updates

20210929115234-algebraic_data_types_are_composable.org

@@ -1,7 +1,13 @@
 :PROPERTIES:
 :ID:       67dab4eb-231f-4af0-bf26-b3cf6d83f9a3
+:ROAM_ALIASES: "Algebraic Data Types are composable"
 :END:
-#+title: Algebraic Data Types are composable
+#+title: Algebraic Data Types
+
+Algebraic Data Types are types built by composing other types. This is done in
+one of two ways:
+- Product Types :: Type T_1 /and/ T_2 /and/ T_n
+- Sum Types :: Type T_1 /or/ T_2 /or/ T_n
 
 Because ADTs are separate from behavior, it's easy to combine them together to
 make more complex types.

20220310115927-monad.org

@@ -4,5 +4,5 @@
 #+title: Monad
 
 #+begin_quote
-A monad is just a monoid in the category of endofunctors.
+A monad is just a [[id:434ee61c-4461-424f-8dba-5c86ddb06c3c][monoid]] in the category of endofunctors.
 #+end_quote

20220312165500-semigroup.org

@@ -0,0 +1,7 @@
+:PROPERTIES:
+:ID:       b22a1c70-02a7-49ce-b5e7-407f1064cd0c
+:END:
+#+title: Semigroup
+
+A category of types such that two values of the type can be combined
+associatively to create a new value of the same type.

20220312165629-monoid.org

@@ -0,0 +1,11 @@
+:PROPERTIES:
+:ID:       434ee61c-4461-424f-8dba-5c86ddb06c3c
+:END:
+#+title: Monoid
+
+A [[id:b22a1c70-02a7-49ce-b5e7-407f1064cd0c][Semigroup]] with an identity value.
+
+* Examples
+- List :: Combined with =append=, identity value is the empty list (=[]=)
+- Number Addition :: Combined with =+=, identity value is =0=
+- Number Multiplication :: Combined with =*=, identity value is =1=

WillKurt2718.org

@@ -4,6 +4,7 @@
 :END:
 #+title: Notes on Will Kurt, Get Programming with Haskell
 
+* [[id:68cedf67-0f59-4a06-9344-77d946129653][Functional Programming]]
 #+begin_quote
 John Backus, who led the team that created Fortran, asked in his Turing Award
 lecture, “Can programming be liberated from the von Neumann style?”
@@ -12,5 +13,23 @@ This question leads to the second way to understand programming, which is the
 subject of the first unit in this book. [[id:68cedf67-0f59-4a06-9344-77d946129653][Functional programming]] attempts to
 liberate programming from the von Neumann style.
 #+end_quote
+* [[id:67dab4eb-231f-4af0-bf26-b3cf6d83f9a3][Algebraic Data Types]]
+#+begin_quote
+The big problem is that you want a single type that represents both vinyl
+records and books so you can make a searchable inventory. Because you can
+compose types only by /and/, you need to develop an abstraction that describes
+everything that records and books have in common. You’ll then implement only the
+differences in the separate classes. This is the fundamental idea behind
+/inheritance/.
+#+end_quote
 
+#+begin_quote
+In theory, creating object hierarchies is elegant and captures an abstraction
+about how everything in the world is interrelated. In practice, creating even
+trivial object hierar- chies is riddled with design challenges. The root of all
+these challenges is that the only way to combine types in most languages is with
+an /and/. This forces you to start from extreme abstraction and move downward.
+Unfortunately, real life is full of strange edge cases that make this much more
+complicated than you’d typically want.
+#+end_quote
 #+print_bibliography: