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:PROPERTIES: :PROPERTIES:
:ID: 67dab4eb-231f-4af0-bf26-b3cf6d83f9a3 :ID: 67dab4eb-231f-4af0-bf26-b3cf6d83f9a3
:ROAM_ALIASES: "Algebraic Data Types are composable"
:END: :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 Because ADTs are separate from behavior, it's easy to combine them together to
make more complex types. make more complex types.

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#+title: Monad #+title: Monad
#+begin_quote #+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 #+end_quote

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: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.

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20220312165629-monoid.org Normal file
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: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=

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:END: :END:
#+title: Notes on Will Kurt, Get Programming with Haskell #+title: Notes on Will Kurt, Get Programming with Haskell
* [[id:68cedf67-0f59-4a06-9344-77d946129653][Functional Programming]]
#+begin_quote #+begin_quote
John Backus, who led the team that created Fortran, asked in his Turing Award John Backus, who led the team that created Fortran, asked in his Turing Award
lecture, “Can programming be liberated from the von Neumann style?” 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 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. liberate programming from the von Neumann style.
#+end_quote #+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. Youll 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 youd typically want.
#+end_quote
#+print_bibliography: #+print_bibliography: