Clojure range-case macro

Question

In the book "The Scheme Programming Language, 4th Edition", by R. Kent Dybvig, on page 86, the author has written a define-syntax (Scheme macro) for a case statement that accepts ranges for its conditions. I thought I would try this in Clojure.

Here is the result.

How can I improve this? I use :ii, :ie, :ei, and :ee for the range operators, indicating inclusive-inclusive, inclusive-exclusive, exclusive-inclusive, and exclusive-exclusive, respectively. Is there a better choice?

I chose to expand to a cond rather than discrete if statements because I felt that I would gain the benefit from any future improvements to the cond macro.

(defmacro range-case [target & cases]
  "Compare the target against a set of ranges or constant values and return
   the first one that matches. If none match, and there exists a case with the
   value :else, return that target. Each range consists of a vector containing
   3 terms: a lower bound, an operator, and an upper bound. The operator must
   be one of :ii, :ie, :ei, or :ee, which indicate that the range comparison
   should be inclusive-inclusive, inclusive-exclusive, exclusive-inclusive,
   or exclusive-exclusive, respectively.
   Example:
     (range-case target
                 [0.0 :ie 1.0] :greatly-disagree
                 [1.0 :ie 2.0] :disagree
                 [2.0 :ie 3.0] :neutral
                 [3.0 :ie 4.0] :agree
                 [4.0 :ii 5.0] :strongly-agree
                 42 :the-answer
                 :else :do-not-care)
   expands to
     (cond
       (and (<= 0.0 target) (< target 1.0)) :greatly-disagree
       (and (<= 1.0 target) (< target 2.0)) :disagree
       (and (<= 2.0 target) (< target 3.0)) :neutral
       (and (<= 3.0 target) (< target 4.0)) :agree
       (<= 4.0 target 5.0) :strongly-agree
       (= target 42) :the-answer
       :else :do-not-care)
    Test cases:
      (use '[clojure.test :only (deftest is run-tests)])
      (deftest unit-tests
        (letfn [(test-range-case [target]
                                 (range-case target
                                             [0.0 :ie 1.0] :greatly-disagree
                                             [1.0 :ie 2.0] :disagree
                                             [2.0 :ie 3.0] :neutral
                                             [3.0 :ie 4.0] :agree
                                             [4.0 :ii 5.0] :strongly-agree
                                             42 :the-answer
                                             :else :do-not-care))]
      (is (= (test-range-case 0.0) :greatly-disagree))
      (is (test-range-case 0.5) :greatly-disagree)
      (is (test-range-case 1.0) :disagree)
      (is (test-range-case 1.5) :disagree)
      (is (test-range-case 2.0) :neutral)
      (is (test-range-case 2.5) :neutral)
      (is (test-range-case 3.0) :agree)
      (is (test-range-case 3.5) :agree)
      (is (test-range-case 4.0) :strongly-agree)
      (is (test-range-case 4.5) :strongly-agree)
      (is (test-range-case 5.0) :strongly-agree)
      (is (test-range-case 42) :the-answer)
      (is (test-range-case -1) :do-not-care)))
    (run-tests)"
  `(cond
    ~@(loop [cases cases ret []]
        (cond
         (empty? cases)
         ret

         (odd? (count cases))
         (throw (IllegalArgumentException.
                 (str "no matching clause: " (first cases))))

         (= :else (first cases))
         (recur (drop 2 cases) (conj ret :else (second cases)))

         (vector? (first cases))
         (let [[lower-bound operator upper-bound] (first cases)
               clause (second cases)

               [condition clause]
               (case operator
                     :ii `((<= ~lower-bound ~target ~upper-bound) ~clause)
                     :ie `((and (<= ~lower-bound ~target)
                                (< ~target ~upper-bound)) ~clause)
                     :ei `((and (< ~lower-bound ~target)
                                (<= ~target ~upper-bound)) ~clause)
                     :ee `((< ~lower-bound ~target ~upper-bound) ~clause)
                     (throw (IllegalArgumentException.
                             (str "unknown operator: " operator))))]
           (recur (drop 2 cases) (conj ret condition clause)))

         :else
         (let [[condition clause]
               `[(= ~target ~(first cases)) ~(second cases)]]
           (recur (drop 2 cases) (conj ret condition clause)))))))

UPDATE: Here is the revised version incorporating changes suggested by mikera and kotarak:

(defmacro range-case [target & cases]
  "Compare the target against a set of ranges or constant values and return
   the first one that matches. If none match, and there exists a case with the
   value :else, return that target. Each range consists of a vector containing
   one of the following patterns:
     [upper-bound]                 if this is the first pattern, match any
                                   target <= upper-bound
                                   otherwise, match any target <= previous
                                   upper-bound and <= upper-bound
     [< upper-bound]               if this is the first pattern, match any
                                   target < upper-bound
                                   otherwise, match any target <= previous
                                   upper-bound and < upper-bound
     [lower-bound upper-bound]     match any target where lower-bound <= target
                                   and target <= upper-bound
     [< lower-bound upper-bound]   match any target where lower-bound < target
                                   and target <= upper-bound
     [lower-bound < upper-bound]   match any target where lower-bound <= target
                                   and target < upper-bound
     [< lower-bound < upper-bound] match any target where lower-bound < target
                                   and target < upper-bound
   Example:
     (range-case target
                 [0 < 1] :strongly-disagree
                 [< 2]     :disagree
                 [< 3]     :neutral
                 [< 4]     :agree
                 [5]       :strongly-agree
                 42          :the-answer
                 :else       :do-not-care)
   expands to
     (cond
       (and (<= 0 target) (< target 1)) :strongly-disagree
       (and (<= 1 target) (< target 2)) :disagree
       (and (<= 2 target) (< target 3)) :neutral
       (and (<= 3 target) (< target 4)) :agree
       (<= 4 target 5) :strongly-agree
       (= target 42) :the-answer
       :else :do-not-care)
    Test cases:
      (use '[clojure.test :only (deftest is run-tests)])
      (deftest unit-tests
        (letfn [(test-range-case [target]
                                 (range-case target
                                             [0 < 1] :strongly-disagree
                                             [< 2]   :disagree
                                             [< 3]   :neutral
                                             [< 4]   :agree
                                             [5]     :strongly-agree
                                             42      :the-answer
                                             :else   :do-not-care))]
      (is (= (test-range-case 0) :strongly-disagree))
      (is (= (test-range-case 0.5) :strongly-disagree))
      (is (= (test-range-case 1) :disagree))
      (is (= (test-range-case 1.5) :disagree))
      (is (= (test-range-case 2) :neutral))
      (is (= (test-range-case 2.5) :neutral))
      (is (= (test-range-case 3) :agree))
      (is (= (test-range-case 3.5) :agree))
      (is (= (test-range-case 4) :strongly-agree))
      (is (= (test-range-case 4.5) :strongly-agree))
      (is (= (test-range-case 5) :strongly-agree))
      (is (= (test-range-case 42) :the-answer))
      (is (= (test-range-case -1) :do-not-care))))
    (run-tests)"
  (if (odd? (count cases))
    (throw (IllegalArgumentException. (str "no matching clause: "
                                           (first cases))))
    `(cond
      ~@(loop [cases cases ret [] previous-upper-bound nil]
          (cond
           (empty? cases)
           ret

           (= :else (first cases))
           (recur (drop 2 cases) (conj ret :else (second cases)) nil)

           (vector? (first cases))
           (let [condition (first cases)
                 clause (second cases)

                 [case-expr prev-upper-bound]
                 (let [length (count condition)]
                   (cond
                    (= length 1)
                    (let [upper-bound (first condition)]
                      [(if previous-upper-bound
                         `(and (<= ~previous-upper-bound ~target)
                               (<= ~target ~upper-bound))
                         `(<= ~target ~upper-bound))
                       upper-bound])

                    (= length 2)
                    (if (= '< (first condition))
                      (let [[_ upper-bound] condition]
                        [(if previous-upper-bound
                           `(and (<= ~previous-upper-bound ~target)
                                 (< ~target ~upper-bound))
                           `(< ~target ~upper-bound))
                         upper-bound])
                      (let [[lower-bound upper-bound] condition]
                        [`(and (<= ~lower-bound ~target)
                               (<= ~target ~upper-bound))
                         upper-bound]))

                    (= length 3)
                    (cond
                     (= '< (first condition))
                     (let [[_ lower-bound upper-bound] condition]
                       [`(and (< ~lower-bound ~target)
                              (<= ~target ~upper-bound))
                        upper-bound])

                     (= '< (second condition))
                     (let [[lower-bound _ upper-bound] condition]
                       [`(and (<= ~lower-bound ~target)
                              (< ~target ~upper-bound))
                        upper-bound])

                     :else
                     (throw (IllegalArgumentException. (str "unknown pattern: "
                                                            condition))))

                    (and (= length 4)
                         (= '< (first condition))
                         (= '< (nth condition 3)))
                    (let [[_ lower-bound _ upper-bound] condition]
                      [`(and (< ~lower-bound ~target) (< ~target ~upper-bound))
                       upper-bound])

                    :else
                    (throw (IllegalArgumentException. (str "unknown pattern: "
                                                           condition)))))]
             (recur (drop 2 cases)
                    (conj ret case-expr clause)
                    prev-upper-bound))

           :else
           (let [[condition clause]
                 `[(= ~target ~(first cases)) ~(second cases)]]
             (recur (drop 2 cases) (conj ret condition clause) nil)))))))

Answer 1

My initial take on it:

(defn make-case [test val]
  (if (vector? test)
    `((and ~@(for [[lower comp upper] (partition 3 2 test)]
               (list comp lower upper)))
      ~val)

    (list :else val)))

(defmacro range-case [& cases]
  (let [cases (partition 2 cases)]
    `(cond ~@(mapcat (partial apply make-case) cases))))

This requires a slight change to syntax, like this:

(range-case 
 [0.0 <= x < 1.0] :greatly-disagree
 [1.0 <= x < 2.0] :disagree
 [2.0 <= x < 3.0] :neutral
 [3.0 <= x < 4.0] :agree
 [4.0 <= x <= 5.0] :strongly-agree
 [42 = x] :the-answer
 :else :do-not-care)

My version may be violating the spirit of the original example, but "advantages" include:

1. You aren't hard-coded to a single target. You also aren't limited to two tests (lower test and upper test). You could do [0 < x <= y < 4 <= z] etc.
2. Syntax more closely resembles mathematical comparison notation.
3. Clojure's comparison operators can be passed as parameters themselves; no need to use keywords and translate those into comparison operators. This way, the comparison operators aren't hard-coded into the function, and removing this layer of indirection makes it read a bit better.
4. Equality is no longer a special case.

Disadvantages?

1. x is repeated a bunch of times. Is grabbing x and putting it at the top worth the increase in complexity and decrease in flexibility?
2. Like your original example, this uses infix notation. It may be a bit jarring, in a world of prefix notation.

Then again, at this point our macro isn't doing much more than changing square brackets into parens and anding a bunch of stuff together. So I question whether you really need a macro at all.

(defn ?? [& xs]
  (every? (fn [[lower comp upper]]
            (comp lower upper))
          (partition 3 2 xs)))

(cond
  (?? 0.0 <= x < 1.0) :greatly-disagree
  (?? 1.0 <= x < 2.0) :disagree
  (?? 2.0 <= x < 3.0) :neutral
  (?? 3.0 <= x < 4.0) :agree
  (?? 4.0 <= x <= 5.0) :strongly-agree
  (= 42 x) :the-answer
  :else :do-not-care)

Answer 2

I would also vote for something slightly more verbose but less ugly to read.

 (range-case target
   [(<= 0.0) (< 1.0)] :greatly-disagree
   [(<= 1.0) (< 2.0)] :disagree
   [(<= 2.0) (< 3.0)] :neutral
   [(<= 3.0) (< 4.0)] :agree
   (<= 4.0 5.0)       :strongly-agree
   42 :the-answer
   :else :do-not-care)

This could be a viable alternative.

Answer 3

Some ideas:

• Have a default value for the operator (e.g. ":ie" would probably be most natural in typical problems)
• Have one of the bounds default to the previous or following upper/lower bound so that you don't need to repeat the same bounding values.
• Consider ifs rather than cond so that you can do interval bisection (would be a performance win if you expect very large numbers of cases)

An alternative might be to make your macro work at the case level like follows:

(cond
  (in-range target [0.0 1.0]) :greatly-disagree)
  (in-range target [1.0 2.0]) :disagree)
  ...)

I personally like this because you can mix your range tests with other predicates if needed.