notes

20220310115927-monad.org

@@ -6,3 +6,20 @@
 #+begin_quote
 A monad is just a [[id:434ee61c-4461-424f-8dba-5c86ddb06c3c][monoid]] in the category of endofunctors.
 #+end_quote
+
+In [[id:9e68d422-cced-4177-96d1-90f777b9a493][Software Development]], this refers to an [[id:10eb4672-19ab-4275-a110-5446c96e7e24][Applicative Functor]] that provides a
+method for applyling a function taking a bare value and returning a wrapped
+value to a value already wrapped in that same type.
+
+In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function to do this is called *bind*, and is available as the
+infix operator ~>>=~. This method is useful for sequentially applying functions
+which generate values wrapped in a Monad, abstracting away logic between each
+sequential application. This behavior leads some people to refer to Monads as
+"programmable semicolons", referring to imperative, C-like languages in which
+each line of code is terminated with a semicolon and executed in sequence.
+Haskell's "do notation" provides syntactic sugar for codifying such sequences.
+
+#+caption: Bind function in Haskell
+#+begin_src haskell :exports code
+  (>>=) :: Monad m => m a -> (a -> m b) -> m b
+#+end_src

20220312165500-semigroup.org

@@ -3,5 +3,20 @@
 :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.
+In [[id:9e68d422-cced-4177-96d1-90f777b9a493][Software Development]], a Semigroup is a category of types such that two values
+of the type can be combined associatively to create a new value of the same
+type.
+
+In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function to combine two semigroup values is =mappend=, also
+available as the infix operator =<>=. =mconcat= is also provided for combining a
+list of semigroup values into a single new value. The =mappend= and =mconcat=
+functions are part of the [[id:434ee61c-4461-424f-8dba-5c86ddb06c3c][Monoid]] type class in Haskell, as it was introduced to
+the language prior to Semigroup, and were given those names as the most common
+[[id:434ee61c-4461-424f-8dba-5c86ddb06c3c][Monoid]] is a list.
+
+#+caption: Semigroup functions in Haskell
+#+begin_src haskell :exports code
+  (<>) :: Semigroup a => a -> a -> a
+  mappend :: Monoid a => a -> a -> a
+  mconcat :: Monoid a => [a] -> a
+#+end_src

20220312165629-monoid.org

@@ -5,7 +5,18 @@
 
 A [[id:b22a1c70-02a7-49ce-b5e7-407f1064cd0c][Semigroup]] with an identity value.
 
+In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function representing the identity value for a given Monoid is
+=mempty=.
+
+#+caption: =mempty= in Haskell
+#+begin_src haskell :exports code
+  mempty :: Monoid a => a
+#+end_src
+
 * 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=
+**  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=

20220316184243-functor.org

@@ -0,0 +1,25 @@
+:PROPERTIES:
+:ID:       7a19b34d-c4bb-462b-8fae-581bf06dfdc4
+:END:
+#+title: Functor
+
+In [[id:9e68d422-cced-4177-96d1-90f777b9a493][Software Development]], this refers to a parameterized data type that wraps a
+value in a context and provides a method for applying a function to the wrapped
+value, independent of the container type.
+
+In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function for applying a function to a value in a functor is
+=fmap=, also available as the infix operator =<$>=.
+
+#+caption: =fmap= in Haskell
+#+begin_src haskell :exports code
+  fmap :: Functor f => (a -> b) -> f a -> f b
+#+end_src
+
+* Examples
+** Maybe
+#+caption: Implementation of Functor for Maybe in Haskell
+#+begin_src haskell :exports code
+  instance Functor Maybe where
+    fmap func (Just n) = Just (func n)
+    fmap func Nothing = Nothing
+#+end_src

20220316185946-applicative.org

@@ -0,0 +1,35 @@
+:PROPERTIES:
+:ID:       10eb4672-19ab-4275-a110-5446c96e7e24
+:END:
+#+title: Applicative
+
+In [[id:9e68d422-cced-4177-96d1-90f777b9a493][Software Development]], this refers to a [[id:7a19b34d-c4bb-462b-8fae-581bf06dfdc4][Functor]] that provides a method for
+applying a function wrapped in such a type to a value wrapped in the same type.
+
+In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function for applying a wrapped function to a value wrapped in
+the same type is available as the infix operator =<*>=, and facilitates the
+application of a function taking an arbitrary number of arguments over multiple
+wrapped values. An applicative must also implement the =pure= function, which
+takes a single argument and returns it wrapped.
+
+#+caption: Applicative functions in Haskell
+#+begin_src haskell :exports code
+  pure :: Applicative f => a -> f a
+  (<*>) :: Applicative f => f (a -> b) -> f a -> f b
+#+end_src
+
+In the following example, =fmap= (=<$>=) first applies the =add= function to the
+value =Just 1=, resulting in a function of the type =Just (Int -> Int)=. The
+applicative infix operator (=<*>=) then applies that function to the remaining
+value =Just 2=, resulting in =Just 3=.
+
+#+caption: Applying a function over multiple wrapped values
+#+begin_src haskell :cache yes :exports both
+  add :: Int -> Int -> Int
+  add x y = x + y
+
+  add <$> Just 1 <*> Just 2
+#+end_src
+
+#+RESULTS[10751e7c3100f27569974ee18b3f34498166dfc5]:
+: Prelude> Just 3

railway_oriented_programming_f_for_fun_and_profit.org

@@ -5,4 +5,4 @@
 #+title: Railway Oriented Programming | F# for fun and profit
 
 A talk on [[id:1a74e6c8-023d-4a04-aae7-74d4428f6de5][Software Architecture]] by Scott Wlaschin on cleanly pipelining
-functions with success and failure cases using monadic binding.
+functions with success and failure cases using [[id:8ee5037f-0673-4968-9ec4-184bf31dd72d][monadic binding]].