From 53f10e967ccbf9405baa35d5247079e8776ea279 Mon Sep 17 00:00:00 2001
From: "Yann Esposito (Yogsototh)"
Date: Thu, 6 Dec 2012 19:12:58 +0100
Subject: [PATCH] revert to zsh version(s) back
---
categories.html | 33 ++++++++++++-------
categories/10_Introduction/020_Plan.html | 1 +
.../140_Untyped_Pure_Programming.html | 2 +-
.../200_Type_Theory_Categories.html | 18 +++++++---
.../180_Monads_are_just_monoids_1_4.html | 12 +++----
.../30_How/180_Monads_are_just_monoids_1_4.md | 12 +++----
6 files changed, 48 insertions(+), 30 deletions(-)
diff --git a/categories.html b/categories.html
index 5bdba5d..3f10073 100644
--- a/categories.html
+++ b/categories.html
@@ -92,6 +92,7 @@
General overview
Math & Abstraction
Programming & Abstraction
+ Categories & Abstraction
What?
@@ -316,7 +317,7 @@ Theory=(Axioms,StringsRules, Y = λf.(λx.f (x x)) (λx.f (x x))
+ Y = λf.(λx.f (x x)) (λx.f (x x))
Y g = g (Y g)
@@ -390,11 +391,19 @@ type Product = Product {getProduct :: a} -- Just a named box
-Type Theory & Categories
-typed λ-calculus | cartesian closed categories
- |
untyped λ-calculus | C-monoids (subclass of categories)
- |
Martin-Löf type theories | locally cartesian closed categories
- |
|
+Type Theory ⇒ Categories
+
+
+ - Type theory helped to remove paradoxes in Set Theory.
+ - Prevent relations between different kind of objects.
+ - Used in computer science
+
+
+
+ - typed λ-calculus ⇒ cartesian closed categories
+ - untyped λ-calculus ⇒ C-monoids (subclass of categories)
+ - Martin-Löf type theories ⇒ locally cartesian closed categories
+
Plan
@@ -886,16 +895,16 @@ Haskell types is fractal:
Monads are just monoids (1/4)
-A monoid is a triplet \((M,⊙,e)\) s.t.
+A monoid is a triplet \((E,∙,e)\) s.t.
-- \(M\) a set
-- \(⊙:E×E→M\)
-- \(e:1→M\)
+- \(E\) a set
+- \(∙:E×E→E\)
+- \(e:1→E\)
Satisfying
-- \(x⊙(y⊙z) = (x⊙y)⊙z, ∀x,y,z∈M\)
-- \(e⊙x = x = x⊙e, ∀x∈M\)
+- \(x∙(y∙z) = (x∙y)∙z, ∀x,y,z∈E\)
+- \(e∙x = x = x∙e, ∀x∈E\)
diff --git a/categories/10_Introduction/020_Plan.html b/categories/10_Introduction/020_Plan.html
index e2e41cc..2037f71 100644
--- a/categories/10_Introduction/020_Plan.html
+++ b/categories/10_Introduction/020_Plan.html
@@ -5,6 +5,7 @@
General overview
Math & Abstraction
Programming & Abstraction
+ Categories & Abstraction
What?
diff --git a/categories/10_Introduction/140_Untyped_Pure_Programming.html b/categories/10_Introduction/140_Untyped_Pure_Programming.html
index 20d6d20..596d638 100644
--- a/categories/10_Introduction/140_Untyped_Pure_Programming.html
+++ b/categories/10_Introduction/140_Untyped_Pure_Programming.html
@@ -4,7 +4,7 @@
Mostly static constructions like pipes.
All pipes can be plugged ⇒ all error at runtime
- (+ 37 "foo")
-
- Y = λf.(λx.f (x x)) (λx.f (x x))
+
- Y = λf.(λx.f (x x)) (λx.f (x x))
- Y g = g (Y g)
diff --git a/categories/10_Introduction/200_Type_Theory_Categories.html b/categories/10_Introduction/200_Type_Theory_Categories.html
index 5ed7049..f21b2ac 100644
--- a/categories/10_Introduction/200_Type_Theory_Categories.html
+++ b/categories/10_Introduction/200_Type_Theory_Categories.html
@@ -1,5 +1,13 @@
-Type Theory & Categories
-typed λ-calculus | cartesian closed categories
- |
untyped λ-calculus | C-monoids (subclass of categories)
- |
Martin-Löf type theories | locally cartesian closed categories
- |
|
+Type Theory ⇒ Categories
+
+
+ - Type theory helped to remove paradoxes in Set Theory.
+ - Prevent relations between different kind of objects.
+ - Used in computer science
+
+
+
+ - typed λ-calculus ⇒ cartesian closed categories
+ - untyped λ-calculus ⇒ C-monoids (subclass of categories)
+ - Martin-Löf type theories ⇒ locally cartesian closed categories
+
diff --git a/categories/30_How/180_Monads_are_just_monoids_1_4.html b/categories/30_How/180_Monads_are_just_monoids_1_4.html
index ab0d225..f561e6f 100644
--- a/categories/30_How/180_Monads_are_just_monoids_1_4.html
+++ b/categories/30_How/180_Monads_are_just_monoids_1_4.html
@@ -1,12 +1,12 @@
Monads are just monoids (1/4)
-A monoid is a triplet \((M,⊙,e)\) s.t.
+A monoid is a triplet \((E,∙,e)\) s.t.
-- \(M\) a set
-- \(⊙:E×E→M\)
-- \(e:1→M\)
+- \(E\) a set
+- \(∙:E×E→E\)
+- \(e:1→E\)
Satisfying
-- \(x⊙(y⊙z) = (x⊙y)⊙z, ∀x,y,z∈M\)
-- \(e⊙x = x = x⊙e, ∀x∈M\)
+- \(x∙(y∙z) = (x∙y)∙z, ∀x,y,z∈E\)
+- \(e∙x = x = x∙e, ∀x∈E\)
diff --git a/categories/30_How/180_Monads_are_just_monoids_1_4.md b/categories/30_How/180_Monads_are_just_monoids_1_4.md
index e456c23..4a4b0b5 100644
--- a/categories/30_How/180_Monads_are_just_monoids_1_4.md
+++ b/categories/30_How/180_Monads_are_just_monoids_1_4.md
@@ -1,13 +1,13 @@
Monads are just monoids (1/4)
-----------------------------
-A monoid is a triplet \\((M,⊙,e)\\) s.t.
+A monoid is a triplet \\((E,∙,e)\\) s.t.
-- \\(M\\) a set
-- \\(⊙:E×E→M\\)
-- \\(e:1→M\\)
+- \\(E\\) a set
+- \\(∙:E×E→E\\)
+- \\(e:1→E\\)
Satisfying
-- \\(x⊙(y⊙z) = (x⊙y)⊙z, ∀x,y,z∈M\\)
-- \\(e⊙x = x = x⊙e, ∀x∈M\\)
+- \\(x∙(y∙z) = (x∙y)∙z, ∀x,y,z∈E\\)
+- \\(e∙x = x = x∙e, ∀x∈E\\)