Monads

Monads is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Functional programming Monads are a mechanism for building types which allow unified handling of more than one underlying type. (This use of this term implies and hides multiple dispatch, however for Rosetta Code we do not require that this be a feature of the language.) Demonstrate in your programming language the following:

1. Construct a Monad (preferably the Option/Maybe Monad or the List Monad) by making bind and unit for that Monad (or just use what the language already has implemented)
2. Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
3. Compose the two functions with bind

Clojure

Maybe Monad

<lang clojure> (defn bind [val f] (if (nil? (:value val)) val (f (:value val)))) (defn unit [val] {:value val})

(defn opt_add_3 [n] (unit (+ 3 n))) ; takes a number and returns a Maybe number (defn opt_str [n] (unit (str n)))  ; takes a number and returns a Maybe string

(bind (unit 4) opt_add_3)  ; evaluates to {:value 7} (bind (unit nil) opt_add_3)  ; evaluates to {:value nil} (bind (bind (unit 8) opt_add_3) opt_str)  ; evaluates to {:value "11"} (bind (bind (unit nil) opt_add_3) opt_str) ; evaluates to {:value nil} </lang>

List Monad

<lang clojure> (defn bind [coll f] (apply vector (mapcat f coll))) (defn unit [val] (vector val))

(defn doubler [n] [(* 2 n)])  ; takes a number and returns a List number (def vecstr (comp vector str)) ; takes a number and returns a List string

(bind (bind (vector 3 4 5) doubler) vecstr) ; evaluates to ["6" "8" "10"] (-> [3 4 5]

 (bind doubler)
 (bind vecstr)) ; also evaluates to ["6" "8" "10"]

</lang>

J

Note that J documentation mentions "monad" but that is an older (much older) use of the term from what is intended here. J documentation uses "box" <to describe the operation mentioned here.

That said, here is an implementation which might be adequate for the current task description:

<lang J>bind=: S:0 unit=: boxopen

m_num=: unit m_str=: unit@":</lang>

Task example:

<lang J> m_str bind m_num 5 ┌─┐ │5│ └─┘</lang>

Ruby

List Monad

<lang ruby> class Array

 def bind(f)
   map(&f).reduce(:concat)
 end
 def self.unit(*args)
   args
 end

end

inc = -> e { Array.unit(e + 1) } str = -> e { Array.unit(e.to_s) }

Array.unit(3,4,5).bind(inc).bind(str) #=> ["4", "5", "6"]

1. Note that inc and str cannot be composed directly,
2. as they don't have compatible type signature.
3. Due to duck typing (Ruby will happily turn arrays into strings),
4. in order to show this, a new function will have to be used:

doub = -> n {[2*n]} [3,4,5].bind(inc).bind(doub) #=> [8, 10, 12]

1. Direct composition will cause a TypeError, as Ruby cannot evaluate 2*[4, 5, 6]

comp = -> f, g {-> x {f[g[x]]}} [3,4,5].bind(comp[doub, inc]) #=> TypeError: Array can't be coerced into Fixnum

1. Composition needs to be defined in terms of bind

class Array

 def bind_comp(f, g)
   bind(g).bind(f)
 end

end

[3,4,5].bind_comp(doub, inc) #=> [8, 10, 12] </lang>