approach defines a monad as a categoric
functor equipped with two natural transformations. This does sounds functor equipped with two natural transformations. This does sound
frightening but this breaks down to rather simple concepts. frightening but this breaks down to rather simple concepts.
Let's start at the beginning. A category is just a collection of objets Let's start at the beginning. A category is just a collection of objets
...@@ -252,13 +252,13 @@ module Make_based_on_map_with_product (M : Based_on_map_with_product) : ...@@ -252,13 +252,13 @@ module Make_based_on_map_with_product (M : Based_on_map_with_product) :
between the objets ['a] and ['b]. As functions are naturally associative between the objets ['a] and ['b]. As functions are naturally associative
and, for any type ['a], one can trivially defines the identity function and, for any type ['a], one can trivially defines the identity function
['a -> 'a], one can conclude that types along with all functions of ['a -> 'a], one can conclude that types along with all functions of
arithy one forms a category. arity one forms a category.
Next, there is the idea of functors. In the category theory, a functor Next, there is the idea of functors. In the category theory, a functor
is a mapping between categories. That means that, given two categories is a mapping between categories. That means that, given two categories
[A] and [B], a functor maps all objects of [A] to an object of [B] and [A] and [B], a functor maps all objects of [A] to an object of [B] and
maps all morphisms of [A] into a morphims of [B]. But, not all mappings maps any morphism of [A] into a morphism of [B]. But, not all mappings
are functors. Indeed, to be a valid functor, one as to preserve the are functors. Indeed, to be a valid functor, one has to preserve the
identity morphisms and the composition of morphims. identity morphisms and the composition of morphims.
The idea of functors can also be seen in a type systems. At least, the The idea of functors can also be seen in a type systems. At least, the
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