- Why?
-
-
- General overview +
- General overview
- Math & Abstraction
- Programming & Abstraction
- Categories & Abstraction @@ -141,6 +141,21 @@
Math Abstraction
A common concept you see in multiple instances.
@@ -178,6 +193,7 @@Numbers ⇒ Sets
+Formalism: A theory is some strings (the axioms), some string manipulation rules, and all strings created by applying these rules to the axioms.
Numbers @@ -250,16 +266,33 @@ ++ +Untyped Pure Programming
+ + +
+ +(+ 42 "foo")
+Typed Pure Programming
- Add shapes to pipes:
-
4 + ["foo",27]forbidden diff --git a/categories/10_Introduction/020_Plan.html b/categories/10_Introduction/020_Plan.html index 2458cc9..2037f71 100644 --- a/categories/10_Introduction/020_Plan.html +++ b/categories/10_Introduction/020_Plan.html @@ -2,7 +2,7 @@- Why?
-
-
- General overview +
- General overview
- Math & Abstraction
- Programming & Abstraction
- Categories & Abstraction diff --git a/categories/10_Introduction/060_Plan.html b/categories/10_Introduction/060_Plan.html new file mode 100644 index 0000000..491c1a5 --- /dev/null +++ b/categories/10_Introduction/060_Plan.html @@ -0,0 +1,13 @@ +
- Why?
+
-
+
- General overview +
- Math & Abstraction +
- Programming & Abstraction +
- Categories & Abstraction +
+ - What? +
- How? +
- Topology -
- Quantum Physics -
- Logic -
- Programming -
- Topology +
- Quantum Physics +
- Logic +
- Computer Science +
- Why?
+
-
+
- General overview +
- Math & Abstraction +
- Programming & Abstraction +
- Categories & Abstraction +
+ - What? +
- How? +
- Encouraged by imperative paradigms.
- Actions & mutable objects. -
- Time is very important: ex. linked list push +
- Time is very important*.
- Synchronizing things is a challenge.
- Time is irrelevant by default.
- Mostly static constructions like pipes.
- All pipes can be plugged ⇒ all error at runtime
-
- (+ ("foo" 27) 32)
+
- (+ 37 "foo")
- Y = λf.(λx.f (x x)) (λx.f (x x))
- Y g = g (Y g)
Untyped Pure Programming
+ + +
+ +(+ 42 "foo")
diff --git a/categories/10_Introduction/130_Typed_Pure_Programming.html b/categories/10_Introduction/160_Typed_Pure_Programming.html
similarity index 100%
rename from categories/10_Introduction/130_Typed_Pure_Programming.html
rename to categories/10_Introduction/160_Typed_Pure_Programming.html
diff --git a/categories/10_Introduction/140_Polymorphism_mappend.html b/categories/10_Introduction/170_Polymorphism_mappend.html
similarity index 100%
rename from categories/10_Introduction/140_Polymorphism_mappend.html
rename to categories/10_Introduction/170_Polymorphism_mappend.html
diff --git a/categories/10_Introduction/150_Polymorphism.html b/categories/10_Introduction/180_Polymorphism.html
similarity index 100%
rename from categories/10_Introduction/150_Polymorphism.html
rename to categories/10_Introduction/180_Polymorphism.html
diff --git a/categories/10_Introduction/160_Programming_Paradigms.html b/categories/10_Introduction/190_Programming_Paradigms.html
similarity index 100%
rename from categories/10_Introduction/160_Programming_Paradigms.html
rename to categories/10_Introduction/190_Programming_Paradigms.html
diff --git a/categories/10_Introduction/170_Type_Theory_Categories.html b/categories/10_Introduction/200_Type_Theory_Categories.html
similarity index 100%
rename from categories/10_Introduction/170_Type_Theory_Categories.html
rename to categories/10_Introduction/200_Type_Theory_Categories.html
diff --git a/categories/head.html b/categories/head.html
index 45d820e..1b1d702 100644
--- a/categories/head.html
+++ b/categories/head.html
@@ -43,7 +43,7 @@
}
-
+
- (+ ("foo" 27) 32)
+
Plan
+-
+
Numbers ⇒ Sets
+Formalism: A theory is some strings (the axioms), some string manipulation rules, and all strings created by applying these rules to the axioms.
Numbers diff --git a/categories/10_Introduction/100_Category_Theory.html b/categories/10_Introduction/100_Category_Theory.html deleted file mode 100644 index 551356b..0000000 --- a/categories/10_Introduction/100_Category_Theory.html +++ /dev/null @@ -1,11 +0,0 @@ -Category Theory
-Categories package entire mathematical theories.
--
-
More general: more things are Categories.
-
- & More precise: better distinction between concepts.Young field: 1942–45, Samuel Eilenberg & Saunders Mac Lane diff --git a/categories/10_Introduction/090_Sets_Categories.html b/categories/10_Introduction/100_Sets_Categories.html similarity index 100% rename from categories/10_Introduction/090_Sets_Categories.html rename to categories/10_Introduction/100_Sets_Categories.html diff --git a/categories/10_Introduction/110_Category_Theory.html b/categories/10_Introduction/110_Category_Theory.html new file mode 100644 index 0000000..b22d01d --- /dev/null +++ b/categories/10_Introduction/110_Category_Theory.html @@ -0,0 +1,13 @@ +
Category Theory
+Categories package entire mathematical theories.
+ +
+Theory=(Axioms,Rules,Theorems)
+(Strings,Strings → Strings, Strings) +-
+
Recent field: 1942–45, Samuel Eilenberg & Saunders Mac Lane diff --git a/categories/10_Introduction/120_Plan.html b/categories/10_Introduction/120_Plan.html new file mode 100644 index 0000000..7a1c696 --- /dev/null +++ b/categories/10_Introduction/120_Plan.html @@ -0,0 +1,13 @@ +
Plan
+-
+
Natural Abstractions: pointers, variables, loop, Objects, Classes...
Representation: a data structure changing other time.
+ +*: Push an element to a linked list for example
diff --git a/categories/10_Introduction/120_Untyped_Pure_Programming.html b/categories/10_Introduction/140_Untyped_Pure_Programming.html similarity index 92% rename from categories/10_Introduction/120_Untyped_Pure_Programming.html rename to categories/10_Introduction/140_Untyped_Pure_Programming.html index 6a6cc96..596d638 100644 --- a/categories/10_Introduction/120_Untyped_Pure_Programming.html +++ b/categories/10_Introduction/140_Untyped_Pure_Programming.html @@ -3,7 +3,7 @@
- Why?
-