diff --git a/cur-doc/cur/scribblings/curnel.scrbl b/cur-doc/cur/scribblings/curnel.scrbl
index 2ff71fa..dcade81 100644
--- a/cur-doc/cur/scribblings/curnel.scrbl
+++ b/cur-doc/cur/scribblings/curnel.scrbl
@@ -17,7 +17,7 @@ Edwin C. Brady.
 @(define curnel-eval (curnel-sandbox "(require cur/stdlib/nat cur/stdlib/bool cur/stdlib/prop)"))
 
 @defform*[((Type n)
-	   Type)]{
+           Type)]{
 Define the universe of types at level @racket[n], where @racket[n] is any natural number.
 @racket[Type] is a synonym for @racket[(Type 0)]. Cur is impredicative
 in @racket[(Type 0)], although this is likely to change to a more
@@ -91,13 +91,16 @@ For instance, Cur does not currently perform strict positivity checking.
           ((((conj Bool) Bool) true) false)]
 }
 
-@defform[(elim type motive-universe)]{
-Returns the inductive eliminator for @racket[type] where the @racket[motive-universe] is the universe
-of the motive.
-The eliminator expects the next argument to be the motive, the next @racket[N] arguments to be the methods for
-each of the @racket[N] constructors of the inductive type @racket[type], the next @racket[P] arguments
-to be the parameters @racket[p_0 ... p_P] of the inductive @racket[type], and the final argument to be the term to
-eliminate of type @racket[(type p_0 ... p_P)].
+@defform[(elim inductive-type motive (index ...) (method ...) disc)]{
+Fold over the term @racket[disc] of the inductively defined type @racket[inductive-type].
+The @racket[motive] is a function that expects the indices of the inductive
+type and a term of the inductive type and produces the type that this
+fold returns.
+The type of @racket[disc] is @racket[(inductive-type index ...)].
+@racket[elim] takes one method for each constructor of @racket[inductive-type].
+Each @racket[method] expects the arguments for its corresponding constructor,
+and the inductive hypotheses generated by recursively eliminating all recursive
+arguments of the constructor.
 
 The following example runs @racket[(sub1 (s z))].
 
@@ -105,11 +108,11 @@ The following example runs @racket[(sub1 (s z))].
           (data Nat : Type
             (z : Nat)
             (s : (Π (n : Nat) Nat)))
-          (((((elim Nat Type)
-              (λ (x : Nat) Nat))
-             z)
-            (λ (n : Nat) (λ (IH : Nat) n)))
-           (s z))]
+          (elim Nat (λ (x : Nat) Nat)
+                ()
+                (z
+                 (λ (n : Nat) (λ (IH : Nat) n)))
+                (s z))]
 }
 
 @defform[(define id expr)]{
@@ -120,9 +123,11 @@ Binds @racket[id] to the result of @racket[expr].
             (z : Nat)
             (s : (Π (n : Nat) Nat)))
           (define sub1 (λ (n : Nat)
-                         (((((elim Nat Type) (λ (x : Nat) Nat))
-                           z)
-                          (λ (n : Nat) (λ (IH : Nat) n))) n)))
+                         (elim Nat (λ (x : Nat) Nat)
+                               ()
+                               (z
+                                (λ (n : Nat) (λ (IH : Nat) n)))
+                               n)))
           (sub1 (s (s z)))
           (sub1 (s z))
           (sub1 z)]
diff --git a/cur-doc/cur/scribblings/reflection.scrbl b/cur-doc/cur/scribblings/reflection.scrbl
index 839c56d..53759b2 100644
--- a/cur-doc/cur/scribblings/reflection.scrbl
+++ b/cur-doc/cur/scribblings/reflection.scrbl
@@ -76,10 +76,10 @@ Runs the Cur term @racket[syn] for one step.
 (eval:alts (cur-step #'((λ (x : Type) x) Bool))
            (eval:result @racket[#'Bool] "" ""))
 (eval:alts (cur-step #'(sub1 (s (s z))))
-           (eval:result @racket[#'(((((elim Nat (Type 0))
-                                      (λ (x2 : Nat) Nat)) z)
-                                    (λ (x2 : Nat) (λ (ih-n2 : Nat) x2)))
-                                   (s (s z)))] "" ""))
+           (eval:result @racket[#'(elim Nat (λ (x2 : Nat) Nat)
+                                        ()
+                                        (z (λ (x2 : Nat) (λ (ih-n2 : Nat) x2)))
+                                        (s (s z)))] "" ""))
 ]
 }
 
diff --git a/cur-doc/cur/scribblings/stdlib/bool.scrbl b/cur-doc/cur/scribblings/stdlib/bool.scrbl
index b38f11f..3dec080 100644
--- a/cur-doc/cur/scribblings/stdlib/bool.scrbl
+++ b/cur-doc/cur/scribblings/stdlib/bool.scrbl
@@ -22,7 +22,7 @@ A syntactic form that expands to the inductive eliminator for @racket[Bool]. Thi
 
 @examples[#:eval curnel-eval
           (if true false true)
-	  (elim Bool Type (λ (x : Bool) Bool) false true true)]
+	  (elim Bool (λ (x : Bool) Bool) () (false true) true)]
 }
 
 @defproc[(not [x Bool])
diff --git a/cur-doc/cur/scribblings/stdlib/sugar.scrbl b/cur-doc/cur/scribblings/stdlib/sugar.scrbl
index 0391117..dfce6b1 100644
--- a/cur-doc/cur/scribblings/stdlib/sugar.scrbl
+++ b/cur-doc/cur/scribblings/stdlib/sugar.scrbl
@@ -82,17 +82,6 @@ a @racket[(: name type)] form appears earlier in the module.
 	  (define (id A a) a)]
 }
 
-@defform[(elim type motive-result-type e ...)]{
-Like the @racket[elim] provided by @racketmodname[cur], but supports
-automatically curries the remaining arguments @racket[e ...].
-
-@examples[#:eval curnel-eval
-          (elim Bool Type (lambda (x : Bool) Bool)
-            false
-            true
-            true)]
-}
-
 @defform*[((define-type name type)
            (define-type (name (a : t) ...) body))]{
 Like @racket[define], but uses @racket[forall] instead of @racket[lambda].
diff --git a/cur-doc/info.rkt b/cur-doc/info.rkt
index 0cf5446..7bf1b5f 100644
--- a/cur-doc/info.rkt
+++ b/cur-doc/info.rkt
@@ -1,6 +1,6 @@
 #lang info
 (define collection 'multi)
 (define deps '("base" "racket-doc"))
-(define build-deps '("scribble-lib" ("cur-lib" #:version "0.2") "sandbox-lib"))
+(define build-deps '("scribble-lib" ("cur-lib" #:version "0.4") "sandbox-lib"))
 (define pkg-desc "Documentation for \"cur\".")
 (define pkg-authors '(wilbowma))
diff --git a/cur-lib/cur/curnel/redex-core.rkt b/cur-lib/cur/curnel/redex-core.rkt
index d815f6f..1271ffe 100644
--- a/cur-lib/cur/curnel/redex-core.rkt
+++ b/cur-lib/cur/curnel/redex-core.rkt
@@ -27,10 +27,10 @@
   (i j k  ::= natural)
   (U ::= (Unv i))
   (D x c ::= variable-not-otherwise-mentioned)
-  (t e ::= U (λ (x : t) e) x (Π (x : t) t) (e e) (elim D U))
-  ;; Δ (signature). (inductive-name : type ((constructor : type) ...))
-  ;; NB: Δ is a map from a name x to a pair of it's type and a map of constructor names to their types
   (Δ   ::= ∅ (Δ (D : t ((c : t) ...))))
+  (t e ::= U (λ (x : t) e) x (Π (x : t) t) (e e)
+     ;; (elim inductive-type motive (indices ...) (methods ...) discriminant)
+     (elim D e (e ...) (e ...) e))
   #:binding-forms
   (λ (x : t) e #:refers-to x)
   (Π (x : t_0) t_1 #:refers-to x))
@@ -108,27 +108,6 @@
   [(Δ-union Δ_2 (Δ_1 (x : t any)))
    ((Δ-union Δ_2 Δ_1) (x : t any))])
 
-;; Returns the inductively defined type that x constructs
-;; NB: Depends on clause order
-(define-metafunction ttL
-  Δ-key-by-constructor : Δ x -> x or #f
-  [(Δ-key-by-constructor (Δ (x : t ((x_0 : t_0) ... (x_c : t_c) (x_1 : t_1) ...))) x_c)
-   x]
-  [(Δ-key-by-constructor (Δ (x_1 : t_1 any)) x)
-   (Δ-key-by-constructor Δ x)]
-  [(Δ-key-by-constructor Δ x)
-   #f])
-
-;; Returns the constructor map for the inductively defined type x_D in the signature Δ
-(define-metafunction ttL
-  Δ-ref-constructor-map : Δ x -> ((x : t) ...) or #f
-  ;; NB: Depends on clause order
-  [(Δ-ref-constructor-map ∅ x_D) #f]
-  [(Δ-ref-constructor-map (Δ (x_D : t_D any)) x_D)
-   any]
-  [(Δ-ref-constructor-map (Δ (x_1 : t_1 any)) x_D)
-   (Δ-ref-constructor-map Δ x_D)])
-
 ;; TODO: Should not use Δ-ref-type
 (define-metafunction ttL
   Δ-ref-constructor-type : Δ x x -> t
@@ -148,14 +127,6 @@
 ;; TODO: Mix of pure Redex/escaping to Racket sometimes is getting confusing.
 ;; TODO: Justify, or stop.
 
-;; Return the number of constructors that D has
-(define-metafunction ttL
-  Δ-constructor-count : Δ D -> natural or #f
-  [(Δ-constructor-count Δ D)
-   ,(length (term (x ...)))
-   (where (x ...) (Δ-ref-constructors Δ D))]
-  [(Δ-constructor-count Δ D) #f])
-
 ;; NB: Depends on clause order
 (define-metafunction ttL
   sequence-index-of : any (any ...) -> natural
@@ -200,39 +171,23 @@
   [(Ξ-apply hole t) t]
   [(Ξ-apply (Π (x : t) Ξ) t_0) (Ξ-apply Ξ (t_0 x))])
 
-;; Compose multiple telescopes into a single telescope:
-(define-metafunction tt-ctxtL
-  Ξ-compose : Ξ Ξ ... -> Ξ
-  [(Ξ-compose Ξ) Ξ]
-  [(Ξ-compose Ξ_0 Ξ_1 Ξ_rest ...)
-   (Ξ-compose (in-hole Ξ_0 Ξ_1) Ξ_rest ...)])
-
 ;; Compute the number of arguments in a Ξ
 (define-metafunction tt-ctxtL
   Ξ-length : Ξ -> natural
   [(Ξ-length hole) 0]
   [(Ξ-length (Π (x : t) Ξ)) ,(add1 (term (Ξ-length Ξ)))])
 
-;; Compute the number of applications in a Θ
-(define-metafunction tt-ctxtL
-  Θ-length : Θ -> natural
-  [(Θ-length hole) 0]
-  [(Θ-length (Θ e)) ,(add1 (term (Θ-length Θ)))])
-
-;; Convert an apply context to a sequence of terms
-(define-metafunction tt-ctxtL
-  Θ->list : Θ -> (e ...)
-  [(Θ->list hole) ()]
-  [(Θ->list (Θ e))
-   (e_r ... e)
-   (where (e_r ...) (Θ->list Θ))])
-
 (define-metafunction tt-ctxtL
   list->Θ : (e ...) -> Θ
   [(list->Θ ()) hole]
   [(list->Θ (e e_r ...))
    (in-hole (list->Θ (e_r ...)) (hole e))])
 
+(define-metafunction tt-ctxtL
+  apply : e e ... -> e
+  [(apply e_f e ...)
+   (in-hole (list->Θ (e ...)) e_f)])
+
 ;; Reference an expression in Θ by index; index 0 corresponds to the the expression applied to a hole.
 (define-metafunction tt-ctxtL
   Θ-ref : Θ natural -> e or #f
@@ -254,15 +209,6 @@
   [(Δ-ref-parameter-Ξ Δ x)
    #f])
 
-;; Return the number of parameters of D
-(define-metafunction tt-ctxtL
-  Δ-parameter-count : Δ D -> natural or #f
-  [(Δ-parameter-count Δ D)
-   (Ξ-length Ξ)
-   (where Ξ (Δ-ref-parameter-Ξ Δ D))]
-  [(Δ-parameter-count Δ D)
-   #f])
-
 ;; Returns the telescope of the arguments for the constructor x_ci of the inductively defined type x_D
 (define-metafunction tt-ctxtL
   Δ-constructor-telescope : Δ x x -> Ξ
@@ -280,21 +226,6 @@
    (where (in-hole Ξ (in-hole Θ x_D))
      (Δ-ref-constructor-type Δ x_D x_ci))])
 
-;; Inner loop for Δ-constructor-noninductive-telescope
-(define-metafunction tt-ctxtL
-  noninductive-loop : x Φ -> Φ
-  [(noninductive-loop x_D hole) hole]
-  [(noninductive-loop x_D (Π (x : (in-hole Φ (in-hole Θ x_D))) Φ_1))
-   (noninductive-loop x_D Φ_1)]
-  [(noninductive-loop x_D (Π (x : t) Φ_1))
-   (Π (x : t) (noninductive-loop x_D Φ_1))])
-
-;; Returns the noninductive arguments to the constructor x_ci of the inductively defined type x_D
-(define-metafunction tt-ctxtL
-  Δ-constructor-noninductive-telescope : Δ x x -> Ξ
-  [(Δ-constructor-noninductive-telescope Δ x_D x_ci)
-   (noninductive-loop x_D (Δ-constructor-telescope Δ x_D x_ci))])
-
 ;; Inner loop for Δ-constructor-inductive-telescope
 ;; NB: Depends on clause order
 (define-metafunction tt-ctxtL
@@ -323,36 +254,6 @@
       (hypotheses-loop x_D t_P Φ_1))
    (where x_h ,(variable-not-in (term (x_D t_P any_0)) 'x-ih))])
 
-;; Returns the inductive hypotheses required for the elimination method of constructor x_ci for
-;; inductive type x_D, when eliminating with motive t_P.
-(define-metafunction tt-ctxtL
-  Δ-constructor-inductive-hypotheses : Δ x x t -> Ξ
-  [(Δ-constructor-inductive-hypotheses Δ x_D x_ci t_P)
-   (hypotheses-loop x_D t_P (Δ-constructor-inductive-telescope Δ x_D x_ci))])
-
-(define-metafunction tt-ctxtL
-  Δ-constructor-method-telescope : Δ x x t -> Ξ
-  [(Δ-constructor-method-telescope Δ x_D x_ci t_P)
-   (Π (x_mi : (in-hole Ξ_a (in-hole Ξ_h ((in-hole Θ_p t_P) (Ξ-apply Ξ_a x_ci)))))
-      hole)
-   (where Θ_p (Δ-constructor-parameters Δ x_D x_ci))
-   (where Ξ_a (Δ-constructor-telescope Δ x_D x_ci))
-   (where Ξ_h (Δ-constructor-inductive-hypotheses Δ x_D x_ci t_P))
-   (where x_mi ,(variable-not-in (term (t_P Δ)) 'x-mi))])
-
-;; fold Ξ-compose over map Δ-constructor-method-telescope over the list of constructors
-(define-metafunction tt-ctxtL
-  method-loop : Δ x t (x ...) -> Ξ
-  [(method-loop Δ x_D t_P ()) hole]
-  [(method-loop Δ x_D t_P (x_0 x_rest ...))
-   (Ξ-compose (Δ-constructor-method-telescope Δ x_D x_0 t_P) (method-loop Δ x_D t_P (x_rest ...)))])
-
-;; Returns the telescope of all methods required to eliminate the type x_D with motive t_P
-(define-metafunction tt-ctxtL
-  Δ-methods-telescope : Δ x t -> Ξ
-  [(Δ-methods-telescope Δ x_D t_P)
-   (method-loop Δ x_D t_P (Δ-ref-constructors Δ x_D))])
-
 ;; Computes the type of the eliminator for the inductively defined type x_D with a motive whose result
 ;; is in universe U.
 ;;
@@ -368,29 +269,40 @@
 ;; Ξ_P*D is the telescope of the parameters of x_D and
 ;;       the witness of type x_D (applied to the parameters)
 ;; Ξ_m   is the telescope of the methods for x_D
+
+;; Returns the inductive hypotheses required for the elimination method of constructor c_i for
+;; inductive type D, when eliminating with motive t_P.
 (define-metafunction tt-ctxtL
-  Δ-elim-type : Δ x U -> t
-  [(Δ-elim-type Δ x_D U)
-   (Π (x_P : (in-hole Ξ_P*D U))
-      ;; The methods Ξ_m for each constructor of type x_D
-      (in-hole Ξ_m
-        ;; And finally, the parameters and discriminant
-        (in-hole Ξ_P*D
-          ;; The result is (P a ... (x_D a ...)), i.e., the motive
-          ;; applied to the paramters and discriminant
-          (Ξ-apply Ξ_P*D x_P))))
-   ;; Get the parameters of x_D
-   (where Ξ (Δ-ref-parameter-Ξ Δ x_D))
+  Δ-constructor-inductive-hypotheses : Δ D c t -> Ξ
+  [(Δ-constructor-inductive-hypotheses Δ D c_i t_P)
+   (hypotheses-loop D t_P (Δ-constructor-inductive-telescope Δ D c_i))])
+
+;; Returns the type of the method corresponding to c_i
+(define-metafunction tt-ctxtL
+  Δ-constructor-method-type : Δ D c t -> t
+  [(Δ-constructor-method-type Δ D c_i t_P)
+   (in-hole Ξ_a (in-hole Ξ_h ((in-hole Θ_p t_P) (Ξ-apply Ξ_a c_i))))
+   (where Θ_p (Δ-constructor-parameters Δ D c_i))
+   (where Ξ_a (Δ-constructor-telescope Δ D c_i))
+   (where Ξ_h (Δ-constructor-inductive-hypotheses Δ D c_i t_P))])
+
+(define-metafunction tt-ctxtL
+  Δ-method-types : Δ D e -> (t ...)
+  [(Δ-method-types Δ D e)
+   ,(map (lambda (c) (term (Δ-constructor-method-type Δ D ,c e))) (term (c ...)))
+   (where (c ...) (Δ-ref-constructors Δ D))])
+
+(define-metafunction tt-ctxtL
+  Δ-motive-type : Δ D U -> t
+  [(Δ-motive-type Δ D U)
+   (in-hole Ξ_P*D U)
+   (where Ξ (Δ-ref-parameter-Ξ Δ D))
    ;; A fresh name to bind the discriminant
-   (where x ,(variable-not-in (term (Δ Γ x_D Ξ)) 'x-D))
+   (where x ,(variable-not-in (term (Δ D Ξ)) 'x-D))
    ;; The telescope (∀ a -> ... -> (D a ...) hole), i.e.,
-   ;; of the parameters and the inductive type applied to the
-   ;; parameters
-   (where Ξ_P*D (in-hole Ξ (Π (x : (Ξ-apply Ξ x_D)) hole)))
-   ;; A fresh name for the motive
-   (where x_P ,(variable-not-in (term (Δ Γ x_D Ξ Ξ_P*D x)) 'x-P))
-   ;; The types of the methods for this inductive.
-   (where Ξ_m (Δ-methods-telescope Δ x_D x_P))])
+   ;; of the indices and the inductive type applied to the
+   ;; indices
+   (where Ξ_P*D (in-hole Ξ (Π (x : (Ξ-apply Ξ D)) hole)))])
 
 ;;; ------------------------------------------------------------------------
 ;;; Dynamic semantics
@@ -398,16 +310,21 @@
 ;;; inductively defined type x with a motive whose result is in universe U
 
 (define-extended-language tt-redL tt-ctxtL
-  ;; NB: (in-hole Θv (elim x U)) is only a value when it's a partially applied elim. However,
-  ;; determining whether or not it is partially applied cannot be done with the grammar alone.
-  (v   ::= x U (Π (x : t) t) (λ (x : t) t) (elim x U) (in-hole Θv x) (in-hole Θv (elim x U)))
-  (Θv  ::= hole (Θv v))
-  ;; call-by-value, plus reduce under Π (helps with typing checking)
-  (E   ::= hole (E e) (v E) (Π (x : v) E) (Π (x : E) e)))
+  (v  ::= x U (Π (x : t) t) (λ (x : t) t) (in-hole Θv c))
+  (Θv ::= hole (Θv v))
+  (C-elim  ::= (elim D t_P (e_i ...) (e_m ...) hole))
+  ;; call-by-value
+  (E  ::= hole (E e) (v E)
+      (elim D e (e ...) (v ... E e ...) e)
+      (elim D e (e ...) (v ...) E)
+      ;; reduce under Π (helps with typing checking)
+      ;; TODO: Should be done in conversion judgment
+      (Π (x : v) E) (Π (x : E) e)))
 
 (define Θv? (redex-match? tt-redL Θv))
 (define E? (redex-match? tt-redL E))
 (define v? (redex-match? tt-redL v))
+
 #|
  | The elim form must appear applied like so:
  | (elim D U v_P m_0 ... m_i m_j ... m_n p ... (c_i a ...))
@@ -423,75 +340,6 @@
  |
  | Using contexts, this appears as (in-hole Θ ((elim D U) v_P))
  |#
-
-
-;;; NB: Next 3 meta-function Assume of Θ n constructors, j parameters, n+j+1-th element is discriminant
-
-;; Given the apply context Θ in which an elimination of D with motive
-;; v of type U appears, extract the parameters p ... from Θ.
-(define-metafunction tt-redL
-  elim-parameters : Δ D Θ -> Θ
-  [(elim-parameters Δ D Θ)
-    ;; Drop the methods, take the parameters
-   (list->Θ
-    ,(take
-      (drop (term (Θ->list Θ)) (term (Δ-constructor-count Δ D)))
-      (term (Δ-parameter-count Δ D))))])
-
-;; Given the apply context Θ in which an elimination of D with motive
-;; v of type U appears, extract the methods m_0 ... m_n from Θ.
-(define-metafunction tt-redL
-  elim-methods : Δ D Θ -> Θ
-  [(elim-methods Δ D Θ)
-   ;; Take the methods, one for each constructor
-   (list->Θ
-    ,(take
-      (term (Θ->list Θ))
-      (term (Δ-constructor-count Δ D))))])
-
-;; Given the apply context Θ in which an elimination of D with motive
-;; v of type U appears, extract the discriminant (c_i a ...) from Θ.
-(define-metafunction tt-redL
-  elim-discriminant : Δ D Θ -> e
-  [(elim-discriminant Δ D Θ)
-   ;; Drop the methods, the parameters, and take the last element
-   ,(car
-     (drop
-      (drop (term (Θ->list Θ)) (term (Δ-constructor-count Δ D)))
-      (term (Δ-parameter-count Δ D))))])
-
-;; Check that Θ is valid and ready to be evaluated as the arguments to an elim.
-;; has length m = n + j + 1 and D has n constructors and j parameters,
-;; and the 1 represents the discriminant.
-;; discharges assumption for previous 3 meta-functions
-(define-metafunction tt-redL
-  Θ-valid : Δ D Θ -> #t or #f
-  [(Θ-valid Δ D Θ)
-   #t
-   (where natural_m (Θ-length Θ))
-   (where natural_n (Δ-constructor-count Δ D))
-   (where natural_j (Δ-parameter-count Δ D))
-   (side-condition (= (+ (term natural_n) (term natural_j) 1) (term natural_m)))
-   ;; As Cur allows reducing (through reflection) open terms, 
-   ;; check that the discriminant is a canonical form so that
-   ;; reduction can proceed; otherwise not valid.
-   (where (in-hole Θ_i c_i) (elim-discriminant Δ D Θ))
-   (where D (Δ-key-by-constructor Δ c_i))]
-  [(Θ-valid Δ D Θ) #f])
-
-(module+ test
-  (require rackunit)
-  (check-equal?
-   (term (Θ-length (((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x))))) zero)))
-   3)
-  (check-true
-   (term
-    (Θ-valid
-     ((∅ (nat : (Unv 0) ((zero : nat) (s : (Π (x : nat) nat))))) (bool : (Unv 0) ((true : bool) (false : bool))))
-     nat
-     (((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x))))) zero)))))
-
-
 (define-metafunction tt-ctxtL
   is-inductive-argument : Δ D t -> #t or #f
   ;; Think this only works in call-by-value. A better solution would
@@ -505,39 +353,34 @@
 ;; x_ci for x_D, for each inductively smaller term t_i of type (in-hole Θ_p x_D) inside Θ_i,
 ;; generate: (elim x_D U t_P  Θ_m ... Θ_p ... t_i)
 ;; TODO TTEESSSSSTTTTTTTT
-(define-metafunction tt-ctxtL
-  Δ-inductive-elim : Δ x U t Θ Θ Θ -> Θ
+(define-metafunction tt-redL
+  Δ-inductive-elim : Δ D C-elim Θ -> Θ
   ;; NB: If metafunction fails, recursive
   ;; NB: elimination will be wrong. This will introduced extremely sublte bugs,
   ;; NB: inconsistency, failure of type safety, and other bad things.
   ;; NB: It should be tested and audited thoroughly
-  [(Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m (Θ_i t_i))
-   ((Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m Θ_i)
-    (in-hole ((in-hole Θ_p Θ_m) t_i) ((elim x_D U) t_P)))
-   (side-condition (term (is-inductive-argument Δ x_D t_i)))]
-  [(Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m (Θ_i t_i))
-   (Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m Θ_i)]
-  [(Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m hole)
-   hole])
+  [(Δ-inductive-elim any ... hole)
+   hole]
+  [(Δ-inductive-elim Δ D C-elim (Θ_c t_i))
+   ((Δ-inductive-elim Δ D C-elim Θ_c)
+    (in-hole C-elim t_i))
+   (side-condition (term (is-inductive-argument Δ D t_i)))]
+  [(Δ-inductive-elim any ... (Θ_c t_i))
+   (Δ-inductive-elim any ... Θ_c)])
 
 (define tt-->
   (reduction-relation tt-redL
     (--> (Δ (in-hole E ((λ (x : t_0) t_1) t_2)))
          (Δ (in-hole E (subst t_1 x t_2)))
          -->β)
-    (--> (Δ (in-hole E (in-hole Θv ((elim D U) v_P))))
-         (Δ (in-hole E (in-hole Θ_r (in-hole Θv_i v_mi))))
-         ;; Check that Θv is valid to avoid capturing other things
-         (side-condition (term (Θ-valid Δ D Θv)))
-          ;; Split Θv into its components: the paramters Θv_P for x_D, the methods Θv_m for x_D, and
-          ;; the discriminant: the constructor c_i applied to its argument Θv_i
-         (where Θv_p (elim-parameters Δ D Θv))
-         (where Θv_m (elim-methods Δ D Θv))
-         (where (in-hole Θv_i c_i) (elim-discriminant Δ D Θv))
-         ;; Find the method for constructor x_ci, relying on the order of the arguments.
-         (where v_mi (Θ-ref Θv_m (Δ-constructor-index Δ D c_i)))
+    (--> (Δ (in-hole E (elim D e_motive (e_i ...) (v_m ...) (in-hole Θv_c c))))
+         (Δ (in-hole E (in-hole Θ_mi v_mi)))
+         ;; Find the method for constructor c_i, relying on the order of the arguments.
+         (where natural (Δ-constructor-index Δ D c))
+         (where v_mi ,(list-ref (term (v_m ...)) (term natural)))
          ;; Generate the inductive recursion
-         (where Θ_r (Δ-inductive-elim Δ D U v_P Θv_p Θv_m Θv_i))
+         (where Θ_ih (Δ-inductive-elim Δ D (elim D e_motive (e_i ...) (v_m ...) hole) Θv_c))
+         (where Θ_mi (in-hole Θ_ih Θv_c))
          -->elim)))
 
 (define-metafunction tt-redL
@@ -698,10 +541,16 @@
    ----------------- "DTR-Application"
    (type-infer Δ Γ (e_0 e_1) t_3)]
 
-  [(where t (Δ-elim-type Δ D U))
-   (type-infer Δ Γ t U_e)
+  [(type-check Δ Γ e_c (apply D e_i ...))
+
+   (type-infer Δ Γ e_motive (name t_motive (in-hole Ξ U)))
+   (convert Δ Γ t_motive (Δ-motive-type Δ D U))
+
+   (where (t_m ...) (Δ-method-types Δ D e_motive))
+   (type-check Δ Γ e_m t_m) ...
    ----------------- "DTR-Elim_D"
-   (type-infer Δ Γ (elim D U) t)])
+   (type-infer Δ Γ (elim D e_motive (e_i ...) (e_m ...) e_c)
+               (apply e_motive e_i ... e_c))])
 
 (define-judgment-form tt-typingL
   #:mode (type-check I I I I)
diff --git a/cur-lib/cur/curnel/redex-lang.rkt b/cur-lib/cur/curnel/redex-lang.rkt
index 34dbcd7..36ce469 100644
--- a/cur-lib/cur/curnel/redex-lang.rkt
+++ b/cur-lib/cur/curnel/redex-lang.rkt
@@ -2,7 +2,7 @@
 ;; This module just provide module language sugar over the redex model.
 
 (require
-  "redex-core.rkt"
+  (except-in "redex-core.rkt" apply)
   redex/reduction-semantics
   racket/provide-syntax
   (for-syntax
@@ -11,7 +11,7 @@
     racket/syntax
     (except-in racket/provide-transform export)
     racket/require-transform
-    "redex-core.rkt"
+    (except-in "redex-core.rkt" apply)
     redex/reduction-semantics))
 (provide
   ;; Basic syntax
@@ -177,10 +177,11 @@
                     [e (parameterize ([gamma (extend-Γ/term gamma x t)])
                          (cur->datum #'e))])
                (term (,(syntax->datum #'b) (,x : ,t) ,e)))]
-            [(elim t1 t2)
-             (let* ([t1 (cur->datum #'t1)]
-                    [t2 (cur->datum #'t2)])
-               (term (elim ,t1 ,t2)))]
+            [(elim D motive (i ...) (m ...) d)
+             (term (elim ,(cur->datum #'D) ,(cur->datum #'motive)
+                         ,(map cur->datum (syntax->list #'(i ...)))
+                         ,(map cur->datum (syntax->list #'(m ...)))
+                         ,(cur->datum #'d)))]
             [(#%app e1 e2)
              (term (,(cur->datum #'e1) ,(cur->datum #'e2)))]))))
     (unless (or (inner-expand?) (type-infer/term reified-term))
@@ -446,9 +447,9 @@
 
 (define-syntax (dep-elim syn)
   (syntax-parse syn
-    [(_ D:id T)
+    [(_ D:id motive (i ...) (m ...) e)
      (syntax->curnel-syntax
-       (quasisyntax/loc syn (elim D T)))]))
+       (quasisyntax/loc syn (elim D motive (i ...) (m ...) e)))]))
 
 (define-syntax-rule (dep-void) (void))
 
diff --git a/cur-lib/cur/olly.rkt b/cur-lib/cur/olly.rkt
index ff4fe25..5db151b 100644
--- a/cur-lib/cur/olly.rkt
+++ b/cur-lib/cur/olly.rkt
@@ -95,8 +95,18 @@
                                      (cur->coq #'t))]))))
                "")]
             [(Type i) "Type"]
-            [(real-elim var t)
-             (format "~a_rect" (cur->coq #'var))]
+            [(real-elim var:id motive (i ...) (m ...) d)
+             (format
+              "(~a_rect ~a~a~a ~a)"
+              (cur->coq #'var)
+              (cur->coq #'motive)
+              (for/fold ([strs ""])
+                        ([m (syntax->list #'(m ...))])
+                (format "~a ~a" strs (cur->coq m)))
+              (for/fold ([strs ""])
+                        ([i (syntax->list #'(i ...))])
+                (format "~a ~a" strs (cur->coq i)))
+              (cur->coq #'d))]
             [(real-app e1 e2)
              (format "(~a ~a)" (cur->coq #'e1) (cur->coq #'e2))]
             [e:id (sanitize-id (format "~a" (syntax->datum #'e)))])))
diff --git a/cur-lib/cur/stdlib/prop.rkt b/cur-lib/cur/stdlib/prop.rkt
index a61bc52..3c3a191 100644
--- a/cur-lib/cur/stdlib/prop.rkt
+++ b/cur-lib/cur/stdlib/prop.rkt
@@ -71,11 +71,12 @@
 (define proof:A-or-A
   (lambda (A : Type) (c : (Or A A))
     ;; TODO: What should the motive be?
-    (elim Or Type (lambda (A : Type) (B : Type) (c : (Or A B)) A)
-      (lambda (A : Type) (B : Type) (a : A) a)
-      ;; TODO: How do we know B is A?
-      (lambda (A : Type) (B : Type) (b : B) b)
-      A A c)))
+    (elim Or (lambda (A : Type) (B : Type) (c : (Or A B)) A)
+          (A A)
+          ((lambda (A : Type) (B : Type) (a : A) a)
+           ;; TODO: How do we know B is A?
+           (lambda (A : Type) (B : Type) (b : B) b))
+          c)))
 
 (qed thm:A-or-A proof:A-or-A)
 |#
diff --git a/cur-lib/cur/stdlib/sugar.rkt b/cur-lib/cur/stdlib/sugar.rkt
index 71654b5..fb7ba99 100644
--- a/cur-lib/cur/stdlib/sugar.rkt
+++ b/cur-lib/cur/stdlib/sugar.rkt
@@ -12,7 +12,6 @@
   #%app
   define
   :
-  elim
   define-type
   match
   recur
@@ -29,7 +28,6 @@
 
 (require
   (only-in "../main.rkt"
-    [elim real-elim]
     [#%app real-app]
     [λ real-lambda]
     [Π real-Π]
@@ -163,8 +161,67 @@
      (quasisyntax/loc syn
        (real-define id body))]))
 
-(define-syntax-rule (elim t1 t2 e ...)
-  ((real-elim t1 t2) e ...))
+#|
+(begin-for-syntax
+  (define (type->telescope syn)
+    (syntax-parse (cur-expand syn)
+      #:literals (real-Π)
+      #:datum-literals (:)
+      [(real-Π (x:id : t) body)
+       (cons #'(x : t) (type->telescope #'body))]
+      [_ '()]))
+
+  (define (type->body syn)
+    (syntax-parse syn
+      #:literals (real-Π)
+      #:datum-literals (:)
+      [(real-Π (x:id : t) body)
+       (type->body #'body)]
+      [e #'e]))
+
+  (define (constructor-indices D syn)
+    (let loop ([syn syn]
+               [args '()])
+      (syntax-parse (cur-expand syn)
+        #:literals (real-app)
+        [D:id args]
+        [(real-app e1 e2)
+         (loop #'e1 (cons #'e2 args))])))
+
+  (define (inductive-index-telescope D)
+    (type->telescope (cur-type-infer D)))
+
+  (define (inductive-method-telescope D motive)
+    (for/list ([syn (cur-constructor-map D)])
+      (with-syntax ([(c : t) syn]
+                    [name (gensym (format-symbol "~a-~a" #'c 'method))]
+                    [((arg : arg-type) ...) (type->telescope #'t)]
+                    [((rarg : rarg-type) ...) (constructor-recursive-args D #'((arg : arg-type) ...))]
+                    [((ih : ih-type) ...) (constructor-inductive-hypotheses #'((rarg : rarg-type) ...) motive)]
+                    [(iarg ...) (constructor-indices D (type->body #'t))]
+                    )
+        #`(name : (forall (arg : arg-type) ...
+                          (ih : ih-type) ...
+                          (motive iarg ...)))))))
+
+(define-syntax (elim syn)
+  (syntax-parse syn
+    [(elim D:id U e ...)
+     (with-syntax ([((x : t) ...) (inductive-index-telescope #'D)]
+                   [motive (gensym 'motive)]
+                   [y (gensym 'y)]
+                   [disc (gensym 'disc)]
+                   [((method : method-type) ...) (inductive-method-telescope #'D #'motive)])
+       #`((lambda
+            (motive : (forall (x : t) ... (y : (D x ...)) U))
+            (method : ) ...
+            (x : t) ...
+            (disc : (D x ...)) ...
+            (real-elim D motive (x ...) (method ...) disc))
+          e ...)
+       )
+     ]))
+|#
 
 ;; Quite fragie to give a syntactic treatment of pattern matching -> eliminator. Replace with "Elimination with a Motive"
 (begin-for-syntax
@@ -366,15 +423,9 @@
      (quasisyntax/loc syn
        (elim
         D.inductive-name
-        #,(or
-           (cur-type-infer (attribute return-type))
-           (raise-syntax-error
-            'match
-            "Could not infer type of motive. Sorry, you'll have to use elim."
-            syn))
         motive
-        c.method ...
-        #,@(attribute D.indices)
+        #,(attribute D.indices)
+        (c.method ...)
         d))]))
 
 (begin-for-syntax
diff --git a/cur-lib/info.rkt b/cur-lib/info.rkt
index 916ccf0..0369661 100644
--- a/cur-lib/info.rkt
+++ b/cur-lib/info.rkt
@@ -3,5 +3,5 @@
 (define deps '("base" ("redex-lib" #:version "1.11")))
 (define build-deps '())
 (define pkg-desc "implementation (no documentation, tests) part of \"cur\".")
-(define version "0.3")
+(define version "0.4")
 (define pkg-authors '(wilbowma))
diff --git a/cur-test/cur/tests/olly.rkt b/cur-test/cur/tests/olly.rkt
index a2cda7b..e40c5cd 100644
--- a/cur-test/cur/tests/olly.rkt
+++ b/cur-test/cur/tests/olly.rkt
@@ -41,11 +41,12 @@
      "\\| T-Bla : \\(forall g : gamma, \\(forall e : term, \\(forall t : type, \\(\\(\\(meow g\\) e\\) t\\)\\)\\)\\)\\."
      (second (string-split t "\n"))))
   (let ([t (cur->coq
-            #'(elim nat Type (lambda (x : nat) nat) z
-                    (lambda (x : nat) (ih-x : nat) ih-x)
+            #'(elim nat (lambda (x : nat) nat)
+                    ()
+                    (z (lambda (x : nat) (ih-x : nat) ih-x))
                     e))])
     (check-regexp-match
-     "\\(\\(\\(\\(nat_rect \\(fun x : nat => nat\\)\\) z\\) \\(fun x : nat => \\(fun ih_x : nat => ih_x\\)\\)\\) e\\)"
+     "\\(nat_rect \\(fun x : nat => nat\\) z \\(fun x : nat => \\(fun ih_x : nat => ih_x\\)\\) e\\)"
      t))
   (check-regexp-match
    "Definition thm_plus_commutes := \\(forall n : nat, \\(forall m : nat, \\(\\(\\(== nat\\) \\(\\(plus n\\) m\\)\\) \\(\\(plus m\\) n\\)\\)\\)\\).\n"
diff --git a/cur-test/cur/tests/redex-core.rkt b/cur-test/cur/tests/redex-core.rkt
index 52ad81d..2c381b1 100644
--- a/cur-test/cur/tests/redex-core.rkt
+++ b/cur-test/cur/tests/redex-core.rkt
@@ -81,23 +81,6 @@
    (Π (a : S) (Π (b : B) ((and S) B)))
    (subst (Π (a : A) (Π (b : B) ((and A) B))) A S))))
 
-;; Various accessor tests
-;; ------------------------------------------------------------------------
-
-(check-equal?
- (term (Δ-key-by-constructor ,Δ zero))
- (term nat))
-(check-equal?
- (term (Δ-key-by-constructor ,Δ s))
- (term nat))
-
-(check-equal?
- (term (Δ-ref-constructor-map ,Δ nat))
- (term ((zero : nat) (s : (Π (x : nat) nat)))))
-(check-equal?
- (term (Δ-ref-constructor-map ,sigma false))
- (term ()))
-
 ;; Telescope tests
 ;; ------------------------------------------------------------------------
 ;; Are these telescopes the same when filled with alpha-equivalent, and equivalently renamed, termed
@@ -115,41 +98,10 @@
  (term (Δ-ref-parameter-Ξ ,Δ4 and))
  (term (Π (A : Type) (Π (B : Type) hole))))
 
-(check-telescope-equiv?
- (term (Ξ-compose
-        (Π (x : t_0) (Π (y : t_1) hole))
-        (Π (z : t_2) (Π (a : t_3) hole))))
- (term (Π (x : t_0) (Π (y : t_1) (Π (z : t_2) (Π (a : t_3) hole))))))
-
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,Δ nat (λ (x : nat) nat)))
- (term (Π (m-zero : ((λ (x : nat) nat) zero))
-          (Π (m-s : (Π (x : nat) (Π (x-ih : ((λ (x : nat) nat) x)) ((λ (x : nat) nat) (s x))))) hole))))
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,Δ nat P))
- (term (Π (m-zero : (P zero))
-          (Π (m-s : (Π (x : nat) (Π (ih-x : (P x)) (P (s x)))))
-             hole))))
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,Δ  nat (λ (x : nat) nat)))
- (term (Π (m-zero :  ((λ (x : nat) nat) zero))
-          (Π (m-s : (Π (x : nat) (Π (ih-x : ((λ (x : nat) nat) x)) ((λ (x : nat) nat) (s x)))))
-             hole))))
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,Δ4 and (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) true)))))
- (term (Π (m-conj : (Π (A : Type) (Π (B : Type) (Π (a : A) (Π (b : B)
-                                                              ((((λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) true)))
-                                                                 A)
-                                                                B)
-                                                               ((((conj A) B) a) b)))))))
-          hole)))
 (check-true (x? (term false)))
 (check-true (Ξ? (term hole)))
 (check-true (t? (term (λ (y : false) (Π (x : Type) x)))))
 (check-true (redex-match? ttL ((x : t) ...) (term ())))
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,sigma false (λ (y : false) (Π (x : Type) x))))
- (term hole))
 
 ;; Tests for inductive elimination
 ;; ------------------------------------------------------------------------
@@ -157,21 +109,32 @@
 (check-true
  (redex-match? tt-ctxtL (in-hole Θ_i (hole (in-hole Θ_r zero))) (term (hole zero))))
 (check-telescope-equiv?
- (term (Δ-inductive-elim ,Δ nat Type (λ (x : nat) nat) hole
-                         ((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+ (term (Δ-inductive-elim ,Δ nat
+                         (elim nat (λ (x : nat) nat) ()
+                               ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                               hole)
                          (hole zero)))
- (term (hole (((((elim nat Type) (λ (x : nat) nat))
-                (s zero))
-               (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-              zero))))
+ (term (hole (elim nat (λ (x : nat) nat)
+                   ()
+                   ((s zero)
+                    (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                   zero))))
 (check-telescope-equiv?
- (term (Δ-inductive-elim ,Δ nat Type (λ (x : nat) nat) hole
-                         ((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+ (term (Δ-inductive-elim ,Δ nat
+                         (elim nat (λ (x : nat) nat) ()
+                               ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                               hole)
                          (hole (s zero))))
- (term (hole (((((elim nat Type) (λ (x : nat) nat))
-                (s zero))
-               (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-              (s zero)))))
+ (term (hole (elim nat (λ (x : nat) nat) ()
+                   ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                   (s zero)))))
+(check-telescope-equiv?
+ (term (Δ-inductive-elim ,Δ nat
+                         (elim nat (λ (x : nat) nat) ()
+                               ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                               hole)
+                         hole))
+ (term hole))
 
 ;; Tests for dynamic semantics
 ;; ------------------------------------------------------------------------
@@ -179,6 +142,8 @@
 (check-true (v? (term (λ (x_0 : (Unv 0)) x_0))))
 (check-true (v? (term (refl Nat))))
 (check-true (v? (term ((refl Nat) z))))
+(check-true (v? (term zero)))
+(check-true (v? (term (s zero))))
 
 ;; TODO: Move equivalence up here, and use in these tests.
 (check-equiv? (term (reduce ∅ (Unv 0))) (term (Unv 0)))
@@ -188,60 +153,68 @@
                   (term (Π (x : t) (Unv 0))))
 (check-not-equiv? (term (reduce ∅ (Π (x : t) ((Π (x_0 : t) (x_0 x)) x))))
                   (term (Π (x : t) (x x))))
-(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
-                                  (s zero))
-                                 (λ (x : nat) (λ (ih-x : nat)
-                                                (s (s x)))))
-                                zero)))
+
+(check-equal? (term (Δ-constructor-index ,Δ nat zero)) 0)
+(check-equiv? (term (reduce ,Δ (elim nat (λ (x : nat) nat)
+                                     ()
+                                     ((s zero)
+                                      (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                                     zero)))
               (term (s zero)))
-(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
-                                  (s zero))
-                                 (λ (x : nat) (λ (ih-x : nat)
-                                                (s (s x)))))
-                                (s zero))))
+(check-equiv? (term (reduce ,Δ (elim nat (λ (x : nat) nat)
+                                     ()
+                                     ((s zero)
+                                      (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                                     (s zero))))
               (term (s (s zero))))
-(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
-                                  (s zero))
-                                 (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+(check-equiv? (term (reduce ,Δ (elim nat (λ (x : nat) nat)
+                                     ()
+                                     ((s zero)
+                                      (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
                                 (s (s (s zero))))))
               (term (s (s (s (s zero))))))
 
 (check-equiv?
  (term (reduce ,Δ
-               (((((elim nat Type) (λ (x : nat) nat))
-                  (s (s zero)))
-                 (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-                (s (s zero)))))
+               (elim nat (λ (x : nat) nat)
+                     ()
+                     ((s (s zero))
+                      (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
+                     (s (s zero)))))
  (term (s (s (s (s zero))))))
 (check-equiv?
  (term (step ,Δ
-             (((((elim nat Type) (λ (x : nat) nat))
-                (s (s zero)))
-               (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-              (s (s zero)))))
+             (elim nat (λ (x : nat) nat)
+                     ()
+                     ((s (s zero))
+                      (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
+                     (s (s zero)))))
  (term
   (((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
     (s zero))
-   (((((elim nat Type) (λ (x : nat) nat))
-      (s (s zero)))
-     (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-    (s zero)))))
+   (elim nat (λ (x : nat) nat)
+         ()
+         ((s (s zero))
+          (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
+         (s zero)))))
 (check-equiv?
  (term (step ,Δ (step ,Δ
                       (((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
                         (s zero))
-                       (((((elim nat Type) (λ (x : nat) nat))
-                          (s (s zero)))
-                         (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-                        (s zero))))))
+                       (elim nat (λ (x : nat) nat)
+                             ()
+                             ((s (s zero))
+                              (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
+                             (s zero))))))
  (term
   ((λ (ih-x1 : nat) (s ih-x1))
    (((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
      zero)
-    (((((elim nat Type) (λ (x : nat) nat))
-       (s (s zero)))
-      (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-     zero)))))
+    (elim nat (λ (x : nat) nat)
+          ()
+          ((s (s zero))
+           (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
+          zero)))))
 
 (define-syntax-rule (check-equivalent e1 e2)
   (check-holds (convert ∅ ∅ e1 e2)))
@@ -343,28 +316,42 @@
                U))
 ;; ---- Elim
 ;; TODO: Clean up/Reorganize these tests
-(check-true
- (redex-match? tt-typingL
-               (in-hole Θ_m (((elim x_D U) e_D) e_P))
-               (term ((((elim truth Type) T) (Π (x : truth) (Unv 1))) (Unv 0)))))
 (define Δtruth (term (∅ (truth : (Unv 0) ((T : truth))))))
 (check-holds (type-infer ,Δtruth ∅ truth (in-hole Ξ U)))
 (check-holds (type-infer ,Δtruth ∅ T (in-hole Θ_ai truth)))
 (check-holds (type-infer ,Δtruth ∅ (λ (x : truth) (Unv 1))
                          (in-hole Ξ (Π (x : (in-hole Θ truth)) U))))
 
-(check-telescope-equiv?
- (term (Δ-methods-telescope ,Δtruth truth (λ (x : truth) (Unv 1))))
- (term (Π (m-T : ((λ (x : truth) (Unv 1)) T)) hole)))
-(check-holds (type-infer ,Δtruth ∅ (elim truth Type) t))
-(check-holds (type-check (∅ (truth : (Unv 0) ((T : truth))))
+(check-equiv?
+ (term (Δ-motive-type ,Δtruth truth (Unv 2)))
+ (term (Π (x : truth) (Unv 2))))
+
+
+(check-holds (type-check ,Δtruth ∅ (Unv 0) ,(car (term (Δ-method-types ,Δtruth truth (λ (x : truth) (Unv 1)))))))
+
+(check-holds (type-check ,Δtruth ∅ (λ (x : truth) (Unv 1)) (Π (x : truth) (Unv 2))))
+
+(check-equiv?
+ (term (apply (λ (x : truth) (Unv 1)) T))
+ (term ((λ (x : truth) (Unv 1)) T)))
+
+(check-holds
+ (convert ,Δtruth ∅ (apply (λ (x : truth) (Unv 1)) T) (Unv 1)))
+
+(check-holds (type-infer ,Δtruth
                          ∅
-                         ((((elim truth (Unv 2)) (λ (x : truth) (Unv 1))) (Unv 0))
-                          T)
+                         (elim truth (λ (x : truth) (Unv 1))
+                               () ((Unv 0)) T)
+                         t))
+
+(check-holds (type-check ,Δtruth
+                         ∅
+                         (elim truth (λ (x : truth) (Unv 1))
+                               () ((Unv 0)) T)
                          (Unv 1)))
 (check-not-holds (type-check (∅ (truth : (Unv 0) ((T : truth))))
                              ∅
-                             ((((elim truth (Unv 1)) Type) Type) T)
+                             (elim truth Type () (Type) T)
                              (Unv 1)))
 (check-holds
  (type-infer ∅ ∅ (Π (x2 : (Unv 0)) (Unv 0)) U))
@@ -382,47 +369,54 @@
   (check-holds (type-check ,Δ syn ...)))
 (nat-test ∅ (Π (x : nat) nat) (Unv 0))
 (nat-test ∅ (λ (x : nat) x) (Π (x : nat) nat))
-(nat-test ∅ (((((elim nat Type) (λ (x : nat) nat)) zero)
-              (λ (x : nat) (λ (ih-x : nat) x))) zero)
+(nat-test ∅ (elim nat (λ (x : nat) nat) ()
+                  (zero (λ (x : nat) (λ (ih-x : nat) x)))
+                  zero)
             nat)
 (nat-test ∅ nat (Unv 0))
 (nat-test ∅ zero nat)
 (nat-test ∅ s (Π (x : nat) nat))
 (nat-test ∅ (s zero) nat)
-;; TODO: Meta-function auto-currying and such
 (check-holds
- (type-infer ,Δ ∅ ((((elim nat (Unv 0)) (λ (x : nat) nat))
-                    zero)
-                   (λ (x : nat) (λ (ih-x : nat) x)))
+ (type-infer ,Δ ∅ (λ (x : nat)
+                    (elim nat (λ (x : nat) nat)
+                          ()
+                          (zero
+                           (λ (x : nat) (λ (ih-x : nat) x)))
+                          x))
              t))
-(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
-               zero)
-              (λ (x : nat) (λ (ih-x : nat) x)))
-             zero)
+(nat-test ∅ (elim nat (λ (x : nat) nat)
+                  ()
+                  (zero (λ (x : nat) (λ (ih-x : nat) x)))
+                  zero)
             nat)
-(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
-               (s zero))
-              (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-             zero)
+(nat-test ∅ (elim nat (λ (x : nat) nat)
+                  ()
+                  ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                  zero)
             nat)
-(nat-test ∅ (((((elim nat Type) (λ (x : nat) nat))
-               (s zero))
-              (λ (x : nat) (λ (ih-x : nat) (s (s x))))) zero)
+(nat-test ∅ (elim nat (λ (x : nat) nat)
+                  ()
+                  ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+                  zero)
             nat)
 (nat-test (∅ n : nat)
-          (((((elim nat (Unv 0)) (λ (x : nat) nat)) zero) (λ (x : nat) (λ (ih-x : nat) x))) n)
+          (elim nat (λ (x : nat) nat)
+                ()
+                (zero (λ (x : nat) (λ (ih-x : nat) x)))
+                n)
           nat)
 (check-holds
  (type-check (,Δ (bool : (Unv 0) ((btrue : bool) (bfalse : bool))))
              (∅ n2 : nat)
-             (((((elim nat (Unv 0)) (λ (x : nat) bool))
-                btrue)
-               (λ (x : nat) (λ (ih-x : bool) bfalse)))
-              n2)
+             (elim nat (λ (x : nat) bool)
+                   ()
+                   (btrue (λ (x : nat) (λ (ih-x : bool) bfalse)))
+                   n2)
              bool))
 (check-not-holds
  (type-check ,Δ ∅
-             ((((elim nat (Unv 0)) nat) (s zero)) zero)
+             (elim nat nat () ((s zero)) zero)
              nat))
 (define lam (term (λ (nat : (Unv 0)) nat)))
 (check-equivalent
@@ -481,15 +475,15 @@
              (in-hole Ξ (Π (x : (in-hole Θ_Ξ and)) U_P))))
 (check-holds
  (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
-             ((((((elim and (Unv 0))
-                  (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
-                                                true))))
-                 (λ (A : (Unv 0))
-                   (λ (B : (Unv 0))
-                     (λ (a : A)
-                       (λ (b : B) tt)))))
-                true) true)
-              ((((conj true) true) tt) tt))
+             (elim and
+                   (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
+                                                 true)))
+                   (true true)
+                   ((λ (A : (Unv 0))
+                      (λ (B : (Unv 0))
+                        (λ (a : A)
+                          (λ (b : B) tt)))))
+                   ((((conj true) true) tt) tt))
              true))
 (check-true (Γ? (term (((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q)))))
 (check-holds
@@ -518,14 +512,15 @@
 (check-holds
  (type-check ,Δ4
              (((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q))
-             ((((((elim and (Unv 0))
-                  (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
-                                                ((and B) A)))))
-                 (λ (A : (Unv 0))
-                   (λ (B : (Unv 0))
-                     (λ (a : A)
-                       (λ (b : B) ((((conj B) A) b) a))))))
-                P) Q) ab)
+             (elim and
+                   (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
+                                                 ((and B) A))))
+                   (P Q)
+                   ((λ (A : (Unv 0))
+                      (λ (B : (Unv 0))
+                        (λ (a : A)
+                          (λ (b : B) ((((conj B) A) b) a))))))
+                   ab)
              ((and Q) P)))
 (check-holds
  (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
@@ -538,14 +533,14 @@
              t))
 (check-holds
  (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
-             ((((((elim and (Unv 0))
+             (elim and
                   (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
-                                                ((and B) A)))))
-                 (λ (A : (Unv 0))
+                                                ((and B) A))))
+                 (true true)
+                 ((λ (A : (Unv 0))
                    (λ (B : (Unv 0))
                      (λ (a : A)
                        (λ (b : B) ((((conj B) A) b) a))))))
-                true) true)
               ((((conj true) true) tt) tt))
              ((and true) true)))
 (define gamma (term (∅ temp863 : pre)))
@@ -568,21 +563,18 @@
 (check-holds
  (type-infer ,sigma (,gamma x : false) (λ (y : false) (Π (x : Type) x))
              (in-hole Ξ (Π (x : (in-hole Θ false)) U))))
-(check-true
- (redex-match? tt-typingL
-               ((in-hole Θ_m ((elim x_D U) e_P)) e_D)
-               (term (((elim false (Unv 1)) (λ (y : false) (Π (x : Type) x)))
-                      x))))
+
 (check-holds
  (type-check ,sigma (,gamma x : false)
-             (((elim false (Unv 0)) (λ (y : false) (Π (x : Type) x))) x)
+             (elim false (λ (y : false) (Π (x : Type) x)) () () x)
              (Π (x : (Unv 0)) x)))
 
 ;; nat-equal? tests
 (define zero?
-  (term ((((elim nat Type) (λ (x : nat) bool))
-          true)
-         (λ (x : nat) (λ (x_ih : bool) false)))))
+  (term (λ (n : nat)
+          (elim nat (λ (x : nat) bool) ()
+              (true (λ (x : nat) (λ (x_ih : bool) false)))
+              n))))
 (check-holds
  (type-check ,Δ ∅ ,zero? (Π (x : nat) bool)))
 (check-equal?
@@ -592,9 +584,12 @@
  (term (reduce ,Δ (,zero? (s zero))))
  (term false))
 (define ih-equal?
-  (term ((((elim nat Type) (λ (x : nat) bool))
-          false)
-         (λ (x : nat) (λ (y : bool) (x_ih x))))))
+  (term (λ (ih : nat)
+          (elim nat (λ (x : nat) bool)
+              ()
+              (false
+               (λ (x : nat) (λ (y : bool) (x_ih x))))
+              ih))))
 (check-holds
  (type-check ,Δ (∅ x_ih : (Π (x : nat) bool))
              ,ih-equal?
@@ -606,10 +601,13 @@
 (check-holds
  (type-infer ,Δ ∅ (λ (x : nat) (Π (x : nat) bool)) (Π (x : nat) (Unv 0))))
 (define nat-equal?
-  (term ((((elim nat Type) (λ (x : nat) (Π (x : nat) bool)))
-          ,zero?)
-         (λ (x : nat) (λ (x_ih : (Π (x : nat) bool))
-                        ,ih-equal?)))))
+  (term (λ (n : nat)
+          (elim nat (λ (x : nat) (Π (x : nat) bool))
+              ()
+              (,zero?
+              (λ (x : nat) (λ (x_ih : (Π (x : nat) bool))
+                             ,ih-equal?)))
+              n))))
 (check-holds
  (type-check ,Δ (∅ nat-equal? : (Π (x-D«4158» : nat) ((λ (x«4159» : nat) (Π (x«4160» : nat) bool)) x-D«4158»)))
              ((nat-equal? zero) zero)
@@ -631,19 +629,12 @@
 (check-true (Δ? Δ=))
 
 (define refl-elim
-  (term (((((((elim == (Unv 0)) (λ (A1 : (Unv 0)) (λ (x1 : A1) (λ (y1 : A1) (λ (p2 : (((==
-                                                                                        A1)
-                                                                                       x1)
-                                                                                      y1))
-                                                                              nat)))))
-             (λ (A1 : (Unv 0)) (λ (x1 : A1) zero))) bool) true) true) ((refl bool) true))))
+  (term (elim == (λ (A1 : (Unv 0)) (λ (x1 : A1) (λ (y1 : A1) (λ (p2 : (((== A1) x1) y1)) nat))))
+                  (bool true true)
+                  ((λ (A1 : (Unv 0)) (λ (x1 : A1) zero)))
+                  ((refl bool) true))))
 (check-holds
  (type-check ,Δ= ∅ ,refl-elim nat))
-(check-true
- (redex-match?
-  tt-redL
-  (Δ (in-hole E (in-hole Θ ((elim x_D U) e_P))))
-  (term (,Δ= ,refl-elim))))
 (check-true
  (redex-match?
   tt-redL
diff --git a/cur-test/cur/tests/stdlib/list.rkt b/cur-test/cur/tests/stdlib/list.rkt
index afda5a8..f560ece 100644
--- a/cur-test/cur/tests/stdlib/list.rkt
+++ b/cur-test/cur/tests/stdlib/list.rkt
@@ -32,11 +32,11 @@
  (:: (lambda (A : Type) (n : Nat) (none A)) (forall (A : Type) (-> Nat (Maybe A)))))
 (check-equal?
  (void)
- (:: (elim List Type (lambda (A : Type) (ls : (List A)) Nat)
-          (lambda (A : Type) z)
-          (lambda (A : Type) (a : A) (ls : (List A)) (ih : Nat)
-                   z)
-          Bool
+ (:: (elim List (lambda (A : Type) (ls : (List A)) Nat)
+           (Bool)
+          ((lambda (A : Type) z)
+           (lambda (A : Type) (a : A) (ls : (List A)) (ih : Nat)
+                   z))
           (nil Bool))
     Nat))
 
diff --git a/cur-test/cur/tests/stdlib/prop.rkt b/cur-test/cur/tests/stdlib/prop.rkt
index ec90b0c..0d8222e 100644
--- a/cur-test/cur/tests/stdlib/prop.rkt
+++ b/cur-test/cur/tests/stdlib/prop.rkt
@@ -11,11 +11,11 @@
 (:: pf:proj1 thm:proj1)
 (:: pf:proj2 thm:proj2)
 (check-equal?
- (elim == Type (λ (A : Type) (x : A) (y : A) (p : (== A x y)) Nat)
-       (λ (A : Type) (x : A) z)
-       Bool
-       true
-       true
+ (elim == (λ (A : Type) (x : A) (y : A) (p : (== A x y)) Nat)
+       (Bool
+        true
+        true)
+       ((λ (A : Type) (x : A) z))
        (refl Bool true))
  z)
 
diff --git a/cur-test/cur/tests/stdlib/typeclass.rkt b/cur-test/cur/tests/stdlib/typeclass.rkt
index 9f6ce6c..fb8bb27 100644
--- a/cur-test/cur/tests/stdlib/typeclass.rkt
+++ b/cur-test/cur/tests/stdlib/typeclass.rkt
@@ -11,9 +11,7 @@
            (equal? : (forall (a : A) (b : A) Bool)))
 (impl (Eqv Bool)
       (define (equal? (a : Bool) (b : Bool))
-        (if a
-            (if b true false)
-            (if b false true))))
+        (if a b (not b))))
 (impl (Eqv Nat)
       (define equal? nat-equal?))
 (check-equal?
diff --git a/cur-test/info.rkt b/cur-test/info.rkt
index 37c408b..bc46632 100644
--- a/cur-test/info.rkt
+++ b/cur-test/info.rkt
@@ -1,7 +1,7 @@
 #lang info
 (define collection 'multi)
 (define deps '())
-(define build-deps '("base" "rackunit-lib" ("cur-lib" #:version "0.2") "sweet-exp"))
+(define build-deps '("base" "rackunit-lib" ("cur-lib" #:version "0.4") "sweet-exp"))
 (define update-implies '("cur-lib"))
 (define pkg-desc "Tests for \"cur\".")
 (define pkg-authors '(wilbowma))