Post on 10-May-2015
description
Monads in ClojureOr why burritos shouldn’t be scary [I]
[I] http://blog.plover.com/prog/burritos.html
Leonardo Borges@leonardo_borges
www.leonardoborges.comwww.thoughtworks.com
Tuesday, 4 March 14
Monads in Clojure
The plan:
Type Signatures in Haskell The Monad Type Class
A few useful monads
This presentation is a super condensed version of my blog post series on monads [II]
[II] http://bit.ly/monads-part-iTuesday, 4 March 14
Prelude
Type signatures in Haskell
Tuesday, 4 March 14
Type signatures in Haskell
import qualified Data.Map as Map -- just giving Data.Map an aliasmkVec :: a -> a -> Map.Map [Char] a -- this is the type signature
Vectors as maps
This is a function of two arguments of type a
Tuesday, 4 March 14
Type signatures in Haskell
import qualified Data.Map as Map -- just giving Data.Map an aliasmkVec :: a -> a -> Map.Map [Char] a -- this is the type signature
Vectors as maps
It returns a Map where keys are of type [Char] and values are of type a
Tuesday, 4 March 14
Type signatures in Haskell
import qualified Data.Map as Map -- just giving Data.Map an aliasmkVec :: a -> a -> Map.Map [Char] a -- this is the type signature
mkVec x y = Map.fromList [("x", x), ("y", y)] -- this is the implementation. You can ignore this part.
Vectors as maps
-- using itmyVec = mkVec 10 15Map.lookup "x" myVec -- Just 10
Tuesday, 4 March 14
Type signatures in HaskellMultiplication
(*) :: Num a => a -> a -> a
This is also a function of two arguments of type a
Tuesday, 4 March 14
Type signatures in HaskellMultiplication
(*) :: Num a => a -> a -> a
Num a is a type constraint
In this case, the type constraint tells the compiler that (*)works on any value a as long as a is an
instance of Num
Tuesday, 4 March 14
Monadswhat on earth are they?
They’re simply an abstraction
...with a funny name to confuse people.
Tuesday, 4 March 14
Monadswhat on earth are they?
They are not however....... a burrito
... an elephant
... a space suit... or a writing desk.
Tuesday, 4 March 14
Monadswhat on earth are they?
Every monad has an associated “context”
It can be useful to think of them as “wrapping” some value
Tuesday, 4 March 14
The Monad Type Class
class Monad m where return :: a -> m a
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b x >> y = x >>= \_ -> y
Let’s understand those type signatures!
Tuesday, 4 March 14
The Monad Type Class
return :: a -> m a
Single argument of type a
Tuesday, 4 March 14
The Monad Type Class
return :: a -> m a
returns a in a “context” m
Tuesday, 4 March 14
The Monad Type Class
return :: a -> m a
This is how we turn plain values into monadic values
Tuesday, 4 March 14
The Monad Type Class
return :: a -> m a
return is an unfortunate name as it is confusing. It has nothing to do with the return keywords in languages like Java. return is sometimes called unit
Tuesday, 4 March 14
The Monad Type Class
(>>=) :: m a -> (a -> m b) -> m b
>>= is pronounced bind and takes two arguments
Tuesday, 4 March 14
The Monad Type Class
(>>=) :: m a -> (a -> m b) -> m b
A monad m a
Tuesday, 4 March 14
The Monad Type Class
(>>=) :: m a -> (a -> m b) -> m b
and a function from values of type a to monads of type m b
Tuesday, 4 March 14
The Monad Type Class
(>>=) :: m a -> (a -> m b) -> m b
Somehow each monad knows how to extract values from its context and “bind” them to the given function
Tuesday, 4 March 14
The Monad Type Class
(>>=) :: m a -> (a -> m b) -> m b
and it returns b in a “context” m
Tuesday, 4 March 14
The Monad Type Class
(>>) :: m a -> m b -> m bx >> y = x >>= \_ -> y
You can work out the type signature all by yourself now :)
Tuesday, 4 March 14
The Monad Type Class
(>>) :: m a -> m b -> m bx >> y = x >>= \_ -> y
>> is pronounced then and includes a default implementation in terms of bind (>>=)
Tuesday, 4 March 14
The Monad Type Class
(>>) :: m a -> m b -> m bx >> y = x >>= \_ -> y
Its second argument to bind is a function which ignores its argument
Tuesday, 4 March 14
The Monad Type Class
(>>) :: m a -> m b -> m bx >> y = x >>= \_ -> y
It simply returns the value yielded by “unwrapping” the context of y
Tuesday, 4 March 14
Example ICalculating all combinations between elements of two lists using the
list monad
combinations :: [(Int,Int)] combinations = [1, 2, 3] >>= \a -> [4, 5] >>= \b -> return (a,b)
-- [(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]
Tuesday, 4 March 14
Example ICalculating all combinations between elements of two lists using the
list monad
meh. It’s damn hard to read. And we don’t want to type that much.
There’s a better way
Tuesday, 4 March 14
Example ICalculating all combinations between elements of two lists using the
list monad (using do notation)
combinations' :: [(Int,Int)] combinations' = do a <- [1, 2, 3] b <- [4, 5] return (a,b)
-- [(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]
Tuesday, 4 March 14
You’ve just seen your first monad, the list monad!
Tuesday, 4 March 14
The Monad Type Class *
class Monad [] where return :: a -> [a]
(>>=) :: [a] -> (a -> [b]) -> [b]
(>>) :: [a] -> [b] -> [b]
As if it worked for lists only
* this isn’t valid Haskell. It’s just to illustrate the conceptTuesday, 4 March 14
Now let’s learn how it does its thing......in Clojure!
Tuesday, 4 March 14
The List MonadLet’s do it together
(def list-m { :return (fn [v] ... ) :bind (fn [mv f] ... ) })
Tuesday, 4 March 14
The List MonadLet’s do it together
(def list-m { :return (fn [v] (list v)) :bind (fn [mv f] ... ) })
Tuesday, 4 March 14
The List MonadLet’s do it together
(def list-m { :return (fn [v] (list v)) :bind (fn [mv f] (mapcat f mv)) })
Tuesday, 4 March 14
The List MonadNow we’re ready to use it
(defn combinations [] (let [bind (:bind list-m) return (:return list-m)] (bind [1 2 3] (fn [a] (bind [4 5] (fn [b] (return [a b])))))))
;; ([1 4] [1 5] [2 4] [2 5] [3 4] [3 5])
Tuesday, 4 March 14
The List MonadNow we’re ready to use it
ugh. Just as ugly.But we know there’s a better way.
Can we use the do notation in Clojure?
Tuesday, 4 March 14
Macros to the rescueHaskell’s do notation in Clojure
(defn m-steps [m [name val & bindings] body] (if (seq bindings) `(-> ~val ((:bind ~m) (fn [~name] ~(m-steps m bindings body)))) `(-> ~val ((:bind ~m) (fn [~name] ((:return ~m) ~body))))))
(defmacro do-m [m bindings body] (m-steps m bindings body))
Tuesday, 4 March 14
Macros to the rescueHaskell’s do notation in Clojure
Ignore the implementation. You can study it later :)
Tuesday, 4 March 14
The List MonadNow we’re ready to use it
(defn combinations [] (do-m list-m [a [1 2 3] b [4 5]] [a b]))
;; ([1 4] [1 5] [2 4] [2 5] [3 4] [3 5])
Tuesday, 4 March 14
Familiar?List comprehension
(defn combinations [] (for [a [1 2 3] b [4 5]] [a b]))
;; ([1 4] [1 5] [2 4] [2 5] [3 4] [3 5])
Tuesday, 4 March 14
Example IIAdding two numbers
(defn add [a b] (+ a b))
(add 1 2) ;; 3
(add 1 nil)
;; NullPointerException
Tuesday, 4 March 14
Example II[Maybe]Adding two numbers
(defn m-add [ma mb] (do-m maybe-m [a ma b mb] (+ a b)))
(m-add 1 2) ;; 3
(m-add nil 1) ;; nil
Tuesday, 4 March 14
The Maybe MonadAgain, everyone together
(def maybe-m { :return (fn [v] ...) :bind (fn [mv f] ... ) })
Tuesday, 4 March 14
The Maybe MonadAgain, everyone together
(def maybe-m { :return (fn [v] v) :bind (fn [mv f] ... ) })
Tuesday, 4 March 14
The Maybe MonadAgain, everyone together
(def maybe-m { :return (fn [v] v) :bind (fn [mv f] (when mv (f mv))) })
Tuesday, 4 March 14
Not too bad, huh? Ready for more?
Tuesday, 4 March 14
Example IIIApplication configuration
(defn connect-to-db [env] (let [db-uri (:db-uri env)] (prn (format "Connected to db at %s" db-uri))))
(defn connect-to-api [env] (let [api-key (:api-key env) env (ask)] (prn (format "Connected to api with key %s" api-key))))
Tuesday, 4 March 14
Example IIIApplication configuration
(defn run-app [env] (do (connect-to-db env) (connect-to-api env) "Done."))
(run-app {:db-uri "user:passwd@host/dbname" :api-key "AF167"});; "Connected to db at user:passwd@host/dbname";; "Connected to api with key AF167";; "Done."
Tuesday, 4 March 14
Example IIIApplication configuration
Passing env on to every single function that depends on it can be cumbersome.
Obviously we don’t want to resort to global vars. Can monads help?
Tuesday, 4 March 14
Example IIIApplication configuration with the Reader Monad
(defn connect-to-db [] (do-m reader-m [db-uri (asks :db-uri)] (prn (format "Connected to db at %s" db-uri))))
(defn connect-to-api [] (do-m reader-m [api-key (asks :api-key) env (ask)] (prn (format "Connected to api with key %s" api-key))))
Bear with me for now. These will be explained soon.
Tuesday, 4 March 14
Example IIIApplication configuration with the Reader Monad
(defn run-app [] (do-m reader-m [_ (m-connect-to-db) _ (m-connect-to-api)] (prn "Done.")))
((run-app) {:db-uri "user:passwd@host/dbname" :api-key "AF167"});; "Connected to db at user:passwd@host/dbname";; "Connected to api with key AF167";; "Done."
Note the env parameter disappeared.
The Reader monad somehow feeds that into our functions.
Also this is now a function call as run-app is now pure
Tuesday, 4 March 14
Example IIIApplication configuration with the Reader Monad
But, how how does it work?!
Tuesday, 4 March 14
The Reader MonadTricky one, but not that tricky
(defn ask [] identity)(defn asks [f] (fn [env] (f env)))
The function names come from Haskell. They are defined in the MonadReader type class.
Tuesday, 4 March 14
The Reader MonadTricky one, but not that tricky
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
There’s a lot going on in bind. Let’s unravel it.
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(defn connect-to-db [] (do-m reader-m [db-uri (asks :db-uri)] (prn (format "Connected to db at %s" db-uri))))
This:
((:bind reader-m) (asks :db-uri) (fn* ([db-uri] ((:return reader-m) (prn "Connected to db at " db-uri)))))
Expands into:
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((:return reader-m) (prn "Connected to db at " db-uri))))] ((fn [r] ((k (m r)) r)) {:db-uri "user:passwd@host/dbname" :api-key "AF167"}))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((:return reader-m) (prn "Connected to db at " db-uri))))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] ((k (m r)) r)))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((:return reader-m) (prn "Connected to db at " db-uri))))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] ((k "user:passwd@host/dbname") r)))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((:return reader-m) nil)))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] ((k "user:passwd@host/dbname") r)))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((fn [a] (fn [_] a) nil)))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] ((k "user:passwd@host/dbname") r)))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((fn [a] (fn [_] a) nil)))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] ((fn [_] nil) r)))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader MonadExpanding connect-to-db
(let [m (fn [env] (:db-uri env)) k (fn* ([db-uri] ((fn [a] (fn [_] a) nil)))] (let [r {:db-uri "user:passwd@host/dbname" :api-key "AF167"}] nil))
(def reader-m {:return (fn [a] (fn [_] a)) :bind (fn [m k] (fn [r] ((k (m r)) r)))})
Tuesday, 4 March 14
The Reader Monad
Simple, right? :)
Tuesday, 4 March 14
Example IVDependency Injection
(require '[app.repository :as repository])
(defn clone! [id user] (let [old-user (repository/fetch-by-id id {}) cloned-user (repository/create! (compute-clone old-user) user) updated-user (assoc old-user :clone-id (:id cloned-user))] (repository/update! old-user updated-user user)))
See the problem?
Tuesday, 4 March 14
Example IVDependency Injection: the problem
• clone! is tightly coupled to the repository namespace• It can’t be tested in isolation without resorting to heavy mocking of the involved functions• It’s limited to a single repository implementation - makes experimenting at the REPL harder• ...
Basically, good software engineering principles apply
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
Let’s start by turning our repository into a module that can
be injected into our function
Tuesday, 4 March 14
Example IV
There’s a couple of ways in which we can do that
I’ll use protocols as they have added performance benefits
Dependency Injection using the Reader Monad
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
(defprotocol UserRepository (fetch-by-id! [this id]) (create! [this user username]) (update! [this old-user new-user username]))
(defn mk-user-repo [] (reify UserRepository (fetch-by-id! [this id] (prn "Fetched user id " id)) (create! [this user username] (prn "Create user triggered by " username)) (update! [this old-user new-user username] (prn "Updated user triggered by " username))))
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
Remember: One of the advantages of the reader monad is not having to pass parameters around to
every single function that needs it
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
With that in mind, let’s rewrite clone!
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
(defn clone! [id user] (do-m reader-m [repo (ask)] (let [old-user (fetch-by-id! repo id) cloned-user (create! repo (compute-clone old-user) user) updated-user (assoc old-user :clone-id (:id cloned-user))] (update! repo old-user updated-user user))))
;; clone! :: Number -> String -> Reader UserRepository Number
It can be helpful to think of clone as having this type signature:
Tuesday, 4 March 14
Example IVDependency Injection using the Reader Monad
(defn run-clone [] (do-m reader-m [_ (clone! 10 "leo")] (prn "Cloned.")))
((run-clone) (mk-user-repo))
And this is how we might use it:
;; "Fetched user id " 10;; "Compute clone for user";; "Create user triggered by " "leo";; "Updated user triggered by " "leo";; "Cloned."
Tuesday, 4 March 14
The Reader MonadA few observations from a clojure perspective
• Useful abstraction for computations that read values from a shared environment• As we saw, it has multiple use cases such as configuration and dependency injection• I’ve cheated in the examples:• Each function using the reader monad also performed IO - via prn• In Haskell, IO is a monad so we would need to use monad transformers to compose them - beyond the scope of this presentation
Tuesday, 4 March 14
Monads: Summary
• Lots of useful abstractions through a common interface• Some monads, such as Maybe and Either, are a lot more powerful in a statically typed language like Haskell or Scala due to its usage being encoded in the type system, as well as native support to pattern matching• Others, such as the Reader monad, can be very useful in a dynamic setting - though you don’t have the type system to tell you when you stuff up at compile time• In such cases, type annotations in comments can be useful
Tuesday, 4 March 14
Questions?Leonardo Borges
@leonardo_borgeswww.leonardoborges.comwww.thoughtworks.com
Tuesday, 4 March 14