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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)*
+
+
+TODO: example in some lang, e.g. haskell