Created
May 23, 2012 18:21
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(ns monads | |
(:require clojure.set)) | |
(declare ^:dynamic return | |
^:dynamic bind) | |
(defn lift-inc [v] | |
(return (inc v))) | |
(defn m-add [mv n] | |
(bind mv (fn [v] (return (+ v n))))) | |
(defn m-div [mv n] | |
(if (zero? n) | |
(return nil) | |
(bind mv (fn [v] (return (/ v n)))))) | |
;; =============================== | |
;; Identity monad | |
(binding [return (fn [v] | |
(fn [] v)) | |
bind (fn [mv f] | |
(f (mv)))] | |
((-> | |
(return 0) | |
(bind lift-inc) | |
(m-add 10) | |
(m-div 2) | |
))) | |
;; -> 11/2 | |
;; =============================== | |
;; maybe monad | |
(binding [return (fn [v] | |
(fn [] v)) | |
bind (fn [mv f] | |
(if-let [v (mv)] | |
(f v) | |
(return nil)))] | |
((-> | |
(return 0) | |
(m-add 10) | |
(m-div 0) | |
(m-add 2)))) | |
;; -> nil | |
;; =============================== | |
;; state monad | |
(defn setf [v] (fn [_] [v v])) | |
(def getf (fn [s] [s s])) | |
(defn set-state [mv] | |
(bind mv setf)) | |
(defn get-state [mv] | |
(bind mv (fn [_] getf))) | |
(defn add-from-state [mv] | |
(bind mv (fn [v] | |
(bind getf | |
(fn [s] (return (+ s v))))))) | |
(binding [return (fn [v] | |
(fn [s] [v s])) | |
bind (fn [mv f] | |
(fn [s] | |
(let [[v sn] (mv s)] | |
((f v) sn))))] | |
[ | |
((-> | |
(return 0) | |
(m-add 10) | |
set-state | |
add-from-state | |
)0) | |
(let [m-count (bind getf (fn [s] | |
(setf (inc s)))) | |
m-inc (fn [mv] | |
(bind mv (fn [v] | |
(bind m-count | |
(fn [_] (return (inc v)))))))] | |
((-> (return 5) | |
(m-add 5) | |
m-inc | |
m-inc | |
)0))]) | |
;; -> [[20 10] [12 2]] | |
;; =============================== | |
;; Continuation monad | |
(defn halt [x] | |
(fn [c] x)) | |
(defn bounce [x] | |
(fn [c] | |
(fn [] (c x)))) | |
(defn mark [x] | |
(fn [c] c)) | |
(binding [return (fn [v] | |
(fn [c] (c v))) | |
bind (fn [mv f] | |
(fn [c] | |
(mv (fn [v] | |
((f v) c)))))] | |
[ | |
((-> (return 21) | |
(bind lift-inc) | |
(bind halt) | |
(m-add 10)) | |
identity) | |
(trampoline | |
((-> (return 21) | |
(bind lift-inc) | |
(bind bounce) | |
(m-add 10)) | |
identity)) | |
(doall (map ((-> (return 21) | |
(bind mark) | |
(m-add 10) | |
(bind lift-inc) | |
)identity) | |
[0 1 2]))]) | |
;; -> [22 32 (11 12 13)] | |
;; =============================== | |
;; List monad | |
(defn lift-id-half-double [x] | |
(return x (/ x 2) (* x 2))) | |
(binding [return (fn [& v] | |
(fn [] (apply list v))) | |
bind (fn [mv f] | |
(fn [] (mapcat (comp #(%) f) | |
(mv))))] | |
((-> | |
(return 4 8) | |
(bind lift-id-half-double) | |
))) | |
;; -> (4 2 8 8 4 16) | |
;; =============================== | |
;; Set monad | |
(binding [return (fn [& v] | |
(fn [] (apply hash-set v))) | |
bind (fn [mv f] | |
(fn [] (apply clojure.set/union | |
(map (comp #(%) f) (mv)))))] | |
((-> | |
(return 4 8) | |
(bind lift-id-half-double) | |
))) | |
;; -> #{2 4 8 16} |
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