More quasisyntax/loc for better error messages

[FAILING] Fixing design and running tests
Fixed up some of the design and started testing.
2016-01-21 16:07:16 -05:00 · 2016-01-21 15:14:13 -05:00 · 2016-01-20 17:52:37 -05:00 · 2016-01-19 16:57:17 -05:00 · 2016-01-19 15:32:03 -05:00 · 2016-01-19 14:25:51 -05:00
31 changed files with 916 additions and 764 deletions
--- a/README.md
+++ b/README.md
@ -45,10 +45,6 @@ Try it out: open up DrRacket and put the following in the definition area:
 (if true
    false
    true)
-
-(: + (-> Nat Nat Nat))
-(define + plus)
-(+ z (s z))
 ```

 Try entering the following in the interaction area:
@ -56,23 +52,6 @@ Try entering the following in the interaction area:
 (sub1 (s (s z)))
 ```

-Don't like parenthesis? Use Cur with sweet-expressions:
-```racket
-#lang sweet-exp cur
-require
- cur/stdlib/sugar
- cur/stdlib/bool
- cur/stdlib/nat
-
-if true
-   false
-   true
-
-define + plus
-
-{z + s(z)}
-```
-
 See the docs: `raco docs cur`.

 Going further
--- 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
@ -33,44 +33,43 @@ restricted impredicative universe.
          Type]
 }

-@defform[(λ (id : type-expr) body-expr)]{
-Produces a single-arity procedure, binding the identifier @racket[id] of type
-@racket[type-expr] in @racket[body-expr] and in the type of @racket[body-expr].
-Both @racket[type-expr] and @racket[body-expr] can contain non-curnel forms,
-such as macros.
+@defform*[((lambda (id : type-expr) body-expr)
+           (λ (id : type-expr) body-expr))]{
+Produces a single arity procedure, binding the identifier @racket[id] of type @racket[type-expr] in @racket[body-expr] and in the type of
+@racket[body-expr].
+Both @racket[type-expr] and @racket[body-expr] can contain non-curnel forms, such as macros.

-Currently, Cur will return the underlying representation of a procedure when a
-@racket[λ] is evaluated at the top-level.
-Do not rely on this representation.
+Currently, Cur will return the underlying representation of a procedure when a @racket[lambda] is
+evaluated at the top-level. Do not rely on this representation.

@examples[#:eval curnel-eval
-          (λ (x : Type) x)]
+          (lambda (x : Type) x)]

@examples[#:eval curnel-eval
-          (λ (x : Type) (λ (y : x) y))]
+          (λ (x : Type) (lambda (y : x) y))]


@defform[(#%app procedure argument)]{
-Applies the single-arity @racket[procedure] to @racket[argument].
+Applies the single arity @racket[procedure] to @racket[argument].
 }

@examples[#:eval curnel-eval
-          ((λ (x : (Type 1)) x) Type)]
+          ((lambda (x : (Type 1)) x) Type)]

@examples[#:eval curnel-eval
-          (#%app (λ (x : (Type 1)) x) Type)]
+          (#%app (lambda (x : (Type 1)) x) Type)]
 }

-@defform[(Π (id : type-expr) body-expr)]{
-Produces a dependent function type, binding the identifier @racket[id] of type
-@racket[type-expr] in @racket[body-expr].
+@defform*[((forall (id : type-expr) body-expr)
+           (∀ (id : type-expr) body-expr))]{
+Produces a dependent function type, binding the identifier @racket[id] of type @racket[type-expr] in @racket[body-expr].


@examples[#:eval curnel-eval
-          (Π (x : Type) Type)]
+          (forall (x : Type) Type)]

@examples[#:eval curnel-eval
-          (λ (x : (Π (x : (Type 1)) Type))
+          (lambda (x : (forall (x : (Type 1)) Type))
            (x Type))]
 }

@ -84,35 +83,32 @@ For instance, Cur does not currently perform strict positivity checking.
          (data Bool : Type
                (true : Bool)
                (false : Bool))
-          ((λ (x : Bool) x) true)
+          ((lambda (x : Bool) x) true)
          (data False : Type)
-          (data And : (Π (A : Type) (Π (B : Type) Type))
-            (conj : (Π (A : Type) (Π (B : Type) (Π (a : A) (Π (b : B) ((And A) B)))))))
+          (data And : (forall (A : Type) (forall (B : Type) Type))
+            (conj : (forall (A : Type) (forall (B : Type) (forall (a : A) (forall (b : B) ((And A) B)))))))
          ((((conj Bool) Bool) true) false)]
 }

-@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.
+@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)].

 The following example runs @racket[(sub1 (s z))].

@examples[#:eval curnel-eval
          (data Nat : Type
            (z : Nat)
-            (s : (Π (n : Nat) Nat)))
-          (elim Nat (λ (x : Nat) Nat)
-                ()
-                (z
-                 (λ (n : Nat) (λ (IH : Nat) n)))
-                (s z))]
+            (s : (forall (n : Nat) Nat)))
+          (((((elim Nat Type)
+              (lambda (x : Nat) Nat))
+             z)
+            (lambda (n : Nat) (lambda (IH : Nat) n)))
+           (s z))]
 }

@defform[(define id expr)]{
@ -121,13 +117,11 @@ Binds @racket[id] to the result of @racket[expr].
@examples[#:eval curnel-eval
          (data Nat : Type
            (z : Nat)
-            (s : (Π (n : Nat) Nat)))
-          (define sub1 (λ (n : Nat)
-                         (elim Nat (λ (x : Nat) Nat)
-                               ()
-                               (z
-                                (λ (n : Nat) (λ (IH : Nat) n)))
-                               n)))
+            (s : (forall (n : Nat) Nat)))
+          (define sub1 (lambda (n : Nat)
+                         (((((elim Nat Type) (lambda (x : Nat) Nat))
+                           z)
+                          (lambda (n : Nat) (lambda (IH : Nat) n))) n)))
          (sub1 (s (s z)))
          (sub1 (s z))
          (sub1 z)]
--- a/cur-doc/cur/scribblings/reflection.scrbl
+++ b/cur-doc/cur/scribblings/reflection.scrbl
@ -25,61 +25,61 @@ phase 1 in Cur.}

@examples[
 (eval:alts (define-syntax-rule (computed-type _) Type) (void))
-(eval:alts (cur-expand #'(λ (x : (computed-type bla)) x))
-           (eval:result @racket[#'(λ (x : Type) x)] "" ""))
+(eval:alts (cur-expand #'(lambda (x : (computed-type bla)) x))
+           (eval:result @racket[#'(lambda (x : Type) x)] "" ""))
 ]
 }

-@defproc[(cur-type-infer [syn syntax?])
+@defproc[(type-infer/syn [syn syntax?])
         (or/c syntax? #f)]{
 Returns the type of the Cur term @racket[syn], or @racket[#f] if no type could be inferred.

@examples[
-(eval:alts (cur-type-infer #'(λ (x : Type) x))
-           (eval:result @racket[#'(Π (x : (Type 0)) (Type 0))] "" ""))
-(eval:alts (cur-type-infer #'Type)
+(eval:alts (type-infer/syn #'(lambda (x : Type) x))
+           (eval:result @racket[#'(forall (x : (Type 0)) (Type 0))] "" ""))
+(eval:alts (type-infer/syn #'Type)
           (eval:result @racket[#'(Type 1)] "" ""))
 ]
 }

-@defproc[(cur-type-check? [syn syntax?])
+@defproc[(type-check/syn? [syn syntax?])
         boolean?]{
 Returns @racket[#t] if the Cur term @racket[syn] is well-typed, or @racket[#f] otherwise.

@examples[
-(eval:alts (cur-type-check? #'(λ (x : Type) x))
+(eval:alts (type-check/syn? #'(lambda (x : Type) x))
           (eval:result @racket[#t] "" ""))
-(eval:alts (cur-type-check? #'Type)
+(eval:alts (type-check/syn? #'Type)
           (eval:result @racket[#t] "" ""))
-(eval:alts (cur-type-check? #'x)
+(eval:alts (type-check/syn? #'x)
           (eval:result @racket[#f] "" ""))
 ]
 }

-@defproc[(cur-normalize [syn syntax?])
+@defproc[(normalize/syn [syn syntax?])
         syntax?]{
 Runs the Cur term @racket[syn] to a value.

@examples[
-(eval:alts (cur-normalize #'((λ (x : Type) x) Bool))
+(eval:alts (normalize/syn #'((lambda (x : Type) x) Bool))
           (eval:result @racket[#'Bool] "" ""))
-(eval:alts (cur-normalize #'(sub1 (s (s z))))
+(eval:alts (normalize/syn #'(sub1 (s (s z))))
           (eval:result @racket[#'(s z)] "" ""))
 ]
 }

-@defproc[(cur-step [syn syntax?])
+@defproc[(step/syn [syn syntax?])
         syntax?]{
 Runs the Cur term @racket[syn] for one step.

@examples[
-(eval:alts (cur-step #'((λ (x : Type) x) Bool))
+(eval:alts (step/syn #'((lambda (x : Type) x) Bool))
           (eval:result @racket[#'Bool] "" ""))
-(eval:alts (cur-step #'(sub1 (s (s z))))
-           (eval:result @racket[#'(elim Nat (λ (x2 : Nat) Nat)
-                                        ()
-                                        (z (λ (x2 : Nat) (λ (ih-n2 : Nat) x2)))
-                                        (s (s z)))] "" ""))
+(eval:alts (step/syn #'(sub1 (s (s z))))
+           (eval:result @racket[#'(((((elim Nat (Type 0))
+                                      (lambda (x2 : Nat) Nat)) z)
+                                    (lambda (x2 : Nat) (lambda (ih-n2 : Nat) x2)))
+                                   (s (s z)))] "" ""))
 ]
 }

@ -90,11 +90,11 @@ equal modulo α and β-equivalence.
@examples[


-(eval:alts (cur-equal? #'(λ (a : Type) a) #'(λ (b : Type) b))
+(eval:alts (cur-equal? #'(lambda (a : Type) a) #'(lambda (b : Type) b))
           (eval:result @racket[#t] "" ""))
-(eval:alts (cur-equal? #'((λ (a : Type) a) Bool) #'Bool)
+(eval:alts (cur-equal? #'((lambda (a : Type) a) Bool) #'Bool)
           (eval:result @racket[#t] "" ""))
-(eval:alts (cur-equal? #'(λ (a : Type) (sub1 (s z))) #'(λ (a : Type) z))
+(eval:alts (cur-equal? #'(lambda (a : Type) (sub1 (s z))) #'(lambda (a : Type) z))
           (eval:result @racket[#f] "" ""))
 ]
 }
@ -106,7 +106,7 @@ Converts @racket[s] to a datum representation of the @tech{curnel form}, after e
@examples[


-(eval:alts (cur->datum #'(λ (a : Type) a))
+(eval:alts (cur-?datum #'(lambda (a : Type) a))
           (eval:result @racket['(λ (a : (Unv 0) a))] "" ""))
 ]
 }
--- a/cur-doc/cur/scribblings/stdlib.scrbl
+++ b/cur-doc/cur/scribblings/stdlib.scrbl
@ -7,10 +7,10 @@ Cur has a small standard library, primary for demonstration purposes.

@local-table-of-contents[]

+@include-section{stdlib/tactics.scrbl}
@include-section{stdlib/sugar.scrbl}
@include-section{stdlib/bool.scrbl}
@include-section{stdlib/nat.scrbl}
@include-section{stdlib/maybe.scrbl}
@include-section{stdlib/list.scrbl}
@include-section{stdlib/typeclass.scrbl}
-@include-section{stdlib/tactics.scrbl}
--- 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 (λ (x : Bool) Bool) () (false true) true)]
+	  (elim Bool Type (λ (x : Bool) Bool) false true true)]
 }

@defproc[(not [x Bool])
--- a/cur-doc/cur/scribblings/stdlib/sugar.scrbl
+++ b/cur-doc/cur/scribblings/stdlib/sugar.scrbl
@ -21,15 +21,12 @@ This library defines various syntactic extensions making Cur easier to write tha
@defform*[((-> decl decl ... type)
           (→ decl decl ... type)
 	   (forall decl decl ... type)
-	   (∀ decl decl ... type)
-	   (Π decl decl ... type)
-	   (Pi decl decl ... type))
+	   (∀ decl decl ... type))
 	  #:grammar
 	  [(decl
 	     type
 	     (code:line (identifier : type)))]]{
 A multi-artiy function type that supports dependent and non-dependent type declarations and automatic currying.
-We provide lots of names for this form, because there are lots of synonyms in the literature.

@examples[#:eval curnel-eval
          (data And : (-> Type Type Type)
@ -62,24 +59,21 @@ Defines multi-arity procedure application via automatic currying.
          (conj Bool Bool true false)]
 }

-@defform[(: name type)]{
-Declare that the @emph{function} which will be defined as @racket[name] has type @racket[type].
-Must precede the definition of @racket[name].
-@racket[type] must expand to a function type of the form @racket[(Π (x : t1) t2)]
-When used, this form allows omitting the annotations on arguments in the definition @racket[name]
-}
-
@defform*[((define name body)
-           (define (name x ...) body)
-	   (define (name (x : t) ...) body))]{
+           (define (name (x : t) ...) body))]{
 Like the @racket[define] provided by @racketmodname[cur], but supports
 defining curried functions via @racket[lambda].
-The second form, @racket[(define (name x ...) body)], can only be used when
-a @racket[(: name type)] form appears earlier in the module.
+}
+
+@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
-          (: id (forall (A : Type) (a : A) A))
-	  (define (id A a) a)]
+          (elim Bool Type (lambda (x : Bool) Bool)
+            false
+            true
+            true)]
 }

@defform*[((define-type name type)
@ -172,7 +166,7 @@ Check that expression @racket[e] has type @racket[type], causing a type-error if
 }

@defform[(run syn)]{
-Like @racket[cur-normalize], but is a syntactic form to be used in surface syntax.
+Like @racket[normalize/syn], but is a syntactic form to be used in surface syntax.
 Allows a Cur term to be written by computing part of the term from
 another Cur term.

@ -182,7 +176,7 @@ another Cur term.
 }

@defform[(step syn)]{
-Like @racket[run], but uses @racket[cur-step] to evaluate only one step and prints intermediate
+Like @racket[run], but uses @racket[step/syn] to evaluate only one step and prints intermediate
 results before returning the result of evaluation.

@examples[#:eval curnel-eval
--- 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 "0.4") "sandbox-lib"))
+(define build-deps '("scribble-lib" ("cur-lib" #:version "0.2") "sandbox-lib"))
 (define pkg-desc "Documentation for \"cur\".")
 (define pkg-authors '(wilbowma))
--- a/cur-lib/cur/main.rkt
+++ b/cur-lib/cur/main.rkt
--- a/cur-lib/cur/curnel/redex-core.rkt
+++ b/cur-lib/cur/curnel/redex-core.rkt
@ -26,11 +26,11 @@
 (define-language ttL
  (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))
+  (D x c ::= variable-not-otherwise-mentioned)
  #:binding-forms
  (λ (x : t) e #:refers-to x)
  (Π (x : t_0) t_1 #:refers-to x))
@ -44,8 +44,6 @@
 ;;; ------------------------------------------------------------------------
 ;;; Universe typing

-;; Universe types
-;; aka Axioms A of a PTS
 (define-judgment-form ttL
  #:mode (unv-type I O)
  #:contract (unv-type U U)
@ -55,7 +53,6 @@
   (unv-type (Unv i_0) (Unv i_1))])

 ;; Universe predicativity rules. Impredicative in (Unv 0)
-;; aka Rules R of a PTS
 (define-judgment-form ttL
  #:mode (unv-pred I I O)
  #:contract (unv-pred U U U)
@ -108,6 +105,27 @@
  [(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
@ -127,6 +145,14 @@
 ;; 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
@ -163,31 +189,47 @@
 ;; TODO: Test
 #| TODO:
 | This essentially eta-expands t at the type-level. Why is this necessary? Shouldn't it be true
- | that (convert t (Ξ-apply Ξ t))?
- | Maybe not. t is a lambda whose type is convert to (Ξ-apply Ξ t)? Yes.
+ | that (equivalent t (Ξ-apply Ξ t))?
+ | Maybe not. t is a lambda whose type is equivalent to (Ξ-apply Ξ t)? Yes.
 |#
 (define-metafunction tt-ctxtL
  Ξ-apply : Ξ t -> t
  [(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
@ -209,6 +251,15 @@
  [(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
@ -226,6 +277,21 @@
   (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
@ -254,6 +320,36 @@
      (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.
 ;;
@ -269,40 +365,29 @@
 ;; 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-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))
+  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))
   ;; A fresh name to bind the discriminant
-   (where x ,(variable-not-in (term (Δ D Ξ)) 'x-D))
+   (where x ,(variable-not-in (term (Δ Γ x_D Ξ)) 'x-D))
   ;; The telescope (∀ a -> ... -> (D a ...) hole), i.e.,
-   ;; 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)))])
+   ;; 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))])

 ;;; ------------------------------------------------------------------------
 ;;; Dynamic semantics
@ -310,21 +395,16 @@
 ;;; inductively defined type x with a motive whose result is in universe U

 (define-extended-language tt-redL tt-ctxtL
-  (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)))
+  ;; 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)))

 (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 ...))
@ -340,6 +420,75 @@
 |
 | 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
@ -353,34 +502,39 @@
 ;; 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-redL
-  Δ-inductive-elim : Δ D C-elim Θ -> Θ
+(define-metafunction tt-ctxtL
+  Δ-inductive-elim : Δ x U t Θ Θ 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 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)])
+  [(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])

 (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 (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)))
+    (--> (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)))
         ;; Generate the inductive recursion
-         (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))
+         (where Θ_r (Δ-inductive-elim Δ D U v_P Θv_p Θv_m Θv_i))
         -->elim)))

 (define-metafunction tt-redL
@ -396,6 +550,16 @@
   (where (_ e_r)
          ,(car (apply-reduction-relation* tt--> (term (Δ e)) #:cache-all? #t)))])

+(define-judgment-form tt-redL
+  #:mode (equivalent I I I)
+  #:contract (equivalent Δ t t)
+
+  [(where t_2 (reduce Δ t_0))
+   (where t_3 (reduce Δ t_1))
+   (side-condition (α-equivalent? t_2 t_3))
+   ----------------- "≡-αβ"
+   (equivalent Δ t_0 t_1)])
+
 ;;; ------------------------------------------------------------------------
 ;;; Type checking and synthesis

@ -405,24 +569,6 @@
  (Γ   ::= ∅ (Γ x : t)))
 (define Γ? (redex-match? tt-typingL Γ))

-(define-judgment-form tt-typingL
-  #:mode (convert I I I I)
-  #:contract (convert Δ Γ t t)
-
-  [(side-condition ,(<= (term i_0) (term i_1)))
-   ----------------- "≼-Unv"
-   (convert Δ Γ (Unv i_0) (Unv i_1))]
-
-  [(where t_2 (reduce Δ t_0))
-   (where t_3 (reduce Δ t_1))
-   (side-condition (α-equivalent? t_2 t_3))
-   ----------------- "≼-αβ"
-   (convert Δ Γ t_0 t_1)]
-
-  [(convert Δ (Γ x : t_0) t_1 t_2)
-   ----------------- "≼-Π"
-   (convert Δ Γ (Π (x : t_0) t_1) (Π (x : t_0) t_2))])
-
 (define-metafunction tt-typingL
  Γ-union : Γ Γ -> Γ
  [(Γ-union Γ ∅) Γ]
@ -541,22 +687,16 @@
   ----------------- "DTR-Application"
   (type-infer Δ Γ (e_0 e_1) t_3)]

-  [(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) ...
+  [(where t (Δ-elim-type Δ D U))
+   (type-infer Δ Γ t U_e)
   ----------------- "DTR-Elim_D"
-   (type-infer Δ Γ (elim D e_motive (e_i ...) (e_m ...) e_c)
-               (apply e_motive e_i ... e_c))])
+   (type-infer Δ Γ (elim D U) t)])

 (define-judgment-form tt-typingL
  #:mode (type-check I I I I)
  #:contract (type-check Δ Γ e t)

  [(type-infer Δ Γ e t_0)
-   (convert Δ Γ t t_0)
+   (equivalent Δ t t_0)
   ----------------- "DTR-Check"
   (type-check Δ Γ e t)])
--- 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
-  (except-in "redex-core.rkt" apply)
+  "redex-core.rkt"
  redex/reduction-semantics
  racket/provide-syntax
  (for-syntax
@ -11,7 +11,7 @@
    racket/syntax
    (except-in racket/provide-transform export)
    racket/require-transform
-    (except-in "redex-core.rkt" apply)
+    "redex-core.rkt"
    redex/reduction-semantics))
 (provide
  ;; Basic syntax
@ -30,10 +30,10 @@
    [dep-provide provide]
    [dep-require require]

-    [dep-lambda λ]
+    [dep-lambda lambda]
    [dep-app #%app]

-    [dep-forall Π]
+    [dep-forall forall]

    [dep-inductive data]

@ -58,13 +58,41 @@
   (all-from-out syntax/parse)
   (all-from-out racket)
   (all-from-out racket/syntax)
-    cur->datum
-    cur-expand
-    cur-type-infer
-    cur-type-check?
-    cur-normalize
-    cur-step
-    cur-equal?))
+   raise-curnel-type-error
+   raise-curnel-syntax-error
+   cur->datum
+   cur-expand
+   type-infer/syn
+   type-check/syn?
+   normalize/syn
+   step/syn
+   cur-equal?))
+
+;; Exceptions
+(begin-for-syntax
+  (provide
+   (struct-out exn:cur)
+   (struct-out exn:cur:curnel)
+   (struct-out exn:cur:curnel:type)
+   (struct-out exn:cur:curnel:syntax))
+  (define-struct (exn:cur exn) () #:transparent)
+  (define-struct (exn:cur:curnel exn:cur) () #:transparent)
+  (define-struct (exn:cur:curnel:type exn:cur) () #:transparent)
+  (define-struct (exn:cur:curnel:syntax exn:cur) () #:transparent)
+
+  (define (raise-curnel-type-error name v . other)
+    (raise
+     (make-exn:cur:curnel:type
+      (for/fold ([msg (format "~a: Cur type error;~n  Typing judgment did not hold in Curnel~n    term: ~a" name v)])
+                ([t other])
+        (format "~a~n   additional context: ~a" msg t))
+      (current-continuation-marks))))
+
+  (define (raise-curnel-syntax-error name v [more ""])
+    (raise
+     (make-exn:cur:curnel:syntax
+      (format "~a: Cur syntax error;~n  Term is invalid Curnel syntax;~a~n    term: ~a" name more v)
+      (current-continuation-marks)))))

 (begin-for-syntax
  ;; TODO: Gamma and Delta seem to get reset inside a module+
@ -73,7 +101,7 @@
      (term ∅)
      (lambda (x)
        (unless (Γ? x)
-          (error 'core-error "We built a bad term environment ~s" x))
+          (raise-curnel-syntax-error 'term-environment "term is not a well-formed Γ"))
        x)))

  (define delta
@ -81,7 +109,7 @@
      (term ∅)
      (lambda (x)
        (unless (Δ? x)
-          (error 'core-error "We built a bad inductive declaration ~s" x))
+          (raise-curnel-syntax-error 'inductive-delcaration x "term is not a well-formed Δ"))
        x)))

  ;; These should be provided by core, so details of envs can be hidden.
@ -118,7 +146,7 @@
     (list null null)
     (lambda (x)
       (unless (subst? x)
-           (error 'core-error "We build a bad subst ~s" x))
+         (raise-curnel-syntax-error 'top-level-bindings x))
       x)))

  (define (add-binding/term! x t)
@ -156,8 +184,6 @@
  (define (cur->datum syn)
    ;; Main loop; avoid type
    (define reified-term
-      ;; TODO: This results in less good error messages. Add an
-      ;; algorithm to find the smallest ill-typed term.
      (parameterize ([inner-expand? #t])
        (let cur->datum ([syn syn])
          (syntax-parse (core-expand syn)
@ -177,16 +203,15 @@
                    [e (parameterize ([gamma (extend-Γ/term gamma x t)])
                         (cur->datum #'e))])
               (term (,(syntax->datum #'b) (,x : ,t) ,e)))]
-            [(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)))]
+            [(elim t1 t2)
+             (let* ([t1 (cur->datum #'t1)]
+                    [t2 (cur->datum #'t2)])
+               (term (elim ,t1 ,t2)))]
            [(#%app e1 e2)
             (term (,(cur->datum #'e1) ,(cur->datum #'e2)))]))))
    (unless (or (inner-expand?) (type-infer/term reified-term))
      #;(printf "Delta: ~s~nGamma: ~s~n" (delta) (gamma))
-      (raise-syntax-error 'cur "term is ill-typed:" reified-term syn))
+      (raise-curnel-type-error 'cur->datum reified-term syn))
    reified-term)

  (define (datum->cur syn t)
@ -224,42 +249,52 @@
      (term (reduce #,(delta) (subst-all #,(cur->datum syn) #,(first (bind-subst)) #,(second (bind-subst)))))))

  ;; Reflection tools
+  ;; TODO: Reflection tools should catch internal errors, e.g., from eval-cur et al. to
+  ;; ensure users can provide better error messages. But should not catch errors caused by user macros.

-  (define (cur-normalize syn)
-    (datum->cur
-      syn
-      (eval-cur syn)))
+  (define (local-env->gamma env)
+    (for/fold ([gamma (gamma)])
+              ([(x t) (in-dict env)])
+      (extend-Γ/syn (thunk gamma) x t)))

-  (define (cur-step syn)
+  (define (normalize/syn syn  #:local-env [env '()])
+    (parameterize ([gamma (local-env->gamma env)])
+      (datum->cur
+       syn
+       (eval-cur syn))))
+
+  (define (step/syn syn)
    (datum->cur
      syn
      (term (step ,(delta) ,(subst-bindings (cur->datum syn))))))

  ;; Are these two terms equivalent in type-systems internal equational reasoning?
  (define (cur-equal? e1 e2)
-    (and (judgment-holds (convert ,(delta) ,(gamma) ,(eval-cur e1) ,(eval-cur e2))) #t))
+    (and (judgment-holds (equivalent ,(delta) ,(eval-cur e1) ,(eval-cur e2))) #t))

  ;; TODO: Document local-env
-  (define (cur-type-infer syn #:local-env [env '()])
-    (parameterize ([gamma (for/fold ([gamma (gamma)])
-                                    ([(x t) (in-dict env)])
-                            (extend-Γ/syn (thunk gamma) x t))])
-      (let ([t (type-infer/term (eval-cur syn))])
-        (and t (datum->cur syn t)))))
+  (define (type-infer/syn #:local-env [env '()] syn)
+    (parameterize ([gamma (local-env->gamma env)])
+      (with-handlers ([exn:cur:curnel:type? (lambda _ #f)])
+        (let ([t (type-infer/term (eval-cur syn))])
+        (and t (datum->cur syn t))))))

-  (define (cur-type-check? syn type)
-    (type-check/term? (eval-cur syn) (eval-cur type)))
+  (define (type-check/syn? syn type)
+    (with-handlers ([exn:cur:curnel:type? (lambda _ #f)])
+      (type-check/term? (eval-cur syn) (eval-cur type))))

  ;; Takes a Cur term syn and an arbitrary number of identifiers ls. The cur term is
  ;; expanded until expansion reaches a Curnel form, or one of the
  ;; identifiers in ls.
-  (define (cur-expand syn . ls)
-    (disarm
-      (local-expand
+  ;; TODO: Holy crap boilerplate
+  (define (cur-expand syn #:local-env [env '()] . ls)
+    (parameterize ([gamma (local-env->gamma env)])
+      (disarm
+       (local-expand
        syn
        'expression
        (append (syntax-e #'(Type dep-inductive dep-lambda dep-app dep-elim dep-forall dep-top))
-                ls)))))
+                ls))))))

 ;; -----------------------------------------------------------------
 ;; Require/provide macros
@ -411,9 +446,8 @@
 ;;
 ;; TODO: Can these be simplified further?
 (define-syntax (dep-lambda syn)
-  (syntax-parse syn
-    #:datum-literals (:)
-    [(_ (x:id : t) e)
+  (syntax-case syn (:)
+    [(_ (x : t) e)
     (syntax->curnel-syntax
       (quasisyntax/loc syn (λ (x : t) e)))]))

@ -424,32 +458,30 @@
       (quasisyntax/loc syn (#%app e1 e2)))]))

 (define-syntax (dep-forall syn)
-  (syntax-parse syn
-    #:datum-literals (:)
-    [(_ (x:id : t) e)
+  (syntax-case syn (:)
+    [(_ (x : t) e)
     (syntax->curnel-syntax
       (quasisyntax/loc syn (Π (x : t) e)))]))

 (define-syntax (Type syn)
-  (syntax-parse syn
-    [(_ i:nat)
+  (syntax-case syn ()
+    [(_ i)
     (syntax->curnel-syntax
       (quasisyntax/loc syn (Unv i)))]
    [_ (quasisyntax/loc syn (Type 0))]))

 (define-syntax (dep-inductive syn)
-  (syntax-parse syn
-    #:datum-literals (:)
-    [(_ i:id : ti (x1:id : t1) ...)
+  (syntax-case syn (:)
+    [(_ i : ti (x1 : t1) ...)
     (begin
       (extend-Δ/syn! delta #'i #'ti #'((x1 : t1) ...))
       #'(void))]))

 (define-syntax (dep-elim syn)
-  (syntax-parse syn
-    [(_ D:id motive (i ...) (m ...) e)
+  (syntax-case syn ()
+    [(_ D T)
     (syntax->curnel-syntax
-       (quasisyntax/loc syn (elim D motive (i ...) (m ...) e)))]))
+       (quasisyntax/loc syn (elim D T)))]))

 (define-syntax-rule (dep-void) (void))

--- a/cur-lib/cur/lang/reader.rkt
+++ b/cur-lib/cur/lang/reader.rkt
@ -1,2 +1,2 @@
 #lang s-exp syntax/module-reader
-cur
+cur/cur
--- a/cur-lib/cur/olly.rkt
+++ b/cur-lib/cur/olly.rkt
@ -1,16 +1,11 @@
-#lang s-exp "main.rkt"
+#lang s-exp "cur.rkt"
 ;; Olly: The OTT-Like LibrarY
 ;; TODO: Automagically create a parser from bnf grammar
 (require
  "stdlib/sugar.rkt"
  "stdlib/nat.rkt"
  ;; TODO: "real-"? More like "curnel-"
-  (only-in
-   "main.rkt"
-   [#%app real-app]
-   [elim real-elim]
-   [Π real-forall]
-   [λ real-lambda]))
+  (only-in "cur.rkt" [#%app real-app] [elim real-elim] [forall real-forall] [lambda real-lambda]))

 (provide
  define-relation
@ -32,7 +27,7 @@
    (coq-defns (format "~a~a~n" (coq-defns) str)))

  (define (constructor-args syn)
-    (syntax-parse (cur-type-infer syn)
+    (syntax-parse (type-infer/syn syn)
      #:datum-literals (Π :)
      [(Π (x:id : t) body)
       (cons #'x (constructor-args #'body))]
@ -48,67 +43,72 @@
  (define (cur->coq syn)
    (parameterize ([coq-defns ""])
      (define output
-        (let cur->coq ([syn syn])
-          (syntax-parse (cur-expand syn #'define #'begin)
+        (let cur->coq ([syn syn]
+                       [local-env (make-immutable-hash)])
+          (syntax-parse (cur-expand #:local-env local-env syn #'define #'begin)
            ;; TODO: Need to add these to a literal set and export it
            ;; Or, maybe overwrite syntax-parse
            #:literals (real-lambda real-forall data real-app real-elim define begin Type)
            [(begin e ...)
             (for/fold ([str ""])
                       ([e (syntax->list #'(e ...))])
-               (format "~a~n" (cur->coq e)))]
+               (format "~a~n" (cur->coq e local-env)))]
            [(define name:id body)
             (begin
               (coq-lift-top-level
                (format "Definition ~a := ~a.~n"
-                        (cur->coq #'name)
-                        (cur->coq #'body)))
+                        (cur->coq #'name local-env)
+                        (cur->coq #'body local-env)))
               "")]
            [(define (name:id (x:id : t) ...) body)
             (begin
+               (define-values (args body-local-env)
+                 (for/fold ([str ""]
+                            [local-env local-env])
+                           ([n (syntax->list #'(x ...))]
+                            [t (syntax->list #'(t ...))])
+                   (values
+                    (format
+                     "~a(~a : ~a) "
+                     str
+                     (cur->coq n local-env)
+                     (cur->coq t local-env))
+                    (dict-set local-env n t))))
               (coq-lift-top-level
                (format "Function ~a ~a := ~a.~n"
-                        (cur->coq #'name)
-                        (for/fold ([str ""])
-                                  ([n (syntax->list #'(x ...))]
-                                   [t (syntax->list #'(t ...))])
-                          (format "~a(~a : ~a) " str (cur->coq n) (cur->coq t)))
-                        (cur->coq #'body)))
+                        (cur->coq #'name local-env)
+                        args
+                        (cur->coq #'body body-local-env)))
               "")]
            [(real-lambda ~! (x:id (~datum :) t) body:expr)
-             (format "(fun ~a : ~a => ~a)" (cur->coq #'x) (cur->coq #'t)
-                     (cur->coq #'body))]
+             (format "(fun ~a : ~a => ~a)" (syntax-e #'x) (cur->coq #'t local-env)
+                     (cur->coq #'body (dict-set local-env #'x #'t)))]
            [(real-forall ~! (x:id (~datum :) t) body:expr)
-             (format "(forall ~a : ~a, ~a)" (syntax-e #'x) (cur->coq #'t)
-                     (cur->coq #'body))]
+             (format "(forall ~a : ~a, ~a)" (syntax-e #'x) (cur->coq #'t local-env)
+                     (cur->coq #'body (dict-set local-env #'x #'t)))]
            [(data ~! n:id (~datum :) t (x*:id (~datum :) t*) ...)
             (begin
               (coq-lift-top-level
                (format "Inductive ~a : ~a :=~a."
                        (sanitize-id (format "~a" (syntax-e #'n)))
-                        (cur->coq #'t)
-                        (for/fold ([strs ""])
-                                  ([clause (syntax->list #'((x* : t*) ...))])
-                          (syntax-parse clause
-                            [(x (~datum :) t)
-                             (format "~a~n| ~a : ~a" strs (syntax-e #'x)
-                                     (cur->coq #'t))]))))
+                        (cur->coq #'t local-env)
+                        (call-with-values
+                         (thunk
+                          (for/fold ([strs ""]
+                                     [local-env (dict-set local-env #'n #'t)])
+                                    ([x (attribute x*)]
+                                     [t (attribute t*)])
+                            (values
+                             (format "~a~n| ~a : ~a" strs (syntax-e x)
+                                     (cur->coq t local-env))
+                             (dict-set local-env x t))))
+                         (lambda (x y) x))))
               "")]
            [(Type i) "Type"]
-            [(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-elim var t)
+             (format "~a_rect" (cur->coq #'var local-env))]
            [(real-app e1 e2)
-             (format "(~a ~a)" (cur->coq #'e1) (cur->coq #'e2))]
+             (format "(~a ~a)" (cur->coq #'e1 local-env) (cur->coq #'e2 local-env))]
            [e:id (sanitize-id (format "~a" (syntax->datum #'e)))])))
      (format
       "~a~a"
@ -206,6 +206,7 @@
              lab:rule-name
              (~var t (conclusion name indices (attribute lab))))
             #:with constr-decl
+             ;; TODO: quasisyntax/loc
             #'(lab : (-> h ... (t.name t.arg ...)))
             ;; TODO: convert meta-vars such as e1 to e_1
             #:attr latex
@ -288,7 +289,8 @@
     #:attr sym (syntax->datum #'x)
     #:fail-when (dict-has-key? (mv-map) (attribute sym)) #f
     #:attr constructor-name
-     (format-id #'x "~a-~a" (lang-name) #'x)))
+     (quasisyntax/loc #'x
+       #,(format-id #'x "~a-~a" (lang-name) #'x))))

  ;; A terminal-args can appear as the argument to a terminal in
  ;; an expression, or as a sub-expression in a terminal-args.
@ -349,9 +351,9 @@
    (pattern
     e:meta-variable
     #:attr constructor-name
-     (format-id #'e "~a->~a" #'e.type non-terminal-type)
+     (quasisyntax/loc #'e #,(format-id #'e "~a->~a" #'e.type non-terminal-type))
     #:attr constr-decl
-     #`(constructor-name : (-> e.type #,non-terminal-type))
+     (quasisyntax/loc #'e (constructor-name : (-> e.type #,non-terminal-type)))
     #:attr latex
     (format "~a" (syntax-e #'e)))

@ -359,7 +361,7 @@
    (pattern
     x:terminal
     #:attr constr-decl
-     #`(x.constructor-name : #,non-terminal-type)
+     (quasisyntax/loc #'x (x.constructor-name : #,non-terminal-type))
     #:attr latex
     (format "~a" (syntax-e #'x)))

@ -367,7 +369,7 @@
    (pattern
     (x:terminal . (~var c (terminal-args non-terminal-type)))
     #:attr constr-decl
-     #`(x.constructor-name : (-> #,@(attribute c.args) #,non-terminal-type))
+     (quasisyntax/loc #'x (x.constructor-name : (-> #,@(attribute c.args) #,non-terminal-type)))
     #:attr latex
     (format "(~a ~a)" (syntax-e #'x) (attribute c.latex))))

@ -378,7 +380,7 @@
      (~optional (~datum ::=))
      ;; Create a name for the type of this non-terminal, from the
      ;; language name and the non-terminal name.
-      (~bind [nt-type (format-id #'name "~a-~a" (lang-name) #'name)])
+      (~bind [nt-type (quasisyntax/loc #'name #,(format-id #'name "~a-~a" (lang-name) #'name))])
      ;; Imperatively update the map from meta-variables to the
      ;; nt-type, to be used when generating the types of the constructors
      ;; for this and later non-terminal.
@ -387,7 +389,7 @@
      (~var c (expression (attribute nt-type))) ...)
     ;; Generates the inductive data type for this non-terminal definition.
     #:attr def
-     #`(data nt-type : Type c.constr-decl ...)
+     (quasisyntax/loc #'name (data nt-type : Type c.constr-decl ...))
     #:attr latex
     (format
      "\\mbox{\\textit{~a}} & ~a & \\bnfdef & ~a\\\\~n"
@ -435,7 +437,7 @@
           (dict-set! (mv-map) (syntax-e x) #'Nat)))])
    (syntax-parse #'non-terminal-defs
      [(def:non-terminal-def ...)
-       (let ([output #`(begin def.def ...)])
+       (let ([output (quasisyntax/loc #'name (begin def.def ...))])
         (when (attribute latex-file)
           (with-output-to-file (syntax-e #'latex-file)
             (thunk (typeset-bnf (attribute def.latex)))
--- a/cur-lib/cur/stdlib/bool.rkt
+++ b/cur-lib/cur/stdlib/bool.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require "sugar.rkt")
 (provide Bool true false if not and or)

--- a/cur-lib/cur/stdlib/list.rkt
+++ b/cur-lib/cur/stdlib/list.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require
 "nat.rkt"
 "maybe.rkt"
--- a/cur-lib/cur/stdlib/maybe.rkt
+++ b/cur-lib/cur/stdlib/maybe.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require "sugar.rkt")
 (provide Maybe none some some/i)

@ -9,5 +9,5 @@
 (define-syntax (some/i syn)
  (syntax-case syn ()
   [(_ a)
-    (let ([a-ty (cur-type-infer #'a)])
+    (let ([a-ty (type-infer/syn #'a)])
      #`(some #,a-ty a))]))
--- a/cur-lib/cur/stdlib/nat.rkt
+++ b/cur-lib/cur/stdlib/nat.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require "sugar.rkt" "bool.rkt")
 ;; TODO: override (all-defined-out) to enable exporting all these
 ;; properly.
--- a/cur-lib/cur/stdlib/prop.rkt
+++ b/cur-lib/cur/stdlib/prop.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require "sugar.rkt")
 ;; TODO: Handle multiple provide forms properly
 ;; TODO: Handle (all-defined-out) properly
@ -31,8 +31,8 @@
 (define-syntax (conj/i syn)
  (syntax-case syn ()
    [(_ a b)
-     (let ([a-type (cur-type-infer #'a)]
-           [b-type (cur-type-infer #'b)])
+     (let ([a-type (type-infer/syn #'a)]
+           [b-type (type-infer/syn #'b)])
       #`(conj #,a-type #,b-type a b))]))

 (define thm:and-is-symmetric
@ -71,12 +71,11 @@
 (define proof:A-or-A
  (lambda (A : Type) (c : (Or A A))
    ;; TODO: What should the motive be?
-    (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)))
+    (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)))

 (qed thm:A-or-A proof:A-or-A)
 |#
--- a/cur-lib/cur/stdlib/sugar.rkt
+++ b/cur-lib/cur/stdlib/sugar.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (provide
  ->
  lambda
@ -6,12 +6,10 @@
    [-> →]
    [-> forall]
    [-> ∀]
-    [-> Π]
-    [-> Pi]
    [lambda λ])
  #%app
  define
-  :
+  elim
  define-type
  match
  recur
@ -27,37 +25,121 @@
  query-type)

 (require
-  (only-in "../main.rkt"
+  (only-in "../cur.rkt"
+    [elim real-elim]
    [#%app real-app]
-    [λ real-lambda]
-    [Π real-Π]
+    [lambda real-lambda]
    [define real-define]))

+;; Exceptions and such
 (begin-for-syntax
-  (define-syntax-class result-type
-    (pattern type:expr))
+  (define-struct (exn:cur:type exn:cur) () #:transparent)

+  (define (deduce-type-infer-error-hints term)
+    (syntax-parse term
+      [x:id
+       "; Seems to be an unbound variable"]
+      [_ "could not infer a type."]))
+
+  (define (cur-type-infer-error-msg name v . other)
+    (format
+     "~aCur type error;~n  Could not infer any type~a~n    term: ~a~a"
+     (if name (format "~a:" name) "")
+     (deduce-type-infer-error-hints v)
+     v
+     (for/fold ([str ""])
+               ([other other])
+       (format "~a~n    context: ~a" str other))))
+
+  (define (raise-cur-type-infer-error . all)
+    (raise
+     (make-exn:cur:type
+      (apply cur-type-infer-error-msg all)
+      (current-continuation-marks)))))
+
+(begin-for-syntax
+  #| TODO
+   | Design of "typed" macros for Cur.
+   |
+   | We can use syntax classes to emulate typed macros. The syntax
+   | class calls the type-checker to ensure the term parsed term is
+   | well-typed. This *must* not expand the the matched term as a side-effect.
+   | Unfortunately, to handle binding, patterns that have variables
+   | must thread binding information through while parsing in syntax
+   | parse.
+   | This can be handled by delaying the expansion and syntax-class
+   | check until the term is under the binder; see delay-check macros.
+   |
+   |#
+  (define-syntax-class cur-syntax
+    (pattern e:expr))
+
+  (define-syntax-class well-typed-cur-term
+    (pattern
+     e:cur-syntax
+     #:attr type (type-infer/syn #'e)
+     #:fail-unless (attribute type)
+     (cur-type-infer-error-msg #f #'e))))
+
+;; For delaying a type-check until the term is under a binder
+;; NB: This is an impressively awesome solution..... need to write something about it.
+(define-syntax (delayed-check syn)
+  (syntax-parse syn
+    [(_ e:well-typed-cur-term) #'e]))
+
+(begin-for-syntax
  (define-syntax-class parameter-declaration
-    (pattern (name:id (~datum :) type:expr))
+    #:commit
+    (pattern
+     (name:id (~datum :) ~! type:cur-syntax))

    (pattern
-     type:expr
-     #:attr name (format-id #'type "~a" (gensym 'anon-parameter)))))
+     type:cur-syntax
+     #:attr name (format-id #'type "~a" (gensym 'anon-parameter))))
+
+  (define-syntax-class well-typed-parameter-declaration
+    #:commit
+    (pattern
+     e:parameter-declaration
+     #:attr type #'(delayed-check e.type)
+     #:attr name #'e.name))
+
+  (define-syntax-class well-typed-argument-declaration
+    #:commit
+    (pattern
+     ;; TODO: Copy pasta from parameter-declaration
+     (name:id (~datum :) ~! _type:cur-syntax)
+     #:attr type #'(delayed-check _type)))
+
+  (define-syntax-class well-typed-parameter-list
+    (pattern
+     (d:well-typed-parameter-declaration ...+)
+     #:attr names (attribute d.name)
+     #:attr types (attribute d.type)))
+
+  (define-syntax-class well-typed-argument-list
+    (pattern
+     (d:well-typed-argument-declaration ...+)
+     #:attr names (attribute d.name)
+     #:attr types (attribute d.type))))

 ;; A multi-arity function type; takes parameter declaration of either
 ;; a binding (name : type), or type whose name is generated.
 ;; E.g.
 ;; (-> (A : Type) A A)
+
 (define-syntax (-> syn)
  (syntax-parse syn
-    [(_ d:parameter-declaration ...+ result:result-type)
+    [(_ d:parameter-declaration ...+ e:cur-syntax)
+     #:with ds #'(d ...)
+     #:declare ds well-typed-parameter-list
     (foldr (lambda (src name type r)
              (quasisyntax/loc src
-                (real-Π (#,name : #,type) #,r)))
-            #'result
-            (attribute d)
-            (attribute d.name)
-            (attribute d.type))]))
+                (forall (#,name : #,type) #,r)))
+            #'(delayed-check e)
+            (syntax->list (attribute ds))
+            (attribute ds.names)
+            (attribute ds.types))]))

 ;; TODO: Add forall macro that allows specifying *names*, with types
 ;; inferred. unlike -> which require types but not names
@ -66,94 +148,76 @@

 ;; TODO: Allows argument-declarations to have types inferred, similar
 ;; to above TODO forall
-(begin-for-syntax
-  ;; eta-expand syntax-class for error messages
-  (define-syntax-class argument-declaration
-    (pattern
-     e:parameter-declaration
-     #:attr name #'e.name
-     #:attr type #'e.type)))
 (define-syntax (lambda syn)
  (syntax-parse syn
-    [(_ d:argument-declaration ...+ body:expr)
+    [(_ d:parameter-declaration ...+ e:cur-syntax)
+     #:with ds #'(d ...)
+     #:declare ds well-typed-argument-list
     (foldr (lambda (src name type r)
              (quasisyntax/loc src
                (real-lambda (#,name : #,type) #,r)))
-            #'body
-            (attribute d)
-            (attribute d.name)
-            (attribute d.type))]))
+            #'(delayed-check e)
+            (syntax->list (attribute ds))
+            (attribute ds.names)
+            (attribute ds.types))]))
+
+(begin-for-syntax
+  (define-syntax-class forall-type
+    (pattern
+     ((~literal forall) ~! (parameter-name:id (~datum :) parameter-type) body)))
+
+  (define-syntax-class well-typed-cur-function
+    (pattern
+     e:well-typed-cur-term
+     #:attr type (attribute e.type)
+     #:fail-unless (syntax-parse (attribute e.type)
+                     [t:forall-type #t]
+                     [_ #f])
+     (format
+      "Expected ~a to be a function, but inferred type ~a"
+      (syntax->datum #'e)
+      (syntax->datum (attribute e.type))))))

-;; TODO: This makes for really bad error messages when an identifier is undefined.
 (define-syntax (#%app syn)
-  (syntax-case syn ()
-    [(_ e)
-     (quasisyntax/loc syn e)]
-    [(_ e1 e2)
-     (quasisyntax/loc syn
-       (real-app e1 e2))]
-    [(_ e1 e2 e3 ...)
-     (quasisyntax/loc syn
-       (#%app (#%app e1 e2) e3 ...))]))
+  (syntax-parse syn
+    [(_ f:well-typed-cur-function ~! e:well-typed-cur-term ...+)
+     ;; Have to thread each argument through, to handle dependency.
+     (for/fold ([type (attribute f.type)])
+               ([arg (attribute e)]
+                [inferred-type (attribute e.type)])
+       (define/syntax-parse expected:forall-type type)
+       (define expected-type (attribute expected.parameter-type))
+       (unless (type-check/syn? arg expected-type)
+         (raise-syntax-error
+          '#%app
+          (format
+           "Expected ~a to have type ~a, but inferred type ~a."
+           (syntax->datum arg)
+           (syntax->datum expected-type)
+           (syntax->datum inferred-type))
+          syn
+          arg))
+       (normalize/syn
+        #`(real-app
+           (real-lambda (expected.parameter-name : expected.parameter-type)
+                        expected.body)
+           #,arg)))
+     (for/fold ([app (quasisyntax/loc syn
+                       (real-app f #,(first (attribute e))))])
+               ([arg (rest (attribute e))])
+       (quasisyntax/loc arg
+         (real-app #,app #,arg)))]))

 (define-syntax define-type
  (syntax-rules ()
    [(_ (name (a : t) ...) body)
-     (define name (-> (a : t) ... body))]
+     (define name (forall (a : t) ... body))]
    [(_ name type)
     (define name type)]))

-;; Cooperates with define to allow Haskell-esque type annotations
-#| TODO NB:
- | This method of cooperating macros is sort of a terrible
- | hack. Instead, need principled way of adding/retrieving information
- | to/from current module. E.g. perhaps provide extensions an interface to
- | module's term environment and inductive signature. Then, :: could add
- | new "id : type" to environment, and define could extract type and use.
- |#
-(begin-for-syntax
-  (define annotation-dict (make-hash))
-  (define (annotation->types type-syn)
-    (let loop ([ls '()]
-               [syn type-syn])
-      (syntax-parse (cur-expand syn)
-        #:datum-literals (:)
-        [(real-Π (x:id : type) body)
-         (loop (cons #'type ls) #'body)]
-        [_ (reverse ls)]))))
-
-(define-syntax (: syn)
-  (syntax-parse syn
-    [(_ name:id type:expr)
-     ;; NB: Unhygenic; need to reuse Racket's identifiers, and make this type annotation a syntax property
-     (syntax-parse (cur-expand #'type)
-      #:datum-literals (:)
-      [(real-Π (x:id : type) body) (void)]
-      [_
-       (raise-syntax-error
-        ':
-        "Can only declare annotations for functions, but not a function type"
-        syn)])
-     (dict-set! annotation-dict (syntax->datum #'name) (annotation->types #'type))
-     #'(void)]))
-
 ;; TODO: Allow inferring types as in above TODOs for lambda, forall
 (define-syntax (define syn)
-  (syntax-parse syn
-    #:datum-literals (:)
-    [(define (name:id x:id ...) body)
-     (cond
-       [(dict-ref annotation-dict (syntax->datum #'name)) =>
-        (lambda (anns)
-          (quasisyntax/loc syn
-            (real-define name (lambda #,@(for/list ([x (syntax->list #'(x ...))]
-                                                    [type anns])
-                                           #`(#,x : #,type)) body))))]
-       [else
-        (raise-syntax-error
-         'define
-         "Cannot omit type annotations unless you have declared them with (: name type) form first."
-         syn)])]
+  (syntax-case syn ()
    [(define (name (x : t) ...) body)
     (quasisyntax/loc syn
       (real-define name (lambda (x : t) ... body)))]
@ -161,72 +225,22 @@
     (quasisyntax/loc syn
       (real-define id body))]))

-#|
-(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 ...)
-       )
-     ]))
-|#
+    [(_ t1 t2 e ...)
+     (maybe-cur-apply
+      #`(real-elim t1 t2)
+      (attribute e))]))

 ;; Quite fragie to give a syntactic treatment of pattern matching -> eliminator. Replace with "Elimination with a Motive"
 (begin-for-syntax
  (define ih-dict (make-hash))

+  (define (maybe-cur-apply f ls)
+    (if (null? ls)
+        f
+        #`(#,f #,@ls)))
+
  (define-syntax-class curried-application
    (pattern
     ((~literal real-app) name:id e:expr)
@ -249,6 +263,10 @@
     #'x
     #:attr indices
     '()
+     #:attr names
+     '()
+     #:attr types
+     '()
     #:attr decls
     (list #`(#,(gensym 'anon-discriminant) : x))
     #:attr abstract-indices
@ -268,7 +286,7 @@
     #:attr types
     ;; TODO: Detect failure, report error/suggestions
     (for/list ([e (attribute indices)])
-       (or (cur-type-infer e)
+       (or (type-infer/syn e)
           (raise-syntax-error
            'match
            (format
@ -289,15 +307,21 @@
     (lambda (return)
       ;; NB: unhygenic
       ;; Normalize at compile-time, for efficiency at run-time
-       (cur-normalize
-        #`((lambda
-              ;; TODO: utteraly fragile; relines on the indices being referred to by name, not computed
-              ;; works only for simple type familes and simply matches on them
-             #,@(for/list ([name (attribute indices)]
-                           [type (attribute types)])
-                 #`(#,name : #,type))
-            #,return)
-          #,@(attribute names))))))
+       (normalize/syn
+        #:local-env
+        (for/fold ([d (make-immutable-hash)])
+                  ([name (attribute names)]
+                   [type (attribute types)])
+          (dict-set d name type))
+        (maybe-cur-apply
+         #`(lambda
+               ;; TODO: utteraly fragile; relines on the indices being referred to by name, not computed
+               ;; works only for simple type familes and simply matches on them
+               #,@(for/list ([name (attribute indices)]
+                             [type (attribute types)])
+                    #`(#,name : #,type))
+             #,return)
+         (attribute names))))))

  ;; todo: Support just names, inferring types
  (define-syntax-class match-declaration
@ -340,19 +364,26 @@
     #:attr decls
     ;; Infer the inductive hypotheses, add them to the pattern decls
     ;; and update the dictionarty for the recur form
-     (for/fold ([decls (attribute d.decls)])
-               ([type-syn (attribute d.types)]
-                [name-syn (attribute d.names)]
-                [src (attribute d.decls)]
-                ;; NB: Non-hygenic
-                ;; BUG TODO: This fails when D is an inductive applied to arguments...
-                #:when (cur-equal? type-syn D))
-       (define/syntax-parse type:inductive-type-declaration (cur-expand type-syn))
-       (let ([ih-name (quasisyntax/loc src #,(format-id name-syn "ih-~a" name-syn))]
-             ;; Normalize at compile-time, for efficiency at run-time
-             [ih-type (cur-normalize #`(#,motive #,@(attribute type.indices) #,name-syn))])
-         (dict-set! ih-dict (syntax->datum name-syn) ih-name)
-         (append decls (list #`(#,ih-name : #,ih-type)))))))
+     (call-with-values
+      (thunk
+       (for/fold ([decls (attribute d.decls)]
+                  [local-env (attribute d.local-env)])
+                 ([type-syn (attribute d.types)]
+                  [name-syn (attribute d.names)]
+                  [src (attribute d.decls)]
+                  ;; NB: Non-hygenic
+                  ;; BUG TODO: This fails when D is an inductive applied to arguments...
+                  #:when (cur-equal? type-syn D))
+         (define/syntax-parse type:inductive-type-declaration (cur-expand type-syn))
+         (let ([ih-name (quasisyntax/loc src #,(format-id name-syn "ih-~a" name-syn))]
+               ;; Normalize at compile-time, for efficiency at run-time
+               [ih-type (normalize/syn #:local-env local-env
+                                       (maybe-cur-apply motive
+                                                        (append (attribute type.indices) (list name-syn))))])
+           (dict-set! ih-dict (syntax->datum name-syn) ih-name)
+           (values (append decls (list #`(#,ih-name : #,ih-type)))
+                   (dict-set local-env ih-name ih-type)))))
+      (lambda (x y) x))))

  (define-syntax-class (match-preclause maybe-return-type)
    (pattern
@ -362,7 +393,7 @@
     (or maybe-return-type
         ;; Ignore errors when trying to infer this type; other attempt might succeed
         (with-handlers ([values (lambda _ #f)])
-           (cur-type-infer #:local-env (attribute p.local-env) #'b)))))
+           (type-infer/syn #:local-env (attribute p.local-env) #'b)))))

  (define-syntax-class (match-clause D motive)
    (pattern
@ -391,6 +422,8 @@
          (syntax->datum #'id))
         syn)))]))

+;; TODO: Better error messages; follow pattern of -> and lambda etc to first parse, then type-check.
+;; TODO: Deprecate #:local-env
 (define-syntax (match syn)
  (syntax-parse syn
    [(_ d
@ -398,7 +431,7 @@
        (~optional
         (~seq #:in ~! t)
         #:defaults
-         ([t (or (cur-type-infer #'d)
+         ([t (or (type-infer/syn #'d)
                 (raise-syntax-error
                  'match
                  "Could not infer discrimnant's type. Try using #:in to declare it."
@ -423,9 +456,15 @@
     (quasisyntax/loc syn
       (elim
        D.inductive-name
+        #,(or
+           (type-infer/syn (attribute return-type))
+           (raise-syntax-error
+            'match
+            "Could not infer type of motive. Sorry, you'll have to use elim."
+            syn))
        motive
-        #,(attribute D.indices)
-        (c.method ...)
+        c.method ...
+        #,@(attribute D.indices)
        d))]))

 (begin-for-syntax
@ -437,14 +476,14 @@
      #:attr type (cond
                    [(attribute t)
                     ;; TODO: Code duplication in ::
-                     (unless (cur-type-check? #'e #'t)
+                     (unless (type-check/syn? #'e #'t)
                       (raise-syntax-error
                         'let
                         (format "Term ~a does not have expected type ~a. Inferred type was ~a"
-                                 (cur->datum #'e) (cur->datum #'t) (cur->datum (cur-type-infer #'e)))
+                                 (cur->datum #'e) (cur->datum #'t) (cur->datum (type-infer/syn #'e)))
                         #'e (quasisyntax/loc #'x (x e))))
                     #'t]
-                    [(cur-type-infer #'e)]
+                    [(type-infer/syn #'e)]
                    [else
                      (raise-syntax-error
                        'let
@ -455,29 +494,29 @@
    [(let (c:let-clause ...) body)
     #'((lambda (c.id : c.type) ... body) c.e ...)]))

-;; Normally type checking will only happen if a term is actually used/appears at top-level.
-;; This forces a term to be checked against a particular type.
+;; Normally type checking will only happen if a term is actually used. This forces a term to be
+;; checked against a particular type.
 (define-syntax (:: syn)
  (syntax-case syn ()
    [(_ pf t)
     (begin
       ;; TODO: Code duplication in let-clause pattern
-       (unless (cur-type-check? #'pf #'t)
+       (unless (type-check/syn? #'pf #'t)
         (raise-syntax-error
           '::
           (format "Term ~a does not have expected type ~a. Inferred type was ~a"
-                   (cur->datum #'pf) (cur->datum #'t) (cur->datum (cur-type-infer #'pf)))
+                   (cur->datum #'pf) (cur->datum #'t) (cur->datum (type-infer/syn #'pf)))
           syn))
       #'(void))]))

 (define-syntax (run syn)
  (syntax-case syn ()
-    [(_ expr) (cur-normalize #'expr)]))
+    [(_ expr) (normalize/syn #'expr)]))

 (define-syntax (step syn)
  (syntax-case syn ()
    [(_ expr)
-     (let ([t (cur-step #'expr)])
+     (let ([t (step/syn #'expr)])
       (displayln (cur->datum t))
       t)]))

@ -493,6 +532,6 @@
  (syntax-case syn ()
    [(_ term)
     (begin
-       (printf "\"~a\" has type \"~a\"~n" (syntax->datum #'term) (syntax->datum (cur-type-infer #'term)))
+       (printf "\"~a\" has type \"~a\"~n" (syntax->datum #'term) (syntax->datum (type-infer/syn #'term)))
       ;; Void is undocumented and a hack, but sort of works
       #'(void))]))
--- a/cur-lib/cur/stdlib/tactics/base.rkt
+++ b/cur-lib/cur/stdlib/tactics/base.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../../main.rkt"
+#lang s-exp "../../cur.rkt"
 (require
  (for-syntax racket/syntax))
 (provide
@ -220,7 +220,7 @@
           [pf (proof-state-proof ps)])
      (unless (proof-state-proof-complete? ps)
        (raise-syntax-error 'qed "Proof contains holes" (pf (current-hole-pretty-symbol))))
-      (unless (cur-type-check? pf t)
+      (unless (type-check/syn? pf t)
        (raise-syntax-error 'qed "Invalid proof" pf t))
      pf)))

--- a/cur-lib/cur/stdlib/tactics/sartactics.rkt
+++ b/cur-lib/cur/stdlib/tactics/sartactics.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../../main.rkt"
+#lang s-exp "../../cur.rkt"
 (require
  "base.rkt"
  (prefix-in basic: "standard.rkt")
--- a/cur-lib/cur/stdlib/tactics/standard.rkt
+++ b/cur-lib/cur/stdlib/tactics/standard.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../../main.rkt"
+#lang s-exp "../../cur.rkt"
 (require
  "base.rkt"
  (for-syntax racket/syntax))
@ -22,7 +22,7 @@
    [(forall (x:id : P:expr) body:expr)
     (let* ([ps (proof-state-extend-env ps name #'P)]
            [ps (proof-state-current-goal-set ps #'body)]
-            [ps (proof-state-fill-proof-hole ps (lambda (x) #`(λ (#,name : P) #,x)))])
+            [ps (proof-state-fill-proof-hole ps (lambda (x) #`(lambda (#,name : P) #,x)))])
       ps)]
    [_ (error 'intro "Can only intro when current goal is of the form (∀ (x : P) body)")]))

--- a/cur-lib/cur/stdlib/typeclass.rkt
+++ b/cur-lib/cur/stdlib/typeclass.rkt
@ -1,4 +1,4 @@
-#lang s-exp "../main.rkt"
+#lang s-exp "../cur.rkt"
 (require
  "nat.rkt"
  "bool.rkt"
@ -38,7 +38,7 @@
              #`(define-syntax (#,name syn)
                  (syntax-case syn ()
                    [(_ arg args (... ...))
-                     #`(#,(format-id syn "~a-~a" '#,name (cur-type-infer #'arg))
+                     #`(#,(format-id syn "~a-~a" '#,name (type-infer/syn #'arg))
                        arg
                        args (... ...))]))))]))

@ -57,7 +57,7 @@
     #`(begin
         #,@(for/list ([def (syntax->list #'(defs ...))])
              (let-values ([(name body) (process-def def)])
-                (unless (cur-type-check?
+                (unless (type-check/syn?
                          body
                          #`(#,(dict-ref
                                 (dict-ref typeclasses (syntax->datum #'class))
--- 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 "0.4")
+(define version "0.2")
 (define pkg-authors '(wilbowma))
--- a/cur-test/cur/tests/olly.rkt
+++ b/cur-test/cur/tests/olly.rkt
@ -6,6 +6,9 @@
 (require
 rackunit
 cur/stdlib/sugar
+ cur/stdlib/nat
+ cur/stdlib/bool
+ cur/stdlib/prop
 cur/olly)

 (begin-for-syntax
@ -30,29 +33,28 @@
   "(forall .+ : Type, Type)"
   (cur->coq #'(-> Type Type)))
  (let ([t (cur->coq
-            #'(define-relation (meow gamma term type)
-                [(g : gamma) (e : term) (t : type)
+            #'(define-relation (meow Nat Bool Nat)
+                [(n : Nat) (b : Bool) (m : Nat)
                 --------------- T-Bla
-                 (meow g e t)]))])
+                 (meow n b m)]))])
    (check-regexp-match
-     "Inductive meow : \\(forall .+ : gamma, \\(forall .+ : term, \\(forall .+ : type, Type\\)\\)\\) :="
+     "Inductive meow : \\(forall .+ : Nat, \\(forall .+ : Bool, \\(forall .+ : Nat, Type\\)\\)\\) :="
     (first (string-split t "\n")))
    (check-regexp-match
-     "\\| T-Bla : \\(forall g : gamma, \\(forall e : term, \\(forall t : type, \\(\\(\\(meow g\\) e\\) t\\)\\)\\)\\)\\."
+     "\\| T-Bla : \\(forall n : Nat, \\(forall b : Bool, \\(forall m : Nat, \\(\\(\\(meow n\\) b\\) m\\)\\)\\)\\)\\."
     (second (string-split t "\n"))))
  (let ([t (cur->coq
-            #'(elim nat (lambda (x : nat) nat)
-                    ()
-                    (z (lambda (x : nat) (ih-x : nat) ih-x))
-                    e))])
+            #'(elim Nat Type (lambda (x : Nat) Nat) z
+                    (lambda (x : Nat) (ih-x : Nat) ih-x)
+                    z))])
    (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\\)\\)\\) z\\)"
     t))
  (check-regexp-match
-   "Definition thm_plus_commutes := \\(forall n : nat, \\(forall m : nat, \\(\\(\\(== nat\\) \\(\\(plus n\\) m\\)\\) \\(\\(plus m\\) n\\)\\)\\)\\).\n"
+   "Definition thm_plus_commutes := \\(forall n : Nat, \\(forall m : Nat, \\(\\(\\(== Nat\\) \\(\\(plus n\\) m\\)\\) \\(\\(plus m\\) n\\)\\)\\)\\).\n"
   (cur->coq
-    #'(define thm:plus-commutes (forall (n : nat) (m : nat)
-                                        (== nat (plus n m) (plus m n))))))
+    #'(define thm:plus-commutes (forall (n : Nat) (m : Nat)
+                                        (== Nat (plus n m) (plus m n))))))
  (check-regexp-match
-   "Function add1 \\(n : nat\\)  := \\(s n\\).\n"
-   (cur->coq #'(define (add1 (n : nat)) (s n)))))
+   "Function add1 \\(n : Nat\\)  := \\(s n\\).\n"
+   (cur->coq #'(define (add1 (n : Nat)) (s n)))))
--- a/cur-test/cur/tests/plus.rkt
+++ b/cur-test/cur/tests/plus.rkt
@ -1,24 +0,0 @@
-#lang cur
-
-(require
- cur/stdlib/sugar
- rackunit)
-
-(data Nat : Type
-  (z : Nat)
-  (s : (Π (x : Nat) Nat)))
-
-(plus . : . (-> Nat Nat Nat))
-(define (plus n m)
-  (match n
-    [z m]
-    [(s (x : Nat))
-     (s (recur x))]))
-
-(check-equal?
- (plus z z)
- z)
-
-(check-equal?
- (plus (s z) z)
- (s z))
--- a/cur-test/cur/tests/redex-core.rkt
+++ b/cur-test/cur/tests/redex-core.rkt
@ -81,6 +81,23 @@
   (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
@ -98,10 +115,41 @@
 (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
 ;; ------------------------------------------------------------------------
@ -109,32 +157,21 @@
 (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
-                         (elim nat (λ (x : nat) nat) ()
-                               ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-                               hole)
+ (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)))))
                         (hole zero)))
- (term (hole (elim nat (λ (x : nat) nat)
-                   ()
-                   ((s zero)
-                    (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-                   zero))))
+ (term (hole (((((elim nat Type) (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
-                         (elim nat (λ (x : nat) nat) ()
-                               ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-                               hole)
+ (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)))))
                         (hole (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))
+ (term (hole (((((elim nat Type) (λ (x : nat) nat))
+                (s zero))
+               (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+              (s zero)))))

 ;; Tests for dynamic semantics
 ;; ------------------------------------------------------------------------
@ -142,8 +179,6 @@
 (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)))
@ -153,71 +188,63 @@
                  (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-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)))
+(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)))
              (term (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))))
+(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))))
              (term (s (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)))))
+(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 (s (s zero))))))
              (term (s (s (s (s zero))))))

 (check-equiv?
 (term (reduce ,Δ
-               (elim nat (λ (x : nat) nat)
-                     ()
-                     ((s (s zero))
-                      (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-                     (s (s zero)))))
+               (((((elim nat Type) (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 (λ (x : nat) nat)
-                     ()
-                     ((s (s zero))
-                      (λ (x : nat) (λ (ih-x : nat) (s ih-x))))
-                     (s (s zero)))))
+             (((((elim nat Type) (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 (λ (x : nat) nat)
-         ()
-         ((s (s zero))
-          (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)))))
 (check-equiv?
 (term (step ,Δ (step ,Δ
                      (((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))))))
+                       (((((elim nat Type) (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 (λ (x : nat) nat)
-          ()
-          ((s (s zero))
-           (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)))))

 (define-syntax-rule (check-equivalent e1 e2)
-  (check-holds (convert ∅ ∅ e1 e2)))
+  (check-holds (equivalent ∅ e1 e2)))
 (check-equivalent
 (λ (x : Type) x) (λ (y : Type) y))
 (check-equivalent
@ -316,42 +343,28 @@
               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-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
+(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))))
                         ∅
-                         (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)
+                         ((((elim truth (Unv 2)) (λ (x : truth) (Unv 1))) (Unv 0))
+                          T)
                         (Unv 1)))
 (check-not-holds (type-check (∅ (truth : (Unv 0) ((T : truth))))
                             ∅
-                             (elim truth Type () (Type) T)
+                             ((((elim truth (Unv 1)) Type) Type) T)
                             (Unv 1)))
 (check-holds
 (type-infer ∅ ∅ (Π (x2 : (Unv 0)) (Unv 0)) U))
@ -369,54 +382,47 @@
  (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 (λ (x : nat) nat) ()
-                  (zero (λ (x : nat) (λ (ih-x : nat) x)))
-                  zero)
+(nat-test ∅ (((((elim nat Type) (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 ∅ (λ (x : nat)
-                    (elim nat (λ (x : nat) nat)
-                          ()
-                          (zero
-                           (λ (x : nat) (λ (ih-x : nat) x)))
-                          x))
+ (type-infer ,Δ ∅ ((((elim nat (Unv 0)) (λ (x : nat) nat))
+                    zero)
+                   (λ (x : nat) (λ (ih-x : nat) x)))
             t))
-(nat-test ∅ (elim nat (λ (x : nat) nat)
-                  ()
-                  (zero (λ (x : nat) (λ (ih-x : nat) x)))
-                  zero)
+(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
+               zero)
+              (λ (x : nat) (λ (ih-x : nat) x)))
+             zero)
            nat)
-(nat-test ∅ (elim nat (λ (x : nat) nat)
-                  ()
-                  ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-                  zero)
+(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
+               (s zero))
+              (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
+             zero)
            nat)
-(nat-test ∅ (elim nat (λ (x : nat) nat)
-                  ()
-                  ((s zero) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
-                  zero)
+(nat-test ∅ (((((elim nat Type) (λ (x : nat) nat))
+               (s zero))
+              (λ (x : nat) (λ (ih-x : nat) (s (s x))))) zero)
            nat)
 (nat-test (∅ n : nat)
-          (elim nat (λ (x : nat) nat)
-                ()
-                (zero (λ (x : nat) (λ (ih-x : nat) x)))
-                n)
+          (((((elim nat (Unv 0)) (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 (λ (x : nat) bool)
-                   ()
-                   (btrue (λ (x : nat) (λ (ih-x : bool) bfalse)))
-                   n2)
+             (((((elim nat (Unv 0)) (λ (x : nat) bool))
+                btrue)
+               (λ (x : nat) (λ (ih-x : bool) bfalse)))
+              n2)
             bool))
 (check-not-holds
 (type-check ,Δ ∅
-             (elim nat nat () ((s zero)) zero)
+             ((((elim nat (Unv 0)) nat) (s zero)) zero)
             nat))
 (define lam (term (λ (nat : (Unv 0)) nat)))
 (check-equivalent
@ -475,15 +481,15 @@
             (in-hole Ξ (Π (x : (in-hole Θ_Ξ and)) U_P))))
 (check-holds
 (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
-             (elim and
-                   (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))
+             ((((((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))
             true))
 (check-true (Γ? (term (((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q)))))
 (check-holds
@ -501,7 +507,7 @@
                                           ((and B) A))))
             (in-hole Ξ (Π (x : (in-hole Θ and)) U))))
 (check-holds
- (convert ,Δ4 ∅
+ (equivalent ,Δ4
             (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (x : ((and A) B)) (Unv 0))))
             (Π (P : (Unv 0)) (Π (Q : (Unv 0)) (Π (x : ((and P) Q)) (Unv 0))))))
 (check-holds
@ -512,15 +518,14 @@
 (check-holds
 (type-check ,Δ4
             (((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q))
-             (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)
+             ((((((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)
             ((and Q) P)))
 (check-holds
 (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
@ -533,14 +538,14 @@
             t))
 (check-holds
 (type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
-             (elim and
+             ((((((elim and (Unv 0))
                  (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
-                                                ((and B) A))))
-                 (true true)
-                 ((λ (A : (Unv 0))
+                                                ((and B) A)))))
+                 (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)))
@ -563,18 +568,21 @@
 (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 (λ (y : false) (Π (x : Type) x)) () () x)
+             (((elim false (Unv 0)) (λ (y : false) (Π (x : Type) x))) x)
             (Π (x : (Unv 0)) x)))

 ;; nat-equal? tests
 (define zero?
-  (term (λ (n : nat)
-          (elim nat (λ (x : nat) bool) ()
-              (true (λ (x : nat) (λ (x_ih : bool) false)))
-              n))))
+  (term ((((elim nat Type) (λ (x : nat) bool))
+          true)
+         (λ (x : nat) (λ (x_ih : bool) false)))))
 (check-holds
 (type-check ,Δ ∅ ,zero? (Π (x : nat) bool)))
 (check-equal?
@ -584,12 +592,9 @@
 (term (reduce ,Δ (,zero? (s zero))))
 (term false))
 (define ih-equal?
-  (term (λ (ih : nat)
-          (elim nat (λ (x : nat) bool)
-              ()
-              (false
-               (λ (x : nat) (λ (y : bool) (x_ih x))))
-              ih))))
+  (term ((((elim nat Type) (λ (x : nat) bool))
+          false)
+         (λ (x : nat) (λ (y : bool) (x_ih x))))))
 (check-holds
 (type-check ,Δ (∅ x_ih : (Π (x : nat) bool))
             ,ih-equal?
@ -601,13 +606,10 @@
 (check-holds
 (type-infer ,Δ ∅ (λ (x : nat) (Π (x : nat) bool)) (Π (x : nat) (Unv 0))))
 (define nat-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))))
+  (term ((((elim nat Type) (λ (x : nat) (Π (x : nat) bool)))
+          ,zero?)
+         (λ (x : nat) (λ (x_ih : (Π (x : nat) bool))
+                        ,ih-equal?)))))
 (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)
@ -629,12 +631,19 @@
 (check-true (Δ? Δ=))

 (define refl-elim
-  (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))))
+  (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))))
 (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
--- 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 (lambda (A : Type) (ls : (List A)) Nat)
-           (Bool)
-          ((lambda (A : Type) z)
-           (lambda (A : Type) (a : A) (ls : (List A)) (ih : Nat)
-                   z))
+ (:: (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
          (nil Bool))
    Nat))

--- 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 == (λ (A : Type) (x : A) (y : A) (p : (== A x y)) Nat)
-       (Bool
-        true
-        true)
-       ((λ (A : Type) (x : A) z))
+ (elim == Type (λ (A : Type) (x : A) (y : A) (p : (== A x y)) Nat)
+       (λ (A : Type) (x : A) z)
+       Bool
+       true
+       true
       (refl Bool true))
 z)

--- a/cur-test/cur/tests/stdlib/typeclass.rkt
+++ b/cur-test/cur/tests/stdlib/typeclass.rkt
@ -11,7 +11,9 @@
           (equal? : (forall (a : A) (b : A) Bool)))
 (impl (Eqv Bool)
      (define (equal? (a : Bool) (b : Bool))
-        (if a b (not b))))
+        (if a
+            (if b true false)
+            (if b false true))))
 (impl (Eqv Nat)
      (define equal? nat-equal?))
 (check-equal?
--- a/cur-test/cur/tests/sweet-exp.rkt
+++ b/cur-test/cur/tests/sweet-exp.rkt
@ -1,16 +0,0 @@
-#lang sweet-exp cur
-require
- cur/stdlib/sugar
- cur/stdlib/bool
- cur/stdlib/nat
- rackunit
-
-check-equal?
-  if true false true
-  false
-
-define + plus
-
-check-equal?
-  {z + s(z)}
-  s(z)
--- 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 "0.4") "sweet-exp"))
+(define build-deps '("base" "rackunit-lib" ("cur-lib" #:version "0.2")))
 (define update-implies '("cur-lib"))
 (define pkg-desc "Tests for \"cur\".")
 (define pkg-authors '(wilbowma))
Author	SHA1	Message	Date
William J. Bowman	14960fd038	More quasisyntax/loc for better error messages	2016-01-21 16:07:16 -05:00
William J. Bowman	cc502671a6	[FAILING] Fixing design and running tests Fixed up some of the design and started testing.	2016-01-21 15:14:13 -05:00
William J. Bowman	83fb144c24	[UNTESTED, DESIGN BUGS] Design for typed macros Started working on a promising design for lifting type checking into the macros for easy syntax extensions over the typed language. Works on some examples, but running into performance issues and haven't tested/finished design.	2016-01-20 17:52:37 -05:00
William J. Bowman	76933bd3b1	Fixed coq->cur to setup local-env, tweaked -> * Fixed up coq->cur to track local-env while expanding. * Tweaked -> to give better error messages	2016-01-19 16:57:17 -05:00
William J. Bowman	87bc0e44bc	[FAILING] cur-lib builds, tests fail New application macro requires many extensions to manually keep up the term environment while expanding/running code at compile-time. This is not unreasonable, but does require some more changes.	2016-01-19 15:32:03 -05:00
William J. Bowman	b52ae2617b	Better error messages for application	2016-01-19 14:25:51 -05:00