diff --git a/utils.rkt b/utils.rkt
index 9d2545f..1b9b9bf 100644
--- a/utils.rkt
+++ b/utils.rkt
@@ -107,7 +107,7 @@
                           ([x form])
                   (extract-symbols x)))]
       [else '()]))
-  (cast (extract-rec form) (Listof Symbol)))
+  (assert (extract-rec form) (make-predicate (Listof Symbol))))
 
 (module+ test
   (test-case "extract-symbols"
@@ -173,7 +173,10 @@
 
 (module+ test
   (test-case "map-sexp"
-    (check-equal? (map-sexp (λ (x) (add1 (cast x Number))) '(1 2 (4 10) 3))
+    (check-equal? (map-sexp (λ (x)
+                              (assert x number?)
+                              (add1 x))
+                            '(1 2 (4 10) 3))
                   '(2 3 (5 11) 4))))
 
 (: read-org-sexp (-> String Any))
@@ -220,7 +223,8 @@
    (λ ([pairs : (Listof (Pair Symbol Any))])
      (make-immutable-hash pairs))
    (λ (sexp)
-     (unstringify-pairs (cast sexp (Listof (GeneralPair String Any)))))
+     (assert sexp (make-predicate (Listof (GeneralPair String Any))))
+     (unstringify-pairs sexp))
    string->any))
 
 ;;; A synonym for read-org-variable-mapping.
@@ -240,7 +244,8 @@
 
 (: read-symbol-list (-> String (Listof Symbol)))
 (define (read-symbol-list str)
-  (cast (string->any (string-append "(" str ")")) (Listof Symbol)))
+  (assert (string->any (string-append "(" str ")"))
+          (make-predicate (Listof Symbol))))
 
 (module+ test
   (test-case "read-symbol-list"
@@ -297,7 +302,8 @@
     (define gr1 (directed-graph '((a b) (b c))))
     (define gr2 (undirected-graph '((a b) (b c))))
     (define (dbl [x : Any])
-      (define x-str (symbol->string (cast x Symbol)))
+      (assert x symbol?)
+      (define x-str (symbol->string x))
       (string->symbol (string-append x-str x-str)))
     (define new-gr1 (update-vertices/unweighted gr1 dbl))
     (define new-gr2 (update-vertices/unweighted gr2 dbl))
@@ -336,14 +342,17 @@
     (define gr1 (directed-graph '((a b) (b c))))
     (define gr2 (undirected-graph '((a b) (b c))))
     (define (dbl [x : Any])
-      (define x-str (symbol->string (cast x Symbol)))
+      (assert x symbol?)
+      (define x-str (symbol->string x))
       (string->symbol (string-append x-str x-str)))
     (define new-gr1-ug (update-graph gr1 #:v-func dbl))
     (define new-gr2-ug (update-graph gr2 #:v-func dbl))
     (define gr3 (weighted-graph/directed '((10 a b) (11 b c))))
     (define new-gr3 (update-graph gr3
                                   #:v-func dbl
-                                  #:e-func (λ (x) (* 2 (cast x Number)))))
+                                  #:e-func (λ (x)
+                                             (assert x number?)
+                                             (* 2 x))))
 
     (check-false (has-vertex? new-gr1-ug 'a))
     (check-true (has-vertex? new-gr1-ug 'aa))