diff --git a/csp/csp.rkt b/csp/csp.rkt
index 0b7d8535..bd12dba4 100644
--- a/csp/csp.rkt
+++ b/csp/csp.rkt
@@ -20,8 +20,8 @@
       [else
        (match-define (cons name other-names) names)
        (for/and ([val (in-list ($csp-vals csp name))])
-                ;; todo: reconsider efficiency of currying every value
-                (($constraint other-names (curry proc val)) csp))])))
+         ;; todo: reconsider efficiency of currying every value
+         (($constraint other-names (curry proc val)) csp))])))
 
 (define/contract (check-name-in-csp! caller csp name)
   (symbol? $csp? $var-name? . -> . void?)
@@ -61,11 +61,11 @@
   (($csp? procedure? (listof (listof $var-name?))) ((or/c #false $var-name?)) . ->* . void?)
   (set-$csp-constraints! csp (append ($csp-constraints csp) 
                                      (for/list ([names (in-list namess)])
-                                               (for ([name (in-list names)])
-                                                    (check-name-in-csp! 'add-constraint! csp name))
-                                               ($constraint names (if proc-name
-                                                                      (procedure-rename proc proc-name)
-                                                                      proc))))))
+                                       (for ([name (in-list names)])
+                                         (check-name-in-csp! 'add-constraint! csp name))
+                                       ($constraint names (if proc-name
+                                                              (procedure-rename proc proc-name)
+                                                              proc))))))
 
 (define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
   (($csp? procedure? (listof $var-name?)) ($var-name?) . ->* . void?)
@@ -78,7 +78,7 @@
 (define/contract (no-solutions? csp)
   ($csp? . -> . boolean?)
   (for/or ([var (in-list ($csp-vars csp))])
-          (empty? ($var-vals var))))
+    (empty? ($var-vals var))))
 
 (struct inconsistency-error () #:transparent)
 
@@ -86,14 +86,14 @@
   ($csp? unary-constraint? . -> . $csp?)
   (match-define ($constraint (list constraint-name) proc) constraint)
   (define new-csp ($csp (for/list ([var (in-list ($csp-vars csp))])
-                                  (match-define ($var name vals) var)
-                                  (if (eq? name constraint-name)
-                                      ;; special rule: use promise for a constant value
-                                      ;; to skip the filtering
-                                      ($var name (if (promise? proc)
-                                                     (force proc)
-                                                     (filter proc vals)))
-                                      var))
+                          (match-define ($var name vals) var)
+                          (if (eq? name constraint-name)
+                              ;; special rule: use promise for a constant value
+                              ;; to skip the filtering
+                              ($var name (if (promise? proc)
+                                             (force proc)
+                                             (filter proc vals)))
+                              var))
                         ;; once the constraint is applied, it can go away
                         ;; ps this is not the same as an "assigned" constraint
                         ;; because the var may still have multiple values
@@ -113,7 +113,7 @@
   (check-name-in-csp! '$csp-vals csp name)
   (for/first ([var (in-list ($csp-vars csp))]
               #:when (eq? name ($var-name var)))
-             ($var-vals var)))
+    ($var-vals var)))
 
 (struct $arc (name constraint) #:transparent)
 
@@ -126,37 +126,37 @@
                    (λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
   (define (satisfies-arc? val)
     (for/or ([other-val (in-list ($csp-vals csp other-name))])
-            (proc val other-val)))
+      (proc val other-val)))
   (apply-unary-constraint csp ($constraint (list name)
                                            (procedure-rename
                                             satisfies-arc?
-                                            (string->symbol (format "satisfies-arc-with-~a?" other-name))))))
+                                            (string->symbol (format "~a-arc-to-~a" (object-name proc)  other-name))))))
 
 (define/contract (binary-constraints->arcs constraints)
   ((listof binary-constraint?) . -> . (listof $arc?))
   (for*/list ([constraint (in-list constraints)]
               [name (in-list ($constraint-names constraint))])
-             ($arc name constraint)))
+    ($arc name constraint)))
 
 (define/contract (terminating-at arcs name)
   ((listof $arc?) $var-name? . -> . (listof $arc?))
   (for/list ([arc (in-list arcs)]
              #:when (eq? name (second ($constraint-names ($arc-constraint arc)))))
-            arc))
+    arc))
 
 (define/contract (constraint-assigned? csp constraint)
   ($csp? $constraint? . -> . any/c)
   (for/and ([name (in-list ($constraint-names constraint))])
-           (memq name (map $var-name (assigned-vars csp)))))
+    (memq name (map $var-name (assigned-vars csp)))))
 
 (define/contract (remove-assigned-constraints csp [arity #false])
-  (($csp?) (exact-nonnegative-integer?) . ->* . $csp?)
+  (($csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . $csp?)
   ($csp
    ($csp-vars csp)
    (for/list ([constraint (in-list ($csp-constraints csp))]
               #:unless (and (if arity (= (length ($constraint-names constraint)) arity) #true)
                             (constraint-assigned? csp constraint)))
-             constraint)))
+     constraint)))
 
 (define (remove-assigned-binary-constraints csp)
   (remove-assigned-constraints csp 2))
@@ -222,24 +222,69 @@
   ($constraint? $var-name? . -> . boolean?)
   (and (memq name ($constraint-names constraint)) #true))
 
-(define/contract (test-assignments csp)
+(define/contract (validate-assignments csp)
   ($csp? . -> . $csp?)
-  (define assigned-names (map $var-name (assigned-vars csp)))
-  (for/fold ([csp csp])
-            ([constraint (in-list ($csp-constraints csp))]
-             #:when (constraint-assigned? csp constraint))
-    (unless (constraint csp) (raise (inconsistency-error)))
-    (remove-assigned-constraints csp)))
+  (for ([constraint (in-list ($csp-constraints csp))]
+        #:when (constraint-assigned? csp constraint))
+    (unless (constraint csp) (raise (inconsistency-error))))
+  (reduce-constraint-arity (remove-assigned-constraints csp)))
 
 (define/contract (assign-val csp name val)
   ($csp? $var-name? any/c . -> . $csp?)
   (define csp-with-assignment (apply-unary-constraint csp ($constraint (list name) (delay (list val)))))
-  (test-assignments csp-with-assignment))
+  (validate-assignments csp-with-assignment))
+
+(define (reduce-arity proc args)
+  (procedure-rename
+   (λ xs
+     (apply proc (for/fold ([acc empty]
+                            [xs xs]
+                            [vals (filter-not symbol? args)]
+                            #:result (reverse acc))
+                           ([arg (in-list args)])
+                   (if (symbol? arg)
+                       (values (cons (car xs) acc) (cdr xs) vals)
+                       (values (cons (car vals) acc) xs (cdr vals))))))
+   (string->symbol (format "reduced-arity-~a" (object-name proc)))))
+
+(module+ test
+  (require rackunit)
+  (define f (λ (a b c d) (+ a b c d)))
+  (check-equal? 10 ((reduce-arity f '(1 b c d)) 2 3 4))
+  (check-equal? 10 ((reduce-arity f '(1 2 c d)) 3 4))
+  (check-equal? 10 ((reduce-arity f '(1 2 3 d)) 4))
+  (check-equal? 10 ((reduce-arity f '(1 b 3 d)) 2 4))
+  (check-equal? 10 ((reduce-arity f '(a b 3 d)) 1 2 4)))
+
+(define/contract (reduce-constraint-arity csp [minimum-arity 3])
+  (($csp?) (exact-nonnegative-integer?) . ->* . $csp?)
+  (define assigned-names (map $var-name (assigned-vars csp)))
+  ($csp ($csp-vars csp)
+        (for/list ([constraint (in-list ($csp-constraints csp))])
+          (match-define ($constraint cnames proc) constraint)
+          (cond
+            [(and (<= minimum-arity (length cnames))
+                  (for/or ([cname (in-list cnames)])
+                    (memq cname assigned-names)))
+             ($constraint (for/list ([cname (in-list cnames)]
+                                     #:unless (memq cname assigned-names))
+                            cname)
+                          (reduce-arity proc (for/list ([cname (in-list cnames)])
+                                               (if (memq cname assigned-names)
+                                                   (car ($csp-vals csp cname))
+                                                   cname))))]
+            [else constraint]))))
+
+(module+ test
+  (define creduce (assign-val ($csp (list ($var 'a '(1 2 3)) ($var 'b '(2 3)) ($var 'c '(1 2 3 4 5))) (list ($constraint '(a b c) (procedure-rename (λ (a b c) (= (+ a b c) 4)) 'summer)))) 'a 1))
+  (check-equal? 
+   (make-arcs-consistent (reduce-constraint-arity creduce))
+   ($csp (list ($var 'a '(1)) ($var 'b '(2)) ($var 'c '(1))) '())))
 
 ;; todo: inferences between assignments
 (define/contract (infer csp)
   ($csp? . -> . $csp?)
-  (test-assignments (make-arcs-consistent csp)))
+  (validate-assignments (make-arcs-consistent csp)))
 
 (define/contract (backtracking-solver csp)
   ($csp? . -> . generator?)
@@ -250,15 +295,15 @@
                  [else ;; we have at least 1 unassigned var
                   (match-define ($var name vals) (select-unassigned-var csp))
                   (for ([val (in-list (order-domain-values vals))])
-                       (with-handlers ([inconsistency-error? void])
-                         (backtrack (infer (assign-val csp name val)))))]))))
+                    (with-handlers ([inconsistency-error? void])
+                      (backtrack (infer (assign-val csp name val)))))]))))
 
 (define/contract (solve* csp [finish-proc values][solution-limit +inf.0])
   (($csp?) (procedure? integer?) . ->* . (listof any/c))
   (define solutions
     (for/list ([solution (in-producer (backtracking-solver csp) (void))]
                [idx (in-range solution-limit)])
-              (finish-proc solution)))
+      (finish-proc solution)))
   (unless (pair? solutions) (raise (inconsistency-error)))
   solutions)