core.clj

(ns hacklheber.core)

(defn flip
  "A function which returns true or false randomly. Can optionally be
   supplied a number for a bias."
  ([]  (> 0.5 (rand)))
  ([p] (> p (rand))))

(defn- memo-bangs 
  "If a variable is bound with a bang, then it will be memoized." 
  [[k v]]
  (if (= \! (last (name k)))
    [k `(memoize ~v)]
    [k v]))

(defn- find-clause 
  "Given a list of clauses and a key, this finds the body of the first
  clause which has the same keyword as the given key." 
  [clauses key]
  (->> clauses
     (filter (fn [[k v]] (= key k)))
     first
     second))

(defmacro query-by-rejection
  "Query a distribution via rejection. See further below for
  examples." 
  [[& bindings] & body-expr]
  (let [{clauses# true pairs# false} (group-by (comp keyword? first)
                                               (partition-all 2 bindings))

        where#     (or (find-clause clauses# :where)
                       '(fn [] true))

        memobound# (->> (find-clause clauses# :memobound) 
                        (mapcat (juxt identity (fn [v] `(memoize ~v))))                        
                        vec)

        pairs#     (vec (mapcat memo-bangs pairs#))]
    `(loop []
       (let [[cond# result#] (binding ~memobound#
                               (let [~@pairs# cond# ~where#] 
                                 [cond# (when cond# (do ~@body-expr))]))]
         (if cond#
           result#
           (recur))))))

(defn normalized-frequencies 
  "Takes in a collection and computes the normalizied frequenicies of
  elements in the colleciton." 
  [col]
  (let [freqs (frequencies col) 
        count (reduce + (map second freqs))
        normalized (for [[k v] freqs] [k (float (/ v count))])]
    (into {} normalized)))

(defmacro sample-by-rejection 
  "Takes in a number n and the body for a query-by-rejection. Executes
  the specified query n times." 
  [n & body]
  `(for [i# (range ~n)] 
     (query-by-rejection ~@body)))

;;Example queries taken from Church
;;http://projects.csail.mit.edu/church/wiki/Conditioning
(defn ^{:dynamic true
        :doc   "Taken from the Church examples."} 
  eye-color
  [person] 
  (rand-nth '(blue green brown)))

;;Persistent randomized functions
(query-by-rejection
 [bob-1   (eye-color :bob)
  alice-1 (eye-color :alice)
  bob-2   (eye-color :bob)
  :where (flip 0.01)
  :memobound [eye-color]]
 [bob-1 alice-1 bob-2])

;;A complex query
(defn complex-samples []
  (sample-by-rejection 
   10000
   [works-in-hospital (flip 0.01)
    smokes            (flip 0.2)
    lung-cancer       (or (flip 0.01) 
                          (and smokes (flip 0.02)))
    TB                (or (flip 0.005) 
                          (and works-in-hospital (flip 0.01)))
    cold              (or (flip 0.2) 
                          (and works-in-hospital (flip 0.25)))
    stomach-flu      (flip 0.1)
    other            (flip 0.1)
    cough            (or (and cold (flip 0.5)) 
                         (and lung-cancer (flip 0.3)) 
                         (and TB (flip 0.7)) 
                         (and other (flip 0.01)))
    fever            (or (and cold (flip 0.3)) 
                         (and stomach-flu (flip 0.5))
                         (and TB (flip 0.2))
                         (and other (flip 0.01)))
    chest-pain       (or (and lung-cancer (flip 0.4)) 
                         (and TB (flip 0.5)) 
                         (and other( flip 0.01)))
    shortness-of-breath (or (and lung-cancer (flip 0.4)) 
                            (and TB (flip 0.5))
                            (and other (flip 0.01)))
    :where (and cough chest-pain shortness-of-breath)]
   (list lung-cancer TB)))


(defn ^{:dynamic true} strength 
  [person]
  (if (flip) 10 5))

(defn lazy 
  [person] 
  (flip (/ 1 3)))

(defn contribution 
  [person]
  (if (lazy person) 
    (/ (strength person) 2) 
    (strength person)))

(defn total-pulling 
  [team]
  (->> team
       (map contribution)
       (reduce +)))

(defn winner [team1 team2]
  (if (< (total-pulling team1) (total-pulling team2)) 
    'team2 'team1))

;;Using persistent values defined outside the query 
(defn tug-of-war-sample []
  (sample-by-rejection 
   10000
   [:memobound  [strength]
    :where      (and (= 'team1 (winner '(bob mary) '(tom sue)))
                     (= 'team1  (winner '(bob sue) '(tom jim))))]
   (strength 'bob)))