;;;; Implementation of general sets and bags for SRFI 113

;;; A "sob" object is the representation of both sets and bags.
;;; This allows each set-* and bag-* procedure to be implemented
;;; using the same code, without having to deal in ugly indirections
;;; over the field accessors.  There are three fields, "sob-multi?",
;;; "sob-hash-table", and "sob-comparator."

;;; The value of "sob-multi?" is #t for bags and #f for sets.
;;; "Sob-hash-table" maps the elements of the sob to the number of times
;;; the element appears, which is always 1 for a set, any positive value
;;; for a bag.  "Sob-comparator" is the comparator for the elements of
;;; the set.

;;; Note that sob-* procedures do not do type checking or (typically) the
;;; copying required for supporting pure functional update.  These things
;;; are done by the set-* and bag-* procedures, which are externally
;;; exposed (but trivial and mostly uncommented below).


;;; Shim to convert from SRFI 69 to the future "intermediate hash tables"
;;; SRFI.  Unfortunately, hash-table-fold is incompatible between the two
;;; and so is not usable.

;; This will be just "make-hash-table" in future.

(define (make-hash-table/comparator comparator)
  (make-hash-table (comparator-equality-predicate comparator)
                   (modulizer (comparator-hash-function comparator))))

;; These two procedures adjust for the mismatch between the hash functions
;; of SRFI 114, which return a potentially unbounded non-negative integer,
;; and the hash functions of SRFI 69, which expect to be able to pass
;; a second argument which is an upper bound.

(define (modulizer hash-function)
  (case-lambda
    ((obj) (hash-function obj))
    ((obj limit) (modulo (hash-function obj) limit))))

;; Simple renaming.  Chicken's implementation of SRFI 69 provides
;; hash-table-for-each as a non-standard extension, with the opposite
;; order, so in the Chicken module we suppress importing it to muffle
;; the conflict warning.

(define hash-table-contains? hash-table-exists?)

(define (hash-table-for-each proc hash-table)
  (hash-table-walk hash-table proc))


;;; Record definition and core typing/checking procedures

(define-record-type sob
  (raw-make-sob hash-table comparator multi?)
  sob?
  (hash-table sob-hash-table)
  (comparator sob-comparator)
  (multi? sob-multi?))

(define (set? obj) (and (sob? obj) (not (sob-multi? obj))))

(define (bag? obj) (and (sob? obj) (sob-multi? obj)))

(define (check-set obj) (if (not (set? obj)) (error "not a set" obj)))

(define (check-bag obj) (if (not (bag? obj)) (error "not a bag" obj)))

;; These procedures verify that not only are their arguments all sets
;; or all bags as the case may be, but also share the same comparator.

(define (check-all-sets list)
  (for-each (lambda (obj) (check-set obj)) list)
  (sob-check-comparators list))

(define (check-all-bags list)
  (for-each (lambda (obj) (check-bag obj)) list)
  (sob-check-comparators list))

(define (sob-check-comparators list)
  (if (not (null? list))
      (for-each
        (lambda (sob)
          (check-same-comparator (car list) sob))
        (cdr list))))

;; This procedure is used directly when there are exactly two arguments.

(define (check-same-comparator a b)
  (if (not (eq? (sob-comparator a) (sob-comparator b)))
    (error "different comparators" a b)))

;; This procedure defends against inserting an element
;; into a sob that violates its constructor, since
;; typical hash-table implementations don't check for us.

(define (check-element sob element)
  (comparator-check-type (sob-comparator sob) element))

;;; Constructors

;; Construct an arbitrary empty sob out of nothing.

(define (make-sob comparator multi?)
  (raw-make-sob (make-hash-table/comparator comparator) comparator multi?))

;; Copy a sob, sharing the constructor.

(define (sob-copy sob)
  (raw-make-sob (hash-table-copy (sob-hash-table sob))
            (sob-comparator sob)
            (sob-multi? sob)))

(define (set-copy set)
  (check-set set)
  (sob-copy set))

(define (bag-copy bag)
  (check-bag bag)
  (sob-copy bag))

;; Construct an empty sob that shares the constructor of an existing sob.

(define (sob-empty-copy sob)
  (make-sob (sob-comparator sob) (sob-multi? sob)))

;; Construct a set or a bag and insert elements into it.  These are the
;; simplest external constructors.

(define (set comparator . elements)
  (let ((result (make-sob comparator #f)))
    (for-each (lambda (x) (sob-increment! result x 1)) elements)
    result))

(define (bag comparator . elements)
  (let ((result (make-sob comparator #t)))
    (for-each (lambda (x) (sob-increment! result x 1)) elements)
    result))

;; The fundamental (as opposed to simplest) constructor: unfold the
;; results of iterating a function as a set.  In line with SRFI 1,
;; we provide an opportunity to map the sequence of seeds through a
;; mapper function.

(define (sob-unfold stop? mapper successor seed comparator multi?)
  (let ((result (make-sob comparator multi?)))
    (let loop ((seed seed))
      (if (stop? seed)
          result
          (begin
            (sob-increment! result (mapper seed) 1)
            (loop (successor seed)))))))

(define (set-unfold continue? mapper successor seed comparator)
  (sob-unfold continue? mapper successor seed comparator #f))

(define (bag-unfold continue? mapper successor seed comparator)
  (sob-unfold continue? mapper successor seed comparator #t))

;;; Predicates

;; Just a wrapper of hash-table-contains?.

(define (sob-contains? sob member)
  (hash-table-contains? (sob-hash-table sob) member))

(define (set-contains? set member)
  (check-set set)
  (sob-contains? set member))

(define (bag-contains? bag member)
  (check-bag bag)
  (sob-contains? bag member))

;; A sob is empty if its size is 0.

(define (sob-empty? sob)
  (= 0 (hash-table-size (sob-hash-table sob))))

(define (set-empty? set)
  (check-set set)
  (sob-empty? set))

(define (bag-empty? bag)
  (check-bag bag)
  (sob-empty? bag))

;; Two sobs are disjoint if, when looping through one, we can't find
;; any of its elements in the other.  We have to try both ways:
;; sob-half-disjoint checks just one direction for simplicity.

(define (sob-half-disjoint? a b)
  (let ((ha (sob-hash-table a))
        (hb (sob-hash-table b)))
    (call/cc
      (lambda (return)
        (hash-table-for-each
          (lambda (key val) (if (hash-table-contains? hb key) (return #f)))
          ha)
      #t))))

(define (set-disjoint? a b)
  (check-set a)
  (check-set b)
  (check-same-comparator a b)
  (and (sob-half-disjoint? a b) (sob-half-disjoint? b a)))

(define (bag-disjoint? a b)
  (check-bag a)
  (check-bag b)
  (check-same-comparator a b)
  (and (sob-half-disjoint? a b) (sob-half-disjoint? b a)))

;; Accessors

;; If two objects are indistinguishable by the comparator's
;; equality procedure, only one of them will be represented in the sob.
;; This procedure lets us find out which one it is; it will return
;; the value stored in the sob that is equal to the element.
;; Note that we have to search the whole hash table item by item.
;; The default is returned if there is no such element.

(define (sob-member sob element default)
  (define (same? a b) (=? (sob-comparator sob) a b))
  (call/cc
    (lambda (return)
      (hash-table-for-each
        (lambda (key val) (if (same? key element) (return key)))
        (sob-hash-table sob))
      default)))

(define (set-member set element default)
  (check-set set)
  (sob-member set element default))

(define (bag-member bag element default)
  (check-bag bag)
  (sob-member bag element default))

;; Retrieve the comparator.

(define (set-element-comparator set)
  (check-set set)
  (sob-comparator set))

(define (bag-element-comparator bag)
  (check-bag bag)
  (sob-comparator bag))


;; Updaters (pure functional and linear update)

;; The primitive operation for adding an element to a sob.
;; There are a few cases where we bypass this for efficiency.

(define (sob-increment! sob element count)
  (check-element sob element)
  (hash-table-update!/default
    (sob-hash-table sob)
    element
    (if (sob-multi? sob)
      (lambda (value) (+ value count))
      (lambda (value) 1))
    0))

;; The primitive operation for removing an element from a sob.  Note this
;; procedure is incomplete: it allows the count of an element to drop below 1.
;; Therefore, whenever it is used it is necessary to call sob-cleanup!
;; to fix things up.  This is done because it is unsafe to remove an
;; object from a hash table while iterating through it.

(define (sob-decrement! sob element count)
  (hash-table-update!/default
    (sob-hash-table sob)
    element
    (lambda (value) (- value count))
    0))

;; This is the cleanup procedure, which happens in two passes: it
;; iterates through the sob, deciding which elements to remove (those
;; with non-positive counts), and collecting them in a list.  When the
;; iteration is done, it is safe to remove the elements using the list,
;; because we are no longer iterating over the hash table.  It returns
;; its argument, because it is often tail-called at the end of some
;; procedure that wants to return the clean sob.

(define (sob-cleanup! sob)
  (let ((ht (sob-hash-table sob)))
    (for-each (lambda (key) (hash-table-delete! ht key))
              (nonpositive-keys ht))
    sob))

(define (nonpositive-keys ht)
  (let ((result '()))
    (hash-table-for-each
      (lambda (key value)
        (when (<= value 0)
          (set! result (cons key result))))
      ht)
    result))

;; We expose these for bags but not sets.

(define (bag-increment! bag element count)
  (check-bag bag)
  (sob-increment! bag element count)
  bag)

(define (bag-decrement! bag element count)
  (check-bag bag)
  (sob-decrement! bag element count)
  (sob-cleanup! bag)
  bag)

;; The primitive operation to add elements from a list.  We expose
;; this two ways: with a list argument and with multiple arguments.

(define (sob-adjoin-all! sob elements)
  (for-each
    (lambda (elem)
      (sob-increment! sob elem 1))
    elements))

(define (set-adjoin! set . elements)
  (check-set set)
  (sob-adjoin-all! set elements)
  set)

(define (bag-adjoin! bag . elements)
  (check-bag bag)
  (sob-adjoin-all! bag elements)
  bag)


;; These versions copy the set or bag before adjoining.

(define (set-adjoin set . elements)
  (check-set set)
  (let ((result (sob-copy set)))
    (sob-adjoin-all! result elements)
    result))

(define (bag-adjoin bag . elements)
  (check-bag bag)
  (let ((result (sob-copy bag)))
    (sob-adjoin-all! result elements)
    result))

;; Given an element which resides in a set, this makes sure that the
;; specified element is represented by the form given.  Thus if a
;; sob contains 2 and the equality predicate is =, then calling
;; (sob-replace! sob 2.0) will replace the 2 with 2.0.  Does nothing
;; if there is no such element in the sob.

(define (sob-replace! sob element)
  (let* ((comparator (sob-comparator sob))
         (= (comparator-equality-predicate comparator))
         (ht (sob-hash-table sob)))
    (comparator-check-type comparator element)
    (call/cc
      (lambda (return)
        (hash-table-for-each
          (lambda (key value)
            (when (= key element)
              (hash-table-delete! ht key)
              (hash-table-set! ht element value)
              (return sob)))
          ht)
        sob))))

(define (set-replace! set element)
  (check-set set)
  (sob-replace! set element)
  set)

(define (bag-replace! bag element)
  (check-bag bag)
  (sob-replace! bag element)
  bag)

;; Non-destructive versions that copy the set first.  Yes, a little
;; bit inefficient because it copies the element to be replaced before
;; actually replacing it.

(define (set-replace set element)
  (check-set set)
  (let ((result (sob-copy set)))
    (sob-replace! result element)
    result))

(define (bag-replace bag element)
  (check-bag bag)
  (let ((result (sob-copy bag)))
    (sob-replace! result element)
    result))

;; The primitive operation to delete elemnets from a list.
;; Like sob-adjoin-all!, this is exposed two ways.  It calls
;; sob-cleanup! itself, so its callers don't need to (though it is safe
;; to do so.)

(define (sob-delete-all! sob elements)
  (for-each (lambda (element) (sob-decrement! sob element 1)) elements)
  (sob-cleanup! sob)
  sob)

(define (set-delete! set . elements)
  (check-set set)
  (sob-delete-all! set elements))

(define (bag-delete! bag . elements)
  (check-bag bag)
  (sob-delete-all! bag elements))

(define (set-delete-all! set elements)
  (check-set set)
  (sob-delete-all! set elements))

(define (bag-delete-all! bag elements)
  (check-bag bag)
  (sob-delete-all! bag elements))

;; Non-destructive version copy first; this is inefficient.

(define (set-delete set . elements)
  (check-set set)
  (sob-delete-all! (sob-copy set) elements))

(define (bag-delete bag . elements)
  (check-bag bag)
  (sob-delete-all! (sob-copy bag) elements))

(define (set-delete-all set elements)
  (check-set set)
  (sob-delete-all! (sob-copy set) elements))

(define (bag-delete-all bag elements)
  (check-bag bag)
  (sob-delete-all! (sob-copy bag) elements))

;; Flag used by sob-search! to represent a missing object.

(define missing (string-copy "missing"))

;; Searches and then dispatches to user-defined procedures on failure
;; and success, which in turn should reinvoke a procedure to take some
;; action on the set (insert, ignore, replace, or remove).

(define (sob-search! sob element failure success)
  (define (insert obj)
    (sob-increment! sob element 1)
    (values sob obj))
  (define (ignore obj)
    (values sob obj))
  (define (update new-elem obj)
    (sob-decrement! sob element 1)
    (sob-increment! sob new-elem 1)
    (values (sob-cleanup! sob) obj))
  (define (remove obj)
    (sob-decrement! sob element 1)
    (values (sob-cleanup! sob) obj))
  (let ((true-element (sob-member sob element missing)))
    (if (eq? true-element missing)
      (failure insert ignore)
      (success true-element update remove))))

(define (set-search! set element failure success)
  (check-set set)
  (sob-search! set element failure success))

(define (bag-search! bag element failure success)
  (check-bag bag)
  (sob-search! bag element failure success))

;; Return the size of a sob.  If it's a set, we can just use the
;; number of associations in the hash table, but if it's a bag, we
;; have to add up the counts.

(define (sob-size sob)
  (if (sob-multi? sob)
    (let ((result 0))
      (hash-table-for-each
        (lambda (elem count) (set! result (+ count result)))
        (sob-hash-table sob))
      result)
    (hash-table-size (sob-hash-table sob))))

(define (set-size set)
  (check-set set)
  (sob-size set))

(define (bag-size bag)
  (check-bag bag)
  (sob-size bag))

;; Search a sob to find something that matches a predicate.  You don't
;; know which element you will get, so this is not as useful as finding
;; an element in a list or other ordered container.  If it's not there,
;; call the failure thunk.

(define (sob-find pred sob failure)
  (call/cc
    (lambda (return)
      (hash-table-for-each
        (lambda (key value)
          (if (pred key) (return key)))
        (sob-hash-table sob))
    (failure))))

(define (set-find pred set failure)
  (check-set set)
  (sob-find pred set failure))

(define (bag-find pred bag failure)
  (check-bag bag)
  (sob-find pred bag failure))

;; Count the number of elements in the sob that satisfy the predicate.
;; This is a special case of folding.

(define (sob-count pred sob)
  (sob-fold
    (lambda (elem total) (if (pred elem) (+ total 1) total))
    0
    sob))

(define (set-count pred set)
  (check-set set)
  (sob-count pred set))

(define (bag-count pred bag)
  (check-bag bag)
  (sob-count pred bag))

;; Check if any of the elements in a sob satisfy a predicate.  Breaks out
;; early (with call/cc) if a success is found.

(define (sob-any? pred sob)
  (call/cc
    (lambda (return)
      (hash-table-for-each
        (lambda (elem value) (if (pred elem) (return #t)))
        (sob-hash-table sob))
      #f)))

(define (set-any? pred set)
  (check-set set)
  (sob-any? pred set))

(define (bag-any? pred bag)
  (check-bag bag)
  (sob-any? pred bag))

;; Analogous to set-any?.  Breaks out early if a failure is found.

(define (sob-every? pred sob)
  (call/cc
    (lambda (return)
      (hash-table-for-each
        (lambda (elem value) (if (not (pred elem)) (return #f)))
        (sob-hash-table sob))
      #t)))

(define (set-every? pred set)
  (check-set set)
  (sob-every? pred set))

(define (bag-every? pred bag)
  (check-bag bag)
  (sob-every? pred bag))


;;; Mapping and folding

;; A utility for iterating a command n times.  This is used by sob-for-each
;; to execute a procedure over the repeated elements in a bag.  Because
;; of the representation of sets, it works for them too.

(define (do-n-times cmd n)
  (let loop ((n n))
    (when (> n 0)
      (cmd)
      (loop (- n 1)))))

;; Basic iterator over a sob.

(define (sob-for-each proc sob)
  (hash-table-for-each
    (lambda (key value) (do-n-times (lambda () (proc key)) value))
    (sob-hash-table sob)))

(define (set-for-each proc set)
  (check-set set)
  (sob-for-each proc set))

(define (bag-for-each proc bag)
  (check-bag bag)
  (sob-for-each proc bag))

;; Fundamental mapping operator.  We map over the associations directly,
;; because each instance of an element in a bag will be treated identically
;; anyway; we insert them all at once with sob-increment!.

(define (sob-map proc comparator sob)
  (let ((result (make-sob comparator (sob-multi? sob))))
    (hash-table-for-each
      (lambda (key value) (sob-increment! result (proc key) value))
      (sob-hash-table sob))
    result))

(define (set-map comparator proc set)
  (check-set set)
  (sob-map comparator proc set))

(define (bag-map comparator proc bag)
  (check-bag bag)
  (sob-map comparator proc bag))

;; The fundamental deconstructor.  Note that there are no left vs. right
;; folds because there is no order.  Each element in a bag is fed into
;; the fold separately.

(define (sob-fold proc nil sob)
  (let ((result nil))
    (sob-for-each
      (lambda (elem) (set! result (proc elem result)))
      sob)
    result))

(define (set-fold proc nil set)
  (check-set set)
  (sob-fold proc nil set))

(define (bag-fold proc nil bag)
  (check-bag bag)
  (sob-fold proc nil bag))

;; Process every element and copy the ones that satisfy the predicate.
;; Identical elements are processed all at once.  This is used for both
;; filter and remove.

(define (sob-filter pred sob)
  (let ((result (sob-empty-copy sob)))
    (hash-table-for-each
      (lambda (key value)
        (if (pred key) (sob-increment! result key value)))
      (sob-hash-table sob))
    result))

(define (set-filter pred set)
  (check-set set)
  (sob-filter pred set))

(define (bag-filter pred bag)
  (check-bag bag)
  (sob-filter pred bag))

(define (set-remove pred set)
  (check-set set)
  (sob-filter (lambda (x) (not (pred x))) set))

(define (bag-remove pred bag)
  (check-bag bag)
  (sob-filter (lambda (x) (not (pred x))) bag))

;; Process each element and remove those that don't satisfy the filter.
;; This does its own cleanup, and is used for both filter! and remove!.

(define (sob-filter! pred sob)
  (hash-table-for-each
    (lambda (key value)
      (if (not (pred key)) (sob-decrement! sob key value)))
    (sob-hash-table sob))
  (sob-cleanup! sob))

(define (set-filter! pred set)
  (check-set set)
  (sob-filter! pred set))

(define (bag-filter! pred bag)
  (check-bag bag)
  (sob-filter! pred bag))

(define (set-remove! pred set)
  (check-set set)
  (sob-filter! (lambda (x) (not (pred x))) set))

(define (bag-remove! pred bag)
  (check-bag bag)
  (sob-filter! (lambda (x) (not (pred x))) bag))

;; Create two sobs and copy the elements that satisfy the predicate into
;; one of them, all others into the other.  This is more efficient than
;; filtering and removing separately.

(define (sob-partition pred sob)
  (let ((res1 (sob-empty-copy sob))
        (res2 (sob-empty-copy sob)))
    (hash-table-for-each
      (lambda (key value)
        (if (pred key)
          (sob-increment! res1 key value)
          (sob-increment! res2 key value)))
      (sob-hash-table sob))
    (values res1 res2)))

(define (set-partition pred set)
  (check-set set)
  (sob-partition pred set))

(define (bag-partition pred bag)
  (check-bag bag)
  (sob-partition pred bag))

;; Create a sob and iterate through the given sob.  Anything that satisfies
;; the predicate is left alone; anything that doesn't is removed from the
;; given sob and added to the new sob.

(define (sob-partition! pred sob)
  (let ((result (sob-empty-copy sob)))
    (hash-table-for-each
      (lambda (key value)
        (if (not (pred key))
          (begin
            (sob-decrement! sob key value)
            (sob-increment! result key value))))
      (sob-hash-table sob))
    (values (sob-cleanup! sob) result)))

(define (set-partition! pred set)
  (check-set set)
  (sob-partition! pred set))

(define (bag-partition! pred bag)
  (check-bag bag)
  (sob-partition! pred bag))


;;; Copying and conversion

;;; Convert a sob to a list; a special case of sob-fold.

(define (sob->list sob)
  (sob-fold (lambda (elem list) (cons elem list)) '() sob))

(define (set->list set)
  (check-set set)
  (sob->list set))

(define (bag->list bag)
  (check-bag bag)
  (sob->list bag))

;; Convert a list to a sob.  Probably could be done using unfold, but
;; since sobs are mutable anyway, it's just as easy to add the elements
;; by side effect.  

(define (list->sob! sob list)
  (for-each (lambda (elem) (sob-increment! sob elem 1)) list)
  sob)

(define (list->set comparator list)
  (list->sob! (make-sob comparator #f) list))

(define (list->bag comparator list)
  (list->sob! (make-sob comparator #t) list))

(define (list->set! set list)
  (check-set set)
  (list->sob! set list))

(define (list->bag! bag list)
  (check-bag bag)
  (list->sob! bag list))


;;; Subsets

;; All of these procedures follow the same pattern.  The
;; sob<op>? procedures are case-lambdas that reduce the multi-argument
;; case to the two-argument case.  As usual, the set<op>? and
;; bag<op>? procedures are trivial layers over the sob<op>? procedure.
;; The dyadic-sob<op>? procedures are where it gets interesting, so see
;; the comments on them.

(define sob=?
  (case-lambda
    ((sob) #t)
    ((sob1 sob2) (dyadic-sob=? sob1 sob2))
    ((sob1 sob2 . sobs)
     (and (dyadic-sob=? sob1 sob2)
          (apply sob=? sob2 sobs)))))

(define (set=? . sets)
  (check-all-sets sets)
  (apply sob=? sets))

(define (bag=? . bags)
  (check-all-bags bags)
  (apply sob=? bags))

;; First we check that there are the same number of entries in the
;; hashtables of the two sobs; if that's not true, they can't be equal.
;; Then we check that for each key, the values are the same (where
;; being absent counts as a value of 0).  If any values aren't equal,
;; again they can't be equal.

(define (dyadic-sob=? sob1 sob2)
  (call/cc
    (lambda (return)
      (let ((ht1 (sob-hash-table sob1))
            (ht2 (sob-hash-table sob2)))
        (if (not (= (hash-table-size ht1) (hash-table-size ht2)))
          (return #f))
        (hash-table-for-each
          (lambda (key value)
            (if (not (= value (hash-table-ref/default ht2 key 0)))
              (return #f)))
          ht1))
     #t)))

(define sob<=?
  (case-lambda
    ((sob) #t)
    ((sob1 sob2) (dyadic-sob<=? sob1 sob2))
    ((sob1 sob2 . sobs)
     (and (dyadic-sob<=? sob1 sob2)
          (apply sob<=? sob2 sobs)))))

(define (set<=? . sets)
  (check-all-sets sets)
  (apply sob<=? sets))

(define (bag<=? . bags)
  (check-all-bags bags)
  (apply sob<=? bags))

;; This is analogous to dyadic-sob=?, except that we have to check
;; both sobs to make sure each value is <= in order to be sure
;; that we've traversed all the elements in either sob.

(define (dyadic-sob<=? sob1 sob2)
  (call/cc
    (lambda (return)
      (let ((ht1 (sob-hash-table sob1))
            (ht2 (sob-hash-table sob2)))
        (if (not (<= (hash-table-size ht1) (hash-table-size ht2)))
          (return #f))
        (hash-table-for-each
          (lambda (key value)
            (if (not (<= value (hash-table-ref/default ht2 key 0)))
              (return #f)))
          ht1))
      #t)))

(define sob>?
  (case-lambda
    ((sob) #t)
    ((sob1 sob2) (dyadic-sob>? sob1 sob2))
    ((sob1 sob2 . sobs)
     (and (dyadic-sob>? sob1 sob2)
          (apply sob>? sob2 sobs)))))

(define (set>? . sets)
  (check-all-sets sets)
  (apply sob>? sets))

(define (bag>? . bags)
  (check-all-bags bags)
  (apply sob>? bags))

;; > is the negation of <=.  Note that this is only true at the dyadic
;; level; we can't just replace sob>? with a negation of sob<=?.

(define (dyadic-sob>? sob1 sob2)
  (not (dyadic-sob<=? sob1 sob2)))

(define sob<?
  (case-lambda
    ((sob) #t)
    ((sob1 sob2) (dyadic-sob<? sob1 sob2))
    ((sob1 sob2 . sobs)
     (and (dyadic-sob<? sob1 sob2)
          (apply sob<? sob2 sobs)))))

(define (set<? . sets)
  (check-all-sets sets)
  (apply sob<? sets))

(define (bag<? . bags)
  (check-all-bags bags)
  (apply sob<? bags))

;; < is the inverse of >.  Again, this is only true dyadically.

(define (dyadic-sob<? sob1 sob2)
  (dyadic-sob>? sob2 sob1))

(define sob>=?
  (case-lambda
    ((sob) #t)
    ((sob1 sob2) (dyadic-sob>=? sob1 sob2))
    ((sob1 sob2 . sobs)
     (and (dyadic-sob>=? sob1 sob2)
          (apply sob>=? sob2 sobs)))))

(define (set>=? . sets)
  (check-all-sets sets)
  (apply sob>=? sets))

(define (bag>=? . bags)
  (check-all-bags bags)
  (apply sob>=? bags))

;; Finally, >= is the negation of <.  Good thing we have tail recursion.

(define (dyadic-sob>=? sob1 sob2)
  (not (dyadic-sob<? sob1 sob2)))


;;; Set theory operations

;; A trivial helper function which upper-bounds n by one if multi? is false.

(define (max-one n multi?)
    (if multi? n (if (> n 1) 1 n)))

;; The logic of union, intersection, difference, and sum is the same: the
;; sob-* and sob-*! procedures do the reduction to the dyadic-sob-*!
;; procedures.  The difference is that the sob-* procedures allocate
;; an empty copy of the first sob to accumulate the results in, whereas
;; the sob-*!  procedures work directly in the first sob.

;; Note that there is no set-sum, as it is the same as set-union.

(define (sob-union sob1 sob2 . sobs)
  (let ((result (sob-empty-copy sob1)))
    (dyadic-sob-union! result sob1 sob2)
    (for-each
      (lambda (sob) (dyadic-sob-union! result result sob))
      sobs)
    result))

;; For union, we take the max of the counts of each element found
;; in either sob and put that in the result.  On the pass through
;; sob2, we know that the intersection is already accounted for,
;; so we just copy over things that aren't in sob1.

(define (dyadic-sob-union! result sob1 sob2)
  (let ((sob1-ht (sob-hash-table sob1))
        (sob2-ht (sob-hash-table sob2))
        (result-ht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (key value1)
        (let ((value2 (hash-table-ref/default sob2-ht key 0)))
          (hash-table-set! result-ht key (max value1 value2))))
      sob1-ht)
    (hash-table-for-each
      (lambda (key value2)
        (let ((value1 (hash-table-ref/default sob1-ht key 0)))
          (if (= value1 0)
              (hash-table-set! result-ht key value2))))
      sob2-ht)))

(define (set-union . sets)
  (check-all-sets sets)
  (apply sob-union sets))

(define (bag-union . bags)
  (check-all-bags bags)
  (apply sob-union bags))

(define (sob-union! sob1 sob2 . sobs)
  (dyadic-sob-union! sob1 sob1 sob2)
  (for-each
    (lambda (sob) (dyadic-sob-union! sob1 sob1 sob))
    sobs)
  sob1)

(define (set-union! . sets)
  (check-all-sets sets)
  (apply sob-union! sets))

(define (bag-union! . bags)
  (check-all-bags bags)
  (apply sob-union! bags))

(define (sob-intersection sob1 sob2 . sobs)
  (let ((result (sob-empty-copy sob1)))
    (dyadic-sob-intersection! result sob1 sob2)
    (for-each
      (lambda (sob) (dyadic-sob-intersection! result result sob))
      sobs)
    (sob-cleanup! result)))

;; For intersection, we compute the min of the counts of each element.
;; We only have to scan sob1.  We clean up the result when we are
;; done, in case it is the same as sob1.

(define (dyadic-sob-intersection! result sob1 sob2)
  (let ((sob1-ht (sob-hash-table sob1))
        (sob2-ht (sob-hash-table sob2))
        (result-ht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (key value1)
        (let ((value2 (hash-table-ref/default sob2-ht key 0)))
          (hash-table-set! result-ht key (min value1 value2))))
      sob1-ht)))

(define (set-intersection . sets)
  (check-all-sets sets)
  (apply sob-intersection sets))

(define (bag-intersection . bags)
  (check-all-bags bags)
  (apply sob-intersection bags))

(define (sob-intersection! sob1 sob2 . sobs)
  (dyadic-sob-intersection! sob1 sob1 sob2)
  (for-each
    (lambda (sob) (dyadic-sob-intersection! sob1 sob1 sob))
    sobs)
  (sob-cleanup! sob1))

(define (set-intersection! . sets)
  (check-all-sets sets)
  (apply sob-intersection! sets))

(define (bag-intersection! . bags)
  (check-all-bags bags)
  (apply sob-intersection! bags))

(define (sob-difference sob1 sob2 . sobs)
  (let ((result (sob-empty-copy sob1)))
    (dyadic-sob-difference! result sob1 sob2)
    (for-each
      (lambda (sob) (dyadic-sob-difference! result result sob))
      sobs)
    (sob-cleanup! result)))

;; For difference, we use (big surprise) the numeric difference, bounded
;; by zero.  We only need to scan sob1, but we clean up the result in
;; case it is the same as sob1.

(define (dyadic-sob-difference! result sob1 sob2)
  (let ((sob1-ht (sob-hash-table sob1))
        (sob2-ht (sob-hash-table sob2))
        (result-ht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (key value1)
        (let ((value2 (hash-table-ref/default sob2-ht key 0)))
          (hash-table-set! result-ht key (- value1 value2))))
      sob1-ht)))

(define (set-difference . sets)
  (check-all-sets sets)
  (apply sob-difference sets))

(define (bag-difference . bags)
  (check-all-bags bags)
  (apply sob-difference bags))

(define (sob-difference! sob1 sob2 . sobs)
  (dyadic-sob-difference! sob1 sob1 sob2)
  (for-each
    (lambda (sob) (dyadic-sob-difference! sob1 sob1 sob))
    sobs)
  (sob-cleanup! sob1))

(define (set-difference! . sets)
  (check-all-sets sets)
  (apply sob-difference! sets))

(define (bag-difference! . bags)
  (check-all-bags bags)
  (apply sob-difference! bags))

(define (sob-sum sob1 sob2 . sobs)
  (let ((result (sob-empty-copy sob1)))
    (dyadic-sob-sum! result sob1 sob2)
    (for-each
      (lambda (sob) (dyadic-sob-sum! result result sob))
      sobs)
    result))

;; Sum is just like union, except that we take the sum rather than the max.

(define (dyadic-sob-sum! result sob1 sob2)
  (let ((sob1-ht (sob-hash-table sob1))
        (sob2-ht (sob-hash-table sob2))
        (result-ht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (key value1)
        (let ((value2 (hash-table-ref/default sob2-ht key 0)))
          (hash-table-set! result-ht key (+ value1 value2))))
      sob1-ht)
    (hash-table-for-each
      (lambda (key value2)
        (let ((value1 (hash-table-ref/default sob1-ht key 0)))
          (if (= value1 0)
              (hash-table-set! result-ht key value2))))
      sob2-ht)))


;; Sum is defined for bags only; for sets, it is the same as union.

(define (bag-sum . bags)
  (check-all-bags bags)
  (apply sob-sum bags))

(define (sob-sum! sob1 sob2 . sobs)
  (dyadic-sob-sum! sob1 sob1 sob2)
  (for-each
    (lambda (sob) (dyadic-sob-sum! sob1 sob1 sob))
    sobs)
  sob1)

(define (bag-sum! . bags)
  (check-all-bags bags)
  (apply sob-sum! bags))

;; For xor exactly two arguments are required, so the above structures are
;; not necessary.  This version accepts a result sob and computes the
;; absolute difference between the counts in the first sob and the
;; corresponding counts in the second.  

;; We start by copying the entries in the second sob but not the first
;; into the first.  Then we scan the first sob, computing the absolute
;; difference of the values and writing them back into the first sob.
;; It's essential to scan the second sob first, as we are not going to
;; damage it in the process.  (Hat tip: Sam Tobin-Hochstadt.)

(define (sob-xor! result sob1 sob2)
  (let ((sob1-ht (sob-hash-table sob1))
        (sob2-ht (sob-hash-table sob2))
        (result-ht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (key value2)
        (let ((value1 (hash-table-ref/default sob1-ht key 0)))
          (if (= value1 0)
              (hash-table-set! result-ht key value2))))
      sob2-ht)
    (hash-table-for-each
      (lambda (key value1)
        (let ((value2 (hash-table-ref/default sob2-ht key 0)))
          (hash-table-set! result-ht key (abs (- value1 value2)))))
      sob1-ht)
    (sob-cleanup! result)))

(define (set-xor set1 set2)
  (check-set set1)
  (check-set set2)
  (check-same-comparator set1 set2)
  (sob-xor! (sob-empty-copy set1) set1 set2))

(define (bag-xor bag1 bag2)
  (check-bag bag1)
  (check-bag bag2)
  (check-same-comparator bag1 bag2)
  (sob-xor! (sob-empty-copy bag1) bag1 bag2))

(define (set-xor! set1 set2)
  (check-set set1)
  (check-set set2)
  (check-same-comparator set1 set2)
  (sob-xor! set1 set1 set2))

(define (bag-xor! bag1 bag2)
  (check-bag bag1)
  (check-bag bag2)
  (check-same-comparator bag1 bag2)
  (sob-xor! bag1 bag1 bag2))


;;; A few bag-specific procedures

(define (sob-product! n result sob)
  (let ((rht (sob-hash-table result)))
    (hash-table-for-each
      (lambda (elem count) (hash-table-set! rht elem (* count n)))
      (sob-hash-table sob))
    result))

(define (valid-n n)
   (and (integer? n) (exact? n) (positive? n)))

(define (bag-product n bag)
  (check-bag bag)
  (valid-n n)
  (sob-product! n (sob-empty-copy bag) bag))

(define (bag-product! n bag)
  (check-bag bag)
  (valid-n n)
  (sob-product! n bag bag))

(define (bag-unique-size bag)
  (check-bag bag)
  (hash-table-size (sob-hash-table bag)))

(define (bag-element-count bag elem)
  (check-bag bag)
  (hash-table-ref/default (sob-hash-table bag) elem 0))

(define (bag-for-each-unique proc bag)
  (check-bag bag)
  (hash-table-for-each
    (lambda (key value) (proc key value))
    (sob-hash-table bag)))

(define (bag-fold-unique proc nil bag)
  (check-bag bag)
  (let ((result nil))
    (hash-table-for-each
      (lambda (elem count) (set! result (proc elem count result)))
      (sob-hash-table bag))
    result))

(define (bag->set bag)
  (check-bag bag)
  (let ((result (make-sob (sob-comparator bag) #f)))
    (hash-table-for-each
      (lambda (key value) (sob-increment! result key value))
      (sob-hash-table bag))
    result))

(define (set->bag set)
  (check-set set)
  (let ((result (make-sob (sob-comparator set) #t)))
    (hash-table-for-each
      (lambda (key value) (sob-increment! result key value))
      (sob-hash-table set))
    result))

(define (set->bag! bag set)
  (check-bag bag)
  (check-set set)
  (check-same-comparator set bag)
  (hash-table-for-each
    (lambda (key value) (sob-increment! bag key value))
    (sob-hash-table set))
  bag)

(define (bag->alist bag)
  (check-bag bag)
  (bag-fold-unique
    (lambda (elem count list) (cons (cons elem count) list))
    '()
    bag))

(define (alist->bag comparator alist)
  (let* ((result (bag comparator))
         (ht (sob-hash-table result)))
    (for-each
      (lambda (assoc)
        (let ((element (car assoc)))
          (if (not (hash-table-contains? ht element))
              (sob-increment! result element (cdr assoc)))))
      alist)
    result))

;;; Comparators

;; Hash over sobs
(define (sob-hash sob)
  (let* ((ht (sob-hash-table sob))
         (hash (comparator-hash-function (sob-comparator sob))))
    (sob-fold
      (lambda (element result) (+ (hash element) (* result 33)))
      5381
      sob)))

;; Set and bag comparator

(define set-comparator (make-comparator set? set=? #f sob-hash))

(define bag-comparator (make-comparator bag? bag=? #f sob-hash))

;;; Register above comparators for use by default-comparator
(comparator-register-default! set-comparator)
(comparator-register-default! bag-comparator)

;;; Set/bag printer (for debugging)

(define (sob-print sob port)
  (display (if (sob-multi? sob) "&bag[" "&set[") port)
  (sob-for-each
    (lambda (elem) (display " " port) (write elem port))
    sob)
  (display " ]" port))

;; Chicken-specific
(cond-expand
  (chicken
    (define-record-printer sob sob-print))
  (else))
