#lang scheme/unit

(require scheme/require (path-up "utils/utils.rkt")
         (except-in 
          (combine-in
           (utils tc-utils)
           (rep free-variance type-rep filter-rep rep-utils)
           (types utils convenience union subtype remove-intersect resolve
                  substitute)
           (env type-name-env index-env tvar-env))
          make-env -> ->* one-of/c)
         "constraint-structs.rkt"
	 "signatures.rkt"                  
         scheme/match
         mzlib/etc
         racket/trace racket/contract
	 unstable/sequence unstable/list unstable/debug unstable/hash
         scheme/list)

(import dmap^ constraints^ promote-demote^)
(export infer^)

(define (empty-set) '())  

(define current-seen (make-parameter (empty-set)))

(define (seen-before s t) (cons (Type-seq s) (Type-seq t)))
(define (remember s t A) (cons (seen-before s t) A))
(define (seen? s t) (member (seen-before s t) (current-seen)))


(define (map/cset f cset)
  (make-cset (for/list ([(cmap dmap) (in-pairs (cset-maps cset))])
               (f cmap dmap))))

(define (singleton-dmap dbound dcon)
  (make-dmap (make-immutable-hash (list (cons dbound dcon)))))

(define (hash-remove* hash keys)
  (for/fold ([h hash]) ([k (in-list keys)]) (hash-remove h k)))

(define (mover cset dbound vars f)
  (map/cset
   (lambda (cmap dmap)
     (cons (hash-remove* cmap (cons dbound vars))           
           (dmap-meet 
            (singleton-dmap 
             dbound
             (f cmap dmap))
            (make-dmap (hash-remove (dmap-map dmap) dbound)))))
   cset))

;; dbound : index variable
;; vars : listof[type variable] - temporary variables
;; cset : the constraints being manipulated
;; takes the constraints on vars and creates a dmap entry contstraining dbound to be |vars| 
;; with the constraints that cset places on vars
(d/c (move-vars-to-dmap cset dbound vars)
  (cset? symbol? (listof symbol?) . -> . cset?)
  (mover cset dbound vars
         (λ (cmap dmap)
           (make-dcon (for/list ([v vars])
                        (hash-ref cmap v 
                                  (λ () (int-err "No constraint for new var ~a" v))))
                      #f))))

;; dbound : index variable
;; cset : the constraints being manipulated
;; 
(d/c (move-rest-to-dmap cset dbound #:exact [exact? #f])
  ((cset? symbol?) (#:exact boolean?) . ->* . cset?)
  (mover cset dbound null
         (λ (cmap dmap)
           ((if exact? make-dcon-exact make-dcon)
            null
            (hash-ref cmap dbound
                      (λ () (int-err "No constraint for bound ~a" dbound)))))))

;; dbound : index variable
;; cset : the constraints being manipulated
;; 
(d/c (move-dotted-rest-to-dmap cset dbound)
  (cset? symbol? . -> . cset?)
  (mover cset dbound null
         (λ (cmap dmap)
           (make-dcon-dotted
            null
            (hash-ref cmap dbound
                      (λ () (int-err "No constraint for bound ~a" dbound)))
            dbound))))

;; This one's weird, because the way we set it up, the rest is already in the dmap.
;; This is because we create all the vars, then recall cgen/arr with the new vars
;; in place, and the "simple" case will then call move-rest-to-dmap.  This means
;; we need to extract that result from the dmap and merge it with the fixed vars
;; we now handled.  So I've extended the mover to give access to the dmap, which we use here.
(d/c (move-vars+rest-to-dmap cset dbound vars #:exact [exact? #f])
  ((cset? symbol? (listof symbol?)) (#:exact boolean?) . ->* . cset?)
  (mover cset dbound vars
         (λ (cmap dmap)
           ((if exact? make-dcon-exact make-dcon)
            (for/list ([v vars])
              (hash-ref cmap v (λ () (int-err "No constraint for new var ~a" v))))
            (match (hash-ref (dmap-map dmap) dbound
                             (λ () (int-err "No constraint for bound ~a" dbound)))
              [(dcon null rest) rest]
              [(dcon-exact null rest) rest]
              [_ (int-err "did not get a rest-only dcon when moving to the dmap")])))))

(define (cgen/filter V X Y s t)
  (match* (s t)
    [(e e) (empty-cset X Y)]
    [(e (Top:)) (empty-cset X Y)]
    ;; FIXME - is there something to be said about the logical ones?
    [((TypeFilter: s p i) (TypeFilter: t p i)) (cset-meet (cgen V X Y s t) (cgen V X Y t s))]
    [((NotTypeFilter: s p i) (NotTypeFilter: t p i)) (cset-meet (cgen V X Y s t) (cgen V X Y t s))]
    [(_ _) (fail! s t)]))

;; s and t must be *latent* filter sets
(define (cgen/filter-set V X Y s t)
  (match* (s t)
    [(e e) (empty-cset X Y)]
    [((FilterSet: s+ s-) (FilterSet: t+ t-))
     (cset-meet (cgen/filter V X Y s+ t+) (cgen/filter V X Y s- t-))]
    [(_ _) (fail! s t)]))

(define (cgen/object V X Y s t)
  (match* (s t)
    [(e e) (empty-cset X Y)]
    [(e (Empty:)) (empty-cset X Y)]
    ;; FIXME - do something here    
    [(_ _) (fail! s t)]))

(define (cgen/arr V X Y s-arr t-arr)
  (define (cg S T) (cgen V X Y S T))
  (match* (s-arr t-arr)
    ;; the simplest case - no rests, drests, keywords
    [((arr: ss s #f #f '())
      (arr: ts t #f #f '()))
     (cset-meet* (list 
                  ;; contravariant
                  (cgen/list V X Y ts ss)
                  ;; covariant
                  (cg s t)))]
    ;; just a rest arg, no drest, no keywords
    [((arr: ss s s-rest #f '())
      (arr: ts t t-rest #f '()))
     (let ([arg-mapping 
            (cond 
              ;; both rest args are present, so make them the same length
              [(and s-rest t-rest)
               (cgen/list V X Y (cons t-rest (extend ss ts t-rest)) (cons s-rest (extend ts ss s-rest)))]
              ;; no rest arg on the right, so just pad the left and forget the rest arg
              [(and s-rest (not t-rest) (<= (length ss) (length ts)))
               (cgen/list V X Y ts (extend ts ss s-rest))]
              ;; no rest arg on the left, or wrong number = fail
              [else (fail! s-arr t-arr)])]
           [ret-mapping (cg s t)])
       (cset-meet* (list arg-mapping ret-mapping)))]
    ;; dotted on the left, nothing on the right
    [((arr: ss s #f (cons dty dbound) '())
      (arr: ts t #f #f                '()))
     (unless (memq dbound Y)
       (fail! s-arr t-arr))
     (unless (<= (length ss) (length ts))
       (fail! ss ts))
     (let* ([vars      (for/list ([n (in-range (- (length ts) (length ss)))])
                         (gensym dbound))]
            [new-tys   (for/list ([var vars])
                         (substitute (make-F var) dbound dty))]
            [new-s-arr (make-arr (append ss new-tys) s #f #f null)]
            [new-cset  (cgen/arr V (append vars X) Y new-s-arr t-arr)])
       (move-vars-to-dmap new-cset dbound vars))]
    ;; dotted on the right, nothing on the left
    [((arr: ss s #f #f                '())
      (arr: ts t #f (cons dty dbound) '()))
     (unless (memq dbound Y)
       (fail! s-arr t-arr))
     (unless (<= (length ts) (length ss))
       (fail! ss ts))
     (let* ([vars     (for/list ([n (in-range (- (length ss) (length ts)))])
                        (gensym dbound))]
            [new-tys  (for/list ([var vars])
                        (substitute (make-F var) dbound dty))]
            [new-t-arr (make-arr (append ts new-tys) t #f #f null)]
            [new-cset (cgen/arr V (append vars X) Y s-arr new-t-arr)])
       (move-vars-to-dmap new-cset dbound vars))]
    ;; this case is just for constrainting other variables, not dbound
    [((arr: ss s #f (cons s-dty dbound) '())
      (arr: ts t #f (cons t-dty dbound) '()))
     (unless (= (length ss) (length ts))
       (fail! ss ts))
     ;; If we want to infer the dotted bound, then why is it in both types?
     (when (memq dbound Y)
       (fail! s-arr t-arr))
     (let* ([arg-mapping (cgen/list V X Y ts ss)]
            [darg-mapping (cgen V X Y t-dty s-dty)]
            [ret-mapping (cg s t)])
       (cset-meet* 
        (list arg-mapping darg-mapping ret-mapping)))]
    ;; bounds are different
    [((arr: ss s #f (cons s-dty (? (λ (db) (memq db Y)) dbound))  '())
      (arr: ts t #f (cons t-dty dbound*) '()))
     (unless (= (length ss) (length ts)) (fail! ss ts))
     (when (memq dbound* Y) (fail! s-arr t-arr))
     (let* ([arg-mapping (cgen/list V X Y ts ss)]
            ;; just add dbound as something that can be constrained
            [darg-mapping (move-dotted-rest-to-dmap (cgen V (cons dbound X) Y t-dty s-dty) dbound)]
            [ret-mapping (cg s t)])
       (cset-meet* 
        (list arg-mapping darg-mapping ret-mapping)))]
    [((arr: ss s #f (cons s-dty dbound)  '())
      (arr: ts t #f (cons t-dty (? (λ (db) (memq db Y)) dbound*)) '()))
     (unless (= (length ss) (length ts)) (fail! ss ts))
     (let* ([arg-mapping (cgen/list V X Y ts ss)]
            ;; just add dbound as something that can be constrained
            [darg-mapping (move-dotted-rest-to-dmap (cgen V (cons dbound* X) Y t-dty s-dty) dbound*)]
            [ret-mapping (cg s t)])
       (cset-meet* 
        (list arg-mapping darg-mapping ret-mapping)))]
    ;; * <: ...
    [((arr: ss s s-rest #f                  '())
      (arr: ts t #f     (cons t-dty dbound) '()))
     (unless (memq dbound Y)
       (fail! s-arr t-arr))
     (if (<= (length ss) (length ts))
         ;; the simple case
         (let* ([arg-mapping (cgen/list V X Y ts (extend ts ss s-rest))]
                [darg-mapping (move-rest-to-dmap (cgen V (cons dbound X) Y t-dty s-rest) dbound)]
                [ret-mapping (cg s t)])
           (cset-meet* (list arg-mapping darg-mapping ret-mapping)))
         ;; the hard case
         (let* ([vars     (for/list ([n (in-range (- (length ss) (length ts)))])
                            (gensym dbound))]
                [new-tys  (for/list ([var vars])
                            (substitute (make-F var) dbound t-dty))]
                [new-t-arr (make-arr (append ts new-tys) t #f (cons t-dty dbound) null)]
                [new-cset (cgen/arr V (append vars X) Y s-arr new-t-arr)])
           (move-vars+rest-to-dmap new-cset dbound vars)))]
    ;; If dotted <: starred is correct, add it below.  Not sure it is.
    [((arr: ss s #f     (cons s-dty dbound) '())
      (arr: ts t t-rest #f                  '()))
     (unless (memq dbound Y)
       (fail! s-arr t-arr))
     (cond [(< (length ss) (length ts))
            ;; the hard case
            (let* ([vars     (for/list ([n (in-range (- (length ts) (length ss)))])
                               (gensym dbound))]
                   [new-tys  (for/list ([var vars])
                               (substitute (make-F var) dbound s-dty))]
                   [new-s-arr (make-arr (append ss new-tys) s #f (cons s-dty dbound) null)]
                   [new-cset (cgen/arr V (append vars X) Y new-s-arr t-arr)])
              (move-vars+rest-to-dmap new-cset dbound vars #:exact #t))]
           [else
            ;; the simple case
            (let* ([arg-mapping (cgen/list V X Y (extend ss ts t-rest) ss)]
                   [darg-mapping (move-rest-to-dmap (cgen V (cons dbound X) Y t-rest s-dty) dbound #:exact #t)]
                   [ret-mapping (cg s t)])
              (cset-meet* (list arg-mapping darg-mapping ret-mapping)))])]
    [(_ _) (fail! s-arr t-arr)]))

(define (cgen/flds V X Y flds-s flds-t)
  (cset-meet*
   (for/list ([s (in-list flds-s)] [t (in-list flds-t)])
     (match* (s t)
       ;; mutable - invariant
       [((fld: s _ #t) (fld: t _ #t)) (cset-meet (cgen V X Y s t) (cgen V X Y t s))]
       ;; immutable - covariant
       [((fld: s _ #f) (fld: t _ #f)) (cgen V X Y s t)]))))

;; V : a set of variables not to mention in the constraints
;; X : the set of type variables to be constrained
;; Y : the set of index variables to be constrained
;; S : a type to be the subtype of T
;; T : a type
;; produces a cset which determines a substitution that makes S a subtype of T
;; implements the V |-_X S <: T => C judgment from Pierce+Turner, extended with
;; the index variables from the TOPLAS paper
(d/c (cgen V X Y S T)
  ((listof symbol?) (listof symbol?) (listof symbol?) Type? Type? . -> . cset?)
  ;; useful quick loop
  (define (cg S T) (cgen V X Y S T))
  ;; this places no constraints on any variables in X
  (define empty (empty-cset X Y))
  ;; this constrains just x (which is a single var)
  (define (singleton S x T)
    (insert empty x S T))
  ;; if we've been around this loop before, we're done (for rec types)
  (if (seen? S T)
      empty
      (parameterize ([match-equality-test (lambda (a b) (if (and (Rep? a) (Rep? b)) (type-equal? a b) (equal? a b)))]
                     ;; remember S and T, and obtain everything we've seen from the context
                     ;; we can't make this an argument since we may call back and forth with subtyping, for example
                     [current-seen (remember S T (current-seen))])
        (match* (S T)
          ;; if they're equal, no constraints are necessary (CG-Refl)
          [(a a) empty]
          ;; CG-Top
          [(_ (Univ:)) empty]

          ;; refinements are erased to their bound
          [((Refinement: S _ _) T)
           (cg S T)]

          ;; variables that are in X and should be constrained
          ;; all other variables are compatible only with themselves
          [((F: (? (λ (e) (memq e X)) v)) T)
           (match T
             ;; only possible when v* is an index
             [(F: v*) (when (and (bound-index? v*) (not (bound-tvar? v*)))
                        (fail! S T))]
             [_ (void)])
           ;; constrain v to be below T (but don't mention V)
           (singleton (Un) v (var-demote T V))]
          [(S (F: (? (lambda (e) (memq e X)) v)))
           (match S
             [(F: v*) (when (and (bound-index? v*) (not (bound-tvar? v*)))
                        (fail! S T))]
             [_ (void)])
           ;; constrain v to be above S (but don't mention V)
           (singleton (var-promote S V) v Univ)]
          
          ;; constrain b1 to be below T, but don't mention the new vars
          [((Poly: v1 b1) T) (cgen (append v1 V) X Y b1 T)]
          
          ;; constrain *each* element of es to be below T, and then combine the constraints
          [((Union: es) T) (cset-meet* (cons empty (for/list ([e es]) (cg e T))))]
          
          ;; find *an* element of es which can be made to be a supertype of S
          ;; FIXME: we're using multiple csets here, but I don't think it makes a difference 
          ;; not using multiple csets will break for: ???
          [(S (Union: es)) 
           (cset-combine
            (filter values
                    (for/list ([e es]) 
                      (with-handlers ([exn:infer? (λ _ #f)]) (cg S e)))))]
          
          ;; two structs with the same name and parent
          ;; just check pairwise on the fields
          [((Struct: nm p flds proc _ _ _ _) (Struct: nm p flds* proc* _ _ _ _))
           (let ([proc-c
                  (cond [(and proc proc*)
                         (cg proc proc*)]
                        [proc* (fail! S T)]
                        [else empty])])
             (cset-meet proc-c (cgen/flds V X Y flds flds*)))]
          
          ;; two struct names, need to resolve b/c one could be a parent
          [((Name: n) (Name: n*))
           (if (free-identifier=? n n*)
               null
               (cg (resolve-once S) (resolve-once T)))]
          ;; pairs are pointwise
          [((Pair: a b) (Pair: a* b*))
           (cset-meet (cg a a*) (cg b b*))]
          ;; sequences are covariant
          [((Sequence: ts) (Sequence: ts*))
           (cgen/list V X Y ts ts*)]
          [((Listof: t) (Sequence: (list t*)))
           (cg t t*)]
          [((List: ts) (Sequence: (list t*)))
           (cset-meet* (for/list ([t (in-list ts)])
                         (cg t t*)))]
          [((HeterogenousVector: ts) (HeterogenousVector: ts*))
           (cset-meet (cgen/list V X Y ts ts*) (cgen/list V X Y ts* ts))]
          [((HeterogenousVector: ts) (Sequence: (list t*)))
           (cset-meet* (for/list ([t (in-list ts)])
                         (cg t t*)))]
          [((Vector: t) (Sequence: (list t*)))
           (cg t t*)]
          [((Base: 'String _) (Sequence: (list t*)))
           (cg -Char t*)]
          [((Base: 'Bytes _) (Sequence: (list t*)))
           (cg -Nat t*)]
          [((Base: 'Input-Port _) (Sequence: (list t*)))
           (cg -Nat t*)]
          [((Vector: t) (Sequence: (list t*)))
           (cg t t*)]
          [((Hashtable: k v) (Sequence: (list k* v*)))
           (cgen/list V X Y (list k v) (list k* v*))]
          ;; ListDots can be below a Listof
          ;; must be above mu unfolding
          [((ListDots: s-dty dbound) (Listof: t-elem))
           (when (memq dbound Y) (fail! S T))
           (cgen V X Y (substitute Univ dbound s-dty) t-elem)]
          ;; two ListDots with the same bound, just check the element type
          [((ListDots: s-dty dbound) (ListDots: t-dty dbound))
           (when (memq dbound Y) (fail! S T))
           (cgen V X Y s-dty t-dty)]
          [((ListDots: s-dty (? (λ (db) (memq db Y)) s-dbound)) (ListDots: t-dty t-dbound))
           ;; What should we do if both are in Y?
           (when (memq t-dbound Y) (fail! S T))
           (move-dotted-rest-to-dmap (cgen V (cons s-dbound X) Y s-dty t-dty) s-dbound)]
          [((ListDots: s-dty s-dbound) (ListDots: t-dty (? (λ (db) (memq db Y)) t-dbound)))
           ;; s-dbound can't be in Y, due to previous rule
           (move-dotted-rest-to-dmap (cgen V (cons t-dbound X) Y s-dty t-dty) t-dbound)]
          
          ;; this constrains `dbound' to be |ts| - |ss|
          [((ListDots: s-dty dbound) (List: ts))
           (unless (memq dbound Y) (fail! S T))
           
           (let* ([vars     (for/list ([n (in-range (length ts))])
                              (gensym dbound))]
                  ;; new-tys are dummy plain type variables, standing in for the elements of dbound that need to be generated
                  [new-tys  (for/list ([var vars])
                              (substitute (make-F var) dbound s-dty))]
                  ;; generate constraints on the prefixes, and on the dummy types
                  [new-cset (cgen/list V (append vars X) Y new-tys ts)])
             ;; now take all the dummy types, and use them to constrain dbound appropriately
             (move-vars-to-dmap new-cset dbound vars))]
          
          ;; if we have two mu's, we rename them to have the same variable
          ;; and then compare the bodies
          ;; This relies on (B 0) only unifying with itself, and thus only hitting the first case of this `match'
          [((Mu-unsafe: s) (Mu-unsafe: t)) 
           (cg s t)]
          
          ;; other mu's just get unfolded
          [(s (? Mu? t)) (cg s (unfold t))]
          [((? Mu? s) t) (cg (unfold s) t)]
                    
          ;; resolve applications
          [((App: _ _ _) _) (cg (resolve-once S) T)]
          [(_ (App: _ _ _)) (cg S (resolve-once T))]
          
          ;; values are covariant
          [((Values: ss) (Values: ts))
           (unless (= (length ss) (length ts))
             (fail! ss ts))
           (cgen/list V X Y ss ts)]
          
          ;; this constrains `dbound' to be |ts| - |ss|
          [((ValuesDots: ss s-dty dbound) (Values: ts))
           (unless (>= (length ts) (length ss)) (fail! ss ts))
           (unless (memq dbound Y) (fail! S T))
           
           (let* ([vars     (for/list ([n (in-range (- (length ts) (length ss)))])
                              (gensym dbound))]
                  ;; new-tys are dummy plain type variables, standing in for the elements of dbound that need to be generated
                  [new-tys  (for/list ([var vars])
                              (substitute (make-F var) dbound s-dty))]
                  ;; generate constraints on the prefixes, and on the dummy types
                  [new-cset (cgen/list V (append vars X) Y (append ss new-tys) ts)])
             ;; now take all the dummy types, and use them to constrain dbound appropriately
             (move-vars-to-dmap new-cset dbound vars))]
          
          ;; identical bounds - just unify pairwise
          [((ValuesDots: ss s-dty dbound) (ValuesDots: ts t-dty dbound))
           (when (memq dbound Y) (fail! ss ts))          
           (cgen/list V X Y (cons s-dty ss) (cons t-dty ts))]
          [((ValuesDots: ss s-dty (? (λ (db) (memq db Y)) s-dbound)) (ValuesDots: ts t-dty t-dbound))
           ;; What should we do if both are in Y?
           (when (memq t-dbound Y) (fail! S T))
           (cset-meet
            (cgen/list V X Y ss ts)
            (move-dotted-rest-to-dmap (cgen V (cons s-dbound X) Y s-dty t-dty) s-dbound))]
          [((ValuesDots: ss s-dty s-dbound) (ValuesDots: ts t-dty (? (λ (db) (memq db Y)) t-dbound)))
           ;; s-dbound can't be in Y, due to previous rule
           (cset-meet
            (cgen/list V X Y ss ts)
            (move-dotted-rest-to-dmap (cgen V (cons t-dbound X) Y s-dty t-dty) t-dbound))]
          ;; vectors are invariant - generate constraints *both* ways
          [((Vector: e) (Vector: e*))
           (cset-meet (cg e e*) (cg e* e))]
          ;; boxes are invariant - generate constraints *both* ways
          [((Box: e) (Box: e*))
           (cset-meet (cg e e*) (cg e* e))]
          [((MPair: s t) (MPair: s* t*))
           (cset-meet* (list (cg s s*) (cg s* s) (cg t t*) (cg t* t)))]
          [((Channel: e) (Channel: e*))
           (cset-meet (cg e e*) (cg e* e))]
          ;; we assume all HTs are mutable at the moment
          [((Hashtable: s1 s2) (Hashtable: t1 t2))
           ;; for mutable hash tables, both are invariant
           (cset-meet* (list (cg t1 s1) (cg s1 t1) (cg t2 s2) (cg s2 t2)))]
          ;; syntax is covariant
          [((Syntax: s1) (Syntax: s2))
           (cg s1 s2)]
          ;; futures are covariant
          [((Future: s1) (Future: s2))
           (cg s1 s2)]
          ;; parameters are just like one-arg functions
          [((Param: in1 out1) (Param: in2 out2))
           (cset-meet (cg in2 in1) (cg out1 out2))]
          ;; every function is trivially below top-arr
          [((Function: _)
            (Function: (list (top-arr:))))
           empty]
          [((Function: (list s-arr ...))
            (Function: (list t-arr ...)))
           (cset-meet*
            (for/list ([t-arr t-arr])
              ;; for each element of t-arr, we need to get at least one element of s-arr that works
              (let ([results (filter values
                                     (for/list ([s-arr s-arr])
                                       (with-handlers ([exn:infer? (lambda (_) #f)])
                                         (cgen/arr V X Y s-arr t-arr))))])
                ;; ensure that something produces a constraint set
                (when (null? results) (fail! S T))
                (cset-combine results))))]
          ;; check each element
          [((Result: s f-s o-s)
            (Result: t f-t o-t))
           (cset-meet* (list (cg s t) 
                             (cgen/filter-set V X Y f-s f-t)
                             (cgen/object V X Y o-s o-t)))]
          [(_ _)
           (cond 
             ;; subtypes are easy - should this go earlier?
             [(subtype S T) empty]
             ;; or, nothing worked, and we fail
             [else (fail! S T)])]))))

;; C : cset? - set of constraints found by the inference engine
;; Y : (listof symbol?) - index variables that must have entries
;; R : Type? - result type into which we will be substituting
(d/c (subst-gen C Y R)
  (cset? (listof symbol?) Type? . -> . (or/c #f substitution/c))
  (define var-hash (free-vars* R))
  (define idx-hash (free-idxs* R))
  ;; v : Symbol - variable for which to check variance
  ;; h : (Hash Symbol Variance) - hash to check variance in (either var or idx hash)
  ;; variable: Symbol - variable to use instead, if v was a temp var for idx extension
  (define (constraint->type v h #:variable [variable #f])
    (match v
      [(c S X T)
       (let ([var (hash-ref h (or variable X) Constant)])
         ;(printf "variance was: ~a\nR was ~a\nX was ~a\nS T ~a ~a\n" var R (or variable X) S T)
         (evcase var 
                 [Constant S]
                 [Covariant S]
                 [Contravariant T]
                 [Invariant 
                  (let ([gS (generalize S)])
                    ;(printf "Inv var: ~a ~a ~a ~a\n" v S gS T)
                    (if (subtype gS T)
                        gS
                        S))]))]))
  ;; Since we don't add entries to the empty cset for index variables (since there is no
  ;; widest constraint, due to dcon-exacts), we must add substitutions here if no constraint
  ;; was found.  If we're at this point and had no other constraints, then adding the
  ;; equivalent of the constraint (dcon null (c Bot X Top)) is okay.
  (define (extend-idxs S)
    (define fi-R (fi R))
    ;; If the index variable v is not used in the type, then
    ;; we allow it to be replaced with the empty list of types;
    ;; otherwise we error, as we do not yet know what an appropriate
    ;; lower bound is.
    (define (demote/check-free v)
      (if (memq v fi-R)
          (int-err "attempted to demote dotted variable")
          (i-subst null)))
    ;; absent-entries is #f if there's an error in the substitution, otherwise
    ;; it's a list of variables that don't appear in the substitution
    (define absent-entries
      (for/fold ([no-entry null]) ([v (in-list Y)])
        (let ([entry (hash-ref S v #f)])
          ;; Make sure we got a subst entry for an index var
          ;; (i.e. a list of types for the fixed portion
          ;;  and a type for the starred portion)
          (cond
            [(not no-entry) no-entry]
            [(not entry) (cons v no-entry)]
            [(or (i-subst? entry) (i-subst/starred? entry) (i-subst/dotted? entry)) no-entry]
            [else #f]))))
    (and absent-entries
         (hash-union
          (for/hash ([missing (in-list absent-entries)])
            (let ([var (hash-ref idx-hash missing Constant)])
              (values missing
                      (evcase var
                              [Constant (demote/check-free missing)]
                              [Covariant (demote/check-free missing)]
                              [Contravariant (i-subst/starred null Univ)]
                              [Invariant (demote/check-free missing)]))))
          S)))
  (match (car (cset-maps C))
    [(cons cmap (dmap dm))
     (let ([subst (hash-union 
                   (for/hash ([(k dc) (in-hash dm)])
                     (match dc
                       [(dcon fixed #f)
                        (values k
                                (i-subst
                                 (for/list ([f fixed])
                                   (constraint->type f idx-hash #:variable k))))]
                       [(dcon fixed rest)
                        (values k
                                (i-subst/starred (for/list ([f fixed])
                                                   (constraint->type f idx-hash #:variable k))
                                                 (constraint->type rest idx-hash)))]
                       [(dcon-exact fixed rest)
                        (values k
                                (i-subst/starred
                                 (for/list ([f fixed])
                                   (constraint->type f idx-hash #:variable k))
                                 (constraint->type rest idx-hash)))]
                       [(dcon-dotted fixed dc dbound)
                        (values k
                                (i-subst/dotted
                                 (for/list ([f fixed])
                                   (constraint->type f idx-hash #:variable k))
                                 (constraint->type dc idx-hash #:variable k)
                                 dbound))]))
                   (for/hash ([(k v) (in-hash cmap)])
                     (values k (t-subst (constraint->type v var-hash)))))])
       ;; verify that we got all the important variables
       (and (for/and ([v (fv R)])
              (let ([entry (hash-ref subst v #f)])
                ;; Make sure we got a subst entry for a type var
                ;; (i.e. just a type to substitute)
                (and entry (t-subst? entry))))
            (extend-idxs subst)))]))

;; V : a set of variables not to mention in the constraints
;; X : the set of type variables to be constrained
;; Y : the set of index variables to be constrained
;; S : a list of types to be the subtypes of T
;; T : a list of types
;; produces a cset which determines a substitution that makes the Ss subtypes of the Ts
(d/c (cgen/list V X Y S T)
  ((listof symbol?) (listof symbol?) (listof symbol?) (listof Type?) (listof Type?) . -> . cset?)
  (unless (= (length S) (length T))
    (fail! S T))
  (cset-meet* (for/list ([s S] [t T]) (cgen V X Y s t))))

;; X : variables to infer
;; Y : indices to infer
;; S : actual argument types
;; T : formal argument types
;; R : result type
;; expected : boolean
;; returns a substitution
;; if R is #f, we don't care about the substituion
;; just return a boolean result
(define (infer X Y S T R [expected #f])
  (with-handlers ([exn:infer? (lambda _ #f)])  
    (let* ([cs (cgen/list null X Y S T)]
           [cs* (if expected 
                    (cset-meet cs (cgen null X Y R expected))
                    cs)])
          (if R (subst-gen cs* Y R) #t))))

;; like infer, but T-var is the vararg type:
(define (infer/vararg X Y S T T-var R [expected #f])
  (define new-T (if T-var (extend S T T-var) T))
  (and ((length S) . >= . (length T))
       (infer X Y S new-T R expected)))

;; like infer, but dotted-var is the bound on the ...
;; and T-dotted is the repeated type
(define (infer/dots X dotted-var S T T-dotted R must-vars #:expected [expected #f])
  (with-handlers ([exn:infer? (lambda _ #f)])
    (let* ([short-S (take S (length T))]
           [rest-S (drop S (length T))]
           [cs-short (cgen/list null X (list dotted-var) short-S T)]
           [new-vars (for/list ([i (in-range (length rest-S))]) (gensym dotted-var))]
           [new-Ts (for/list ([v new-vars])
                     (substitute (make-F v) dotted-var 
                                 (substitute-dots (map make-F new-vars) #f dotted-var T-dotted)))]
           [cs-dotted (cgen/list null (append new-vars X) (list dotted-var) rest-S new-Ts)]
           [cs-dotted* (move-vars-to-dmap cs-dotted dotted-var new-vars)]
           [cs (cset-meet cs-short cs-dotted*)])
      (if (not expected)
          (subst-gen cs (list dotted-var) R)
          (subst-gen (cset-meet cs (cgen null X (list dotted-var) R expected)) (list dotted-var) R)))))

;(trace cgen)
