CENSORE

monad.md

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-# Monad
-
-{ This is my poor understanding of a monad. ~drummyfish }
-
-Monad is a [mathematical](math.md) concept which has become useful in [functional programming](functional.md) and is one of the very basic [design patterns](design_pattern.md) in this paradigm. A monad basically wraps some [data type](data_type) into an "envelope" type and gives a way to operate with these wrapped data types which greatly simplifies things like error checking or abstracting [input/output](io.md) side effects.
-
-A typical example is a **maybe** monad which wraps a type such as integer to handle exceptions such as division by zero. A maybe monad consists of:
-
-1. The *maybe(T)* data type where *T* is some other data type, e.g. *maybe(int)*. Type *maybe(T)* can have these values:
-  - *just(X)* where *X* is any possible value of *T* (for int: -1, 0, 1, 2, ...), or
-  - *nothing*, a special value that says no value is present
-2. A special function *return(X)* that converts value of given type into this maybe type, e.g. *return(3)* will return *just(3)*
-3. A special combinator *X >>= f* which takes a monadic (*maybe*) values *X* and a function *f* and does the following:
-  - if *X* is *nothing*, gives back *nothing*
-  - if *X* is a value *just(N)*, gives back the value *f(N)* (i.e. unwraps the value and hand it over to the function)
-
-Let's look at a pseudocode example of writing a safe division function. Without using the combinator it's kind of ugly:
-
-```
-divSafe(x,y) = // takes two maybe values, returns a maybe value
-  if x == nothing
-    nothing else
-    if y == nothing
-      nothing else
-        if y == 0
-          nothing else
-            just(x / y)
-```
-
-With the combinator it gets much nicer (note the use of [lambda expression](lambda.md)):
-
-```
-divSafe(x,y) =
-  x >>= { a: y >== { b: if b == 0 nothing else a / b } }
-```
-
-Languages  will typicall make this even nicer with a [syntax sugar](syntax_sugar.md) such as:
-
-```
-divSafe(x,y) = do
-  a <- x,
-  b <- y,
-  if y == 0 nothing else return(a / b)
-```
-
-TODO: I/O monad
-TODO: general monad
-TODO: example in real lang, e.g. haskell