From 76b790f844def6f9b0e1f6519281845b623a5aa5 Mon Sep 17 00:00:00 2001
From: Yann Esposito
Only identities
+ diff --git a/categories/10_Introduction/025_Categlory.html b/categories/10_Introduction/025_Categlory.html new file mode 100644 index 0000000..aaf3051 --- /dev/null +++ b/categories/10_Introduction/025_Categlory.html @@ -0,0 +1,6 @@ ++Category Theory is a new language/framework for Math
Programming is doing Math
+Strong relations between type theory and category theory.
Not convinced?
Certainly a vocabulary problem.
One of the goal of Category Theory is to create a homogeneous vocabulary between different disciplines.
diff --git a/categories/10_Introduction/050_Math_Programming_relation.md b/categories/10_Introduction/050_Math_Programming_relation.md index 90c39b7..7731cb1 100644 --- a/categories/10_Introduction/050_Math_Programming_relation.md +++ b/categories/10_Introduction/050_Math_Programming_relation.md @@ -5,6 +5,8 @@ Math Programming relation Programming *is* doing Math +Strong relations between type theory and category theory. + Not convinced? Certainly a _vocabulary_ problem. diff --git a/categories/20_What/205.html b/categories/20_What/205.html new file mode 100644 index 0000000..74a9ed5 --- /dev/null +++ b/categories/20_What/205.html @@ -0,0 +1,4 @@ +The same object can be seen in many different way as a category.
+You can choose what are object, morphisms and composition.
+ex: Str and discrete(Σ*)
diff --git a/categories/20_What/205.md b/categories/20_What/205.md new file mode 100644 index 0000000..e4c0cd0 --- /dev/null +++ b/categories/20_What/205.md @@ -0,0 +1,8 @@ +Choice +------ + +The same object can be seen in many different way as a category. + +You can choose what are object, morphisms and composition. + +ex: **Str** and discrete(Σ*) diff --git a/categories/30_How/010_Plan.html b/categories/30_How/010_Plan.html index dbe04b5..2e24030 100644 --- a/categories/30_How/010_Plan.html +++ b/categories/30_How/010_Plan.html @@ -1,11 +1,12 @@Types have kinds; The kind is to type what type is to function. Kind are the types for types (so meta).
Int, Char :: *
[], Maybe :: * -> *
-(,) :: * -> * -> *
+(,), (->) :: * -> * -> *
[Int], Maybe Char, Maybe [Int] :: *
diff --git a/categories/30_How/030_Haskell_Kinds.md b/categories/30_How/030_Haskell_Kinds.md
index f01c67b..10ac72e 100644
--- a/categories/30_How/030_Haskell_Kinds.md
+++ b/categories/30_How/030_Haskell_Kinds.md
@@ -11,6 +11,6 @@ Kind are the types for types (so meta).
~~~
Int, Char :: *
[], Maybe :: * -> *
-(,) :: * -> * -> *
+(,), (->) :: * -> * -> *
[Int], Maybe Char, Maybe [Int] :: *
~~~
diff --git a/categories/30_How/200_Monads/160_Monads_useful.html b/categories/30_How/200_Monads/160_Monads_useful.html
index 96508e6..08e235b 100644
--- a/categories/30_How/200_Monads/160_Monads_useful.html
+++ b/categories/30_How/200_Monads/160_Monads_useful.html
@@ -4,7 +4,7 @@
main = drawImage (width,height)
drawImage :: Screen -> DrawScene
-drawImage screen =
+drawImage screen = do
drawPoint p screen
drawCircle c screen
drawRectangle r screen
diff --git a/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.html b/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.html
index 8a6ae9f..9685c76 100644
--- a/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.html
+++ b/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.html
@@ -2,6 +2,6 @@
Where is the missing information?
- Functor operator
fmap
-- Algebra representing the
(+1)
and also knowing the 0
.
+- Algebra representing the
(+1)
and also knowing about the 0
.
First example, make length
on [Char]
diff --git a/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.md b/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.md
index d0eed85..f736a77 100644
--- a/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.md
+++ b/categories/30_How/300_Catamorphisms/040_morphism_Missing_Information.md
@@ -4,6 +4,6 @@
Where is the missing information?
- Functor operator `fmap`
-- Algebra representing the `(+1)` and also knowing the `0`.
+- Algebra representing the `(+1)` and also knowing about the `0`.
First example, make `length` on `[Char]`
diff --git a/categories/30_How/300_Catamorphisms/050_morphism_Type_work.html b/categories/30_How/300_Catamorphisms/050_morphism_Type_work.html
index 540a31b..ad23bc6 100644
--- a/categories/30_How/300_Catamorphisms/050_morphism_Type_work.html
+++ b/categories/30_How/300_Catamorphisms/050_morphism_Type_work.html
@@ -1,10 +1,11 @@
κατα-morphism: Type work
data StrF a = Cons Char a | Nil
-data Str = StrF Str
+data Str' = StrF Str'
-- generalize the construction of Str to other datatype
--- Mu :: type fixed point
+-- Mu: type fixed point
+-- Mu :: (* -> *) -> *
data Mu f = InF { outF :: f (Mu f) }
data Str = Mu StrF
diff --git a/categories/30_How/300_Catamorphisms/050_morphism_Type_work.md b/categories/30_How/300_Catamorphisms/050_morphism_Type_work.md
index b43e653..72fe78b 100644
--- a/categories/30_How/300_Catamorphisms/050_morphism_Type_work.md
+++ b/categories/30_How/300_Catamorphisms/050_morphism_Type_work.md
@@ -3,10 +3,11 @@
data StrF a = Cons Char a | Nil
-data Str = StrF Str
+data Str' = StrF Str'
-- generalize the construction of Str to other datatype
--- Mu :: type fixed point
+-- Mu: type fixed point
+-- Mu :: (* -> *) -> *
data Mu f = InF { outF :: f (Mu f) }
data Str = Mu StrF
diff --git a/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.html b/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.html
index b138384..4d64dbc 100644
--- a/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.html
+++ b/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.html
@@ -1,7 +1,11 @@
κατα-morphism: missing information retrieved
-type Algebra f a = f a -> a
+type Algebra f a = f a -> a
instance Functor (StrF a) =
fmap f (Cons c x) = Cons c (f x)
fmap _ Nil = Nil
-cata :: Functor f => Algebra f a -> Mu f -> a
+
+cata :: Functor f => Algebra f a -> Mu f -> a
cata f = f . fmap (cata f) . outF
+
+
+
diff --git a/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.md b/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.md
index 5f4b18b..80b4c46 100644
--- a/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.md
+++ b/categories/30_How/300_Catamorphisms/060_morphism_missing_information_retrieved.md
@@ -1,15 +1,11 @@
κατα-morphism: missing information retrieved
--------------------------------------------
-~~~
-type Algebra f a = f a -> a
+type Algebra f a = f a -> a
instance Functor (StrF a) =
fmap f (Cons c x) = Cons c (f x)
- fmap _ Nil = Nil
-~~~
+ fmap _ Nil = Nil
-~~~
-cata :: Functor f => Algebra f a -> Mu f -> a
-cata f = f . fmap (cata f) . outF
-~~~
+cata :: Functor f => Algebra f a -> Mu f -> a
+cata f = f . fmap (cata f) . outF
diff --git a/categories/40_Conclusion/010_Conclusion.html b/categories/40_Conclusion/010_Conclusion.html
index 1dba2f7..a0e58d8 100644
--- a/categories/40_Conclusion/010_Conclusion.html
+++ b/categories/40_Conclusion/010_Conclusion.html
@@ -6,3 +6,4 @@
- Better modularity
- Better control through properties of types
No cat were harmed in the making of this presentation.
diff --git a/categories/40_Conclusion/010_Conclusion.md b/categories/40_Conclusion/010_Conclusion.md index 4466ee6..fa3762e 100644 --- a/categories/40_Conclusion/010_Conclusion.md +++ b/categories/40_Conclusion/010_Conclusion.md @@ -7,3 +7,5 @@ Category Theory oriented Programming: - Extreme generalisation - Better modularity - Better control through properties of types + +No cat were harmed in the making of this presentation. diff --git a/categories/img/categlory.jpg b/categories/img/categlory.jpg new file mode 100644 index 0000000000000000000000000000000000000000..9295419696816159f07a9b985a3f5669b761ae65 GIT binary patch literal 59251 zcmb@t1ymi))+XEscXxM(;O_43kOX&!;2NCZ?h@SHB@hVi?s|aW!9wsM_s)C2nYF&P z=AVB}ozvaV*;Tcxp5EP6dsp{)U4GpL(B!4%qyZ2J06=da;Pnh3Qnhk)b9A+GbRy$m zVFh@_<&>bHfPbaeUDRl^uA``Ana`X##PGtE<6F%7fuT2o=g7rt*)=wuH0G#1*4dYrq}K zw%CK2M(uLbl>?y;Rr1Tp-B5kagT5rVyppwM{JYVn>9=%G@ZpgX?h<+>G<&@`h&mP| z#3((;OYng1E*|=k%LD1@d--vaerpDj7`i8|vyj{#lt--yc2o>PcIrY-x(!ApimC8{ 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