(module infer2 mzscheme
  (require "" "" "" "" "" ""
           (lib ""))
  (provide infer infer/list)

  ;; exn representing failure of inference
  ;; s,t both types
  (define-struct (exn:infer exn:fail) (s t))
  ;; inference failure - masked before it gets to the user program
  (define (fail! s t) (raise (make-exn:infer "inference failed" (current-continuation-marks) s t)))
  ;; conveneice function
  (define (alist->mapping vars) (table:alist->eq (map (lambda (x) (cons x 'fail)) vars)))
  ;; flag is one of: 'co, 'contra, #f
  ;; Mapping is a table that maps symbols to Results
  ;; A Result is one of:
  ;; - 'fail (not yet filled in)
  ;; - #f (not a variable we're concerned with)
  ;; - (list flag type)
  ;; s, t : Type
  ;; vars : Listof[Symbol]
  ;; produces a substitution for vars, or #f
  ;; the substitution makes s a supertype of t
  ;; only vars will be substituted, regardless of other free vars
  (define ((mk-infer f) s t vars)
    (let ([mapping (alist->mapping vars)])
          ([exn:infer? (lambda _ #f)])
        (mapping->subst (f s t mapping 'co)))))
  ;; table[symbol, (list flag )] -> substitution
  ;; convert a mapping to a substitution
  (define (mapping->subst x) 
    (define sexp (table:to-sexp x))
    (define result (filter (lambda (x) (list? (cadr x))) sexp))
    (map (lambda (x) (list (car x) (cadr (cadr x)))) result))
  ;; combine: flag -> Result Result -> Result
  ;; combine two results into one
  (define ((combine flag) s t)
    (match (list s t)
      [('fail t) t]
      [(t 'fail) t]
      [((sf s) (tf t))
         [(and sf tf (type-equal? s t)) (list (if (eq? sf tf) sf 'both) s)] ;; equal is fine
         [(memq 'both (list sf tf)) (fail! s t)] ;; not equal, needed to be
         [(and sf tf (not (eq? sf tf))) (fail! s t)] ;; not equal, needed to be
          (let ([flag (or sf tf flag)])
            ;(printf "flag is ~a~n" flag)
              [(and (eq? 'co flag) (subtype s t)) (list 'co t)]
              [(and (eq? 'co flag) (subtype t s)) (list 'co s)]
              [(and (eq? 'contra flag) (subtype s t)) (list 'contra s)]
              [(and (eq? 'contra flag) (subtype t s)) (list 'contra t)]
              [else (fail! s t)]))])]))

  ;(trace combine)
  ;; combine two tables
  ;; table:un : flag -> Mapping Mapping -> Mapping
  (define ((table:un flag) a b) (table:union/value a b (combine flag)))

  ;; infer/int/list : Listof[Type] Listof[Type] Mapping Flag -> Mapping
  (define (infer/int/list ss ts mapping flag)
    (unless (= (length ss) (length ts))
      (fail! ss ts))
    (let ([l (map (lambda (x y) (infer/int x y mapping flag)) ss ts)])
      (foldl (table:un flag) (table:make-eq) l)))
  ;; Flag -> Flag
  (define (swap flag) (case flag
                        [(co) 'contra]
                        [(contra) 'co]
                        [else (int-err "bad flag: ~a" flag)]))
  (define (co? x) (eq? x 'co))
  (define (contra? x) (eq? x 'contra))
  ;; type type mapping -> mapping
  (define (infer/int s t mapping flag)
    (let ([fail! (case-lambda [() (fail! s t)]
                              [(s t) (fail! s t)])])
      (parameterize ([match-equality-test type-equal?])
        (match (list s t)
          [(t t) mapping]
          [(($ tvar v) t)
           (let ([cur (table:lookup v mapping)])
             (match cur
               ;; we haven't yet seen this variable
               ['fail (table:insert v (list #f t) mapping)]
               ;; we are ignoring this variable, but they weren't the same
               [#f (fail!)] 
               ;; this variable has already been unified
               [(cur-flag cur-t) (cond
                                   [(or (not cur-flag) (eq? flag cur-flag))
                                    ;; this variable has only been handled once, or
                                    ;; we're still going in the correct direction
                                      ;; this is the same type we've already seen, so don't change the flag
                                      [(equiv? cur-t t) mapping]
                                      ;; this is a supertype of what's been found before
                                      [(and (eq? flag 'co) (subtype cur-t t)) 
                                       (table:insert v (list flag t) mapping)] 
                                      ;; this is a subtype of what's been found before
                                      [(and (eq? flag 'co) (subtype t cur-t))
                                       (table:insert v (list flag cur-t) mapping)] 
                                      ;; this is a subtype of what we found before
                                      [(and (eq? flag 'contra) (subtype t cur-t))  
                                       (table:insert v (list flag t) mapping)]
                                      ;; this is a supertype of what we found before
                                      [(and (eq? flag 'contra) (subtype t cur-t))
                                       (table:insert v (list flag cur-t) mapping)]
                                      ;; impossible
                                      [else (error 'internal-error "bad flag value" flag)])]
                                   ;; we've switched directions at least once
                                   [(type-equal? cur-t t) 
                                    ;; we're still ok
                                    (table:insert (list 'both cur-t) mapping)]
                                    ;; we're not ok
                                    (fail! cur-t t)])]))]
          ;; anything works with dynamic
          [(or (_ ($ dynamic)) (($ dynamic) _)) mapping]
          ;; vectors just recur
          [(($ vec s) ($ vec t)) (infer/int s t mapping flag)]
          ;; pairs just recur
          [(($ pair-ty s1 s2) ($ pair-ty t1 t2))
           (infer/int/list (list s1 s2) (list t1 t2) mapping flag)]
          ;; structs just recur
          [(($ struct-ty nm p flds) ($ struct-ty nm p flds*))
           (infer/int/list flds flds* mapping flag)]
          ;; if we have two mu's, we rename them to have the same variable
          ;; and then compare the bodies
          [((? mu? s) (? mu? t)) (let ([l (rename s t)])
                                   (infer/int (car l) (cadr l) mapping flag))]
          ;; other mu's just get unfolded
          [(s (? mu? t)) (infer/int s (unfold t) mapping flag)]
          [((? mu? s) t) (infer/int (unfold s) t mapping flag)]
          ;; two unions with the same number of elements, so we just try to unify them pairwise
          [(($ union e1) ($ union e2)) (=> unmatch)
           (let ([l1 (set:elements e1)]
                 [l2 (set:elements e2)])
             (if (= (length l1) (length l2))
                 (infer/int/list l1 l2 mapping flag)
          ;; arrow types - just add a whole bunch of new constraints
          [(($ funty (($ arr ts t t-rest t-thn-eff t-els-eff) ...)) ($ funty (($ arr ss s s-rest s-thn-eff s-els-eff) ...)))
           ;(printf "Danger: Arrow Type in unifier!!!!!~n")
           (define (compatible-rest t-rest s-rest)
             (andmap (lambda (x y) (or (and x y) (and (not x) (not y)))) ;; either both #f or both not #f
                     t-rest s-rest))
           (unless (and (= (length ts) (length ss))
                        (compatible-rest t-rest s-rest)
                        (equiv? t-els-eff s-els-eff)
                        (equiv? t-thn-eff s-thn-eff))
           (let ([arg-mapping (infer/int/list (apply append ts) (apply append ss) mapping (swap flag))]
                   [ret-mapping (infer/int/list t s mapping flag)])
             ((table:un flag) arg-mapping ret-mapping))]
          ;; if s is a union, we can just try to find one of its elements that works
          [(($ union e1) t) 
             (lambda (e)
                   ([exn:infer? (lambda _ #f)])
                 (infer/int e t mapping flag)))
             (set:elements e1))
          ;; otherwise, if we have a {sub,super}type, we're all good
          [else (cond [(and (co? flag) (subtype t s)) mapping]
                      [(and (contra? flag) (subtype s t)) mapping]
                      ;; or, nothing worked, and we fail
                      [else (fail!)])]
  ;; infer: Type Type List[Symbol] -> Substitution
  (define infer (mk-infer infer/int))
  ;; infer/list: Listof[Type] Listof[Type] List[Symbol] -> Substitution
  (define infer/list (mk-infer infer/int/list))
  ;(trace infer/int)