diff --git a/turnstile/examples/dep2-assist.rkt b/turnstile/examples/dep2-assist.rkt
new file mode 100644
index 0000000..ba67ac1
--- /dev/null
+++ b/turnstile/examples/dep2-assist.rkt
@@ -0,0 +1,629 @@
+#lang turnstile/lang
+
+; second attempt at a basic dependently-typed calculus
+; initially copied from dep.rkt
+
+; Π  λ ≻ ⊢ ≫ → ∧ (bidir ⇒ ⇐) τ⊑
+
+(provide (rename-out [#%type *])
+         Π → ∀
+         = eq-refl eq-elim
+         Nat (rename-out [Zero Z][Succ S]) nat-ind #;nat-rec
+         λ (rename-out [app #%app]) ann
+         define define-type-alias
+)
+
+;; TODO:
+;; - map #%datum to S and Z
+;; - rename define-type-alias to define
+;; - add "assistant" part
+;; - provide match and match/lambda so nat-ind can be fn
+;;   - eg see https://gist.github.com/AndrasKovacs/6769513
+;; - add dependent existential
+;; - remove debugging code?
+
+;; #;(begin-for-syntax
+;;   (define old-ty= (current-type=?))
+;;   (current-type=?
+;;    (λ (t1 t2)
+;;      (displayln (stx->datum t1))
+;;      (displayln (stx->datum t2))
+;;      (old-ty= t1 t2)))
+;;   (current-typecheck-relation (current-type=?)))
+
+;(define-syntax-category : kind) ; defines #%kind for #%type
+
+;; set Type : Type
+;; alternatively, could define new base type Type,
+;; and make #%type typecheck with Type
+(begin-for-syntax
+  (define debug? #f)
+  (define type-eq-debug? #f)
+  (define debug-match? #f)
+
+  ;; TODO: fix `type` stx class
+  ;; (define old-type? (current-type?))
+  ;; (current-type?
+  ;;  (lambda (t) (or (#%type? t) (old-type? t))))
+  (define old-relation (current-typecheck-relation))
+  (current-typecheck-relation
+   (lambda (t1 t2)
+     (when type-eq-debug?
+       (pretty-print (stx->datum t1))
+       (pretty-print (stx->datum t2)))
+     ;; assumed #f can only come from (typeof #%type)
+     ;; (so this wont work when interacting with untyped code)
+     (or (and (false? (syntax-e t1)) (#%type? t2)) ; assign Type : Type
+         (old-relation t1 t2)))))
+(define-for-syntax Type ((current-type-eval) #'#%type))
+
+(define-internal-type-constructor →) ; equiv to Π with no uses on rhs
+(define-internal-binding-type ∀)     ; equiv to Π with #%type for all params
+
+;; Π expands into combination of internal →- and ∀-
+;; uses "let*" syntax where X_i is in scope for τ_i+1 ...
+;; TODO: add tests to check this
+(define-typed-syntax (Π ([X:id : τ_in] ...) τ_out) ≫
+  ;; TODO: check that τ_in and τ_out have #%type?
+  [[X ≫ X- : τ_in] ... ⊢ [τ_out ≫ τ_out- ⇐ #%type] [τ_in ≫ τ_in- ⇐ #%type] ...]
+  -------
+  [⊢ (∀- (X- ...) (→- τ_in- ... τ_out-)) ⇒ #%type])
+
+;; abbrevs for Π
+;; (→ τ_in τ_out) == (Π (unused : τ_in) τ_out)
+(define-simple-macro (→ τ_in ... τ_out)
+  #:with (X ...) (generate-temporaries #'(τ_in ...))
+  (Π ([X : τ_in] ...) τ_out))
+;; (∀ (X) τ) == (∀ ([X : #%type]) τ)
+(define-simple-macro (∀ (X ...)  τ)
+  (Π ([X : #%type] ...) τ))
+
+;; pattern expanders
+(begin-for-syntax
+  (define-syntax ~Π
+    (pattern-expander
+     (syntax-parser
+       [(_ ([x:id : τ_in] ... (~and (~literal ...) ooo)) τ_out)
+        #'(~∀ (x ... ooo) (~→ τ_in ... ooo τ_out))]
+       [(_ ([x:id : τ_in] ...)  τ_out)
+        #'(~∀ (x ...) (~→ τ_in ... τ_out))]))))
+
+;; equality -------------------------------------------------------------------
+(define-internal-type-constructor =)
+(define-typed-syntax (= t1 t2) ≫
+  [⊢ t1 ≫ t1- ⇒ ty]
+  [⊢ t2 ≫ t2- ⇐ ty]
+  ;; #:do [(printf "t1: ~a\n" (stx->datum #'t1-))
+  ;;       (printf "t2: ~a\n" (stx->datum #'t2-))]
+;  [t1- τ= t2-]
+  ---------------------
+  [⊢ (=- t1- t2-) ⇒ #%type])
+
+;; Q: what is the operational meaning of eq-refl?
+(define-typed-syntax (eq-refl e) ≫
+  [⊢ e ≫ e- ⇒ _]
+  ----------
+  [⊢ (#%app- void-) ⇒ (= e- e-)])
+
+;; eq-elim: t : T
+;;          P : (T -> Type)
+;;          pt : (P t)
+;;          w : T
+;;          peq : (= t w)
+;;       -> (P w)
+(define-typed-syntax (eq-elim t P pt w peq) ≫
+  [⊢ t ≫ t- ⇒ ty]
+  [⊢ P ≫ P- ⇐ (→ ty #%type)]
+  [⊢ pt ≫ pt- ⇐ (app P- t-)]
+  [⊢ w ≫ w- ⇐ ty]
+  [⊢ peq ≫ peq- ⇐ (= t- w-)]
+  --------------
+  [⊢ pt- ⇒ (app P- w-)])
+
+;; lambda and #%app -----------------------------------------------------------
+
+;; TODO: fix `type` stx class
+(define-typed-syntax λ
+  ;; expected ty only
+  [(_ (y:id ...) e) ⇐ (~Π ([x:id : τ_in] ... ) τ_out) ≫
+   ;; must use free-identifier=? to work with prove/define and `?`
+   [[x ≫ x- : τ_in] ... ⊢ #,(substs #'(x ...) #'(y ...) #'e free-identifier=?) ≫ e- ⇐ τ_out]
+   ---------
+   [⊢ (λ- (x- ...) e-)]]
+  ;; both expected ty and annotations
+  [(_ ([y:id : τ_in*] ...) e) ⇐ (~Π ([x:id : τ_in] ...) τ_out) ≫
+;  [(_ ([y:id : τy_in:type] ...) e) ⇐ (~Π ([x:id : τ_in] ...) τ_out) ≫
+   #:fail-unless (stx-length=? #'(y ...) #'(x ...))
+                 "function's arity does not match expected type"
+   [⊢ τ_in* ≫ τ_in** ⇐ #%type] ...
+;   #:when (typechecks? (stx-map (current-type-eval) #'(τ_in* ...))
+   #:when (typechecks? #'(τ_in** ...) #'(τ_in ...))
+;   #:when (typechecks? #'(τy_in.norm ...) #'(τ_in ...))
+;   [τy_in τ= τ_in] ...
+   [[x ≫ x- : τ_in] ... ⊢ #,(substs #'(x ...) #'(y ...) #'e) ≫ e- ⇐ τ_out]
+   -------
+   [⊢ (λ- (x- ...) e-)]]
+  ;; annotations only
+  [(_ ([x:id : τ_in] ...) e) ≫
+   [[x ≫ x- : τ_in] ... ⊢ [e ≫ e- ⇒ τ_out] [τ_in ≫ τ_in- ⇒ _] ...]
+   -------
+   [⊢ (λ- (x- ...) e-) ⇒ (Π ([x- : τ_in-] ...) τ_out)]])
+
+;; ;; classes for matching number literals
+;; (begin-for-syntax
+;;   (define-syntax-class nat
+;;     (pattern (~or n:exact-nonnegative-integer (_ n:exact-nonnegative-integer))
+;;              #:attr val
+;;              #'n))
+;;   (define-syntax-class nats
+;;     (pattern (n:nat ...) #:attr vals #'(n.val ...)))
+;;   ; extract list of quoted numbers
+;;   (define stx->nat (syntax-parser [n:nat (stx-e #'n.val)]))
+;;   (define (stx->nats stx) (stx-map stx->nat stx))
+;;   (define (stx+ ns) (apply + (stx->nats ns)))
+;;   (define (delta op-stx args)
+;;     (syntax-parse op-stx
+;;       [(~literal +-) (stx+ args)]
+;;       [(~literal zero?-) (apply zero? (stx->nats args))])))
+
+;; TODO: fix orig after subst, for err msgs
+;; app/eval should not try to ty check anymore
+(define-syntax app/eval
+  (syntax-parser
+    #;[(_ f . args) #:do[(printf "app/evaling ")
+                       (printf "f: ~a\n" (stx->datum #'f))
+                       (printf "args: ~a\n" (stx->datum #'args))]
+     #:when #f #'void]
+    [(_ f:id n P zc sc)
+     #:with (_ m/d . _) (local-expand #'(#%app match/delayed 'do 'nt 'ca 're) 'expression null)
+     #:when (free-identifier=? #'m/d #'f)
+     ;; TODO: need to attach type?
+     #'(match/nat n P zc sc)]
+    ;; TODO: apply to only lambda args or all args?
+    [(_ (~and f ((~literal #%plain-lambda) (x ...) e)) e_arg ...)
+     #:do[(when debug?
+            (printf "apping: ~a\n" (stx->datum #'f))
+            (printf "args\n")
+            (pretty-print (stx->datum #'(e_arg ...)))
+            (printf "expected type\n")
+            (pretty-print (stx->datum (typeof this-syntax))))]
+;     #:with (~Π ([X : _] ...) τ_out) (typeof #'f) ; must re-subst in type
+     ;; TODO: need to replace all #%app- in this result with app/eval again
+     ;; and then re-expand
+;     #:with ((~literal #%plain-app) newf . newargs) #'e
+ ;    #:do[(displayln #'newf)(displayln #'newargs)(displayln (stx-car #'e+))]
+     #:with r-app (datum->syntax (if (identifier? #'e) #'e (stx-car #'e)) '#%app)
+     ;; TODO: is this assign-type needed only for tests?
+     ;; eg, see id tests in dep2-peano.rkt
+     #:with ty (typeof this-syntax)
+     #:with e-inst (substs #'(app/eval e_arg ...) #'(r-app x ...) #'e free-identifier=?)
+     ;; some apps may not have type (eg in internal reps)
+     #:with e+ (if (syntax-e #'ty) (assign-type #'e-inst #'ty) #'e-inst)
+     #:do[(when debug?
+            (displayln "res:--------------------")
+            (pretty-print (stx->datum #'e+))
+            ;; (displayln "actual type:")
+            ;; (pretty-print (stx->datum (typeof #'e+)))
+            ;; (displayln "new type:")
+            ;; (pretty-print (stx->datum (substs #'(e_arg ...) #'(X ...) (typeof #'e+))))
+            ;; (displayln "res expanded:------------------------")
+            ;; (pretty-print
+            ;;  (stx->datum (local-expand (substs #'(e_arg ...) #'(x ...) #'e) 'expression null)))
+            (displayln "res app/eval re-expanding-----------------------"))]
+     #:with ((~literal let-values) () ((~literal let-values) () e++))
+            (local-expand
+             #'(let-syntax (#;[app (make-rename-transformer #'app/eval)]
+                            #;[x (make-variable-like-transformer #'e_arg)]) e+)
+                 'expression null)
+     #:do[(when debug?
+            (pretty-print (stx->datum #'e++))
+;            (pretty-print (stx->datum (typeof #'e++)))
+            #;(local-expand
+             #'(let-syntax ([app (make-rename-transformer #'app/eval)]
+                            #;[x (make-variable-like-transformer #'e_arg)]) e+)
+             'expression null))]
+     #'e++ #;(substs #'(e_arg ...) #'(x ...) #'e)]
+    [(_ f . args)
+    #:do[(when debug?
+           (printf "not apping\n")
+           (pretty-print (stx->datum #'f))
+           (displayln "args")
+           (pretty-print (stx->datum #'args)))]
+     #:with f+ (expand/df #'f)
+     #:with args+ (stx-map expand/df #'args)
+     ;; TODO: need to attach type?
+;     #:with ty (typeof this-syntax)
+     (syntax-parse #'f+
+       [((~literal #%plain-lambda) . _)
+        #'(app/eval f+ . args+)]
+       [_
+        #'(#%app- f+ . args+)])]))
+     
+;; TODO: fix orig after subst
+(define-typed-syntax app
+  ;; matching, ; TODO: where to put this?
+  #;[(_ f:id . args) ≫
+   #:with (_ m/d . _) (local-expand #'(match/delayed 1 2 3 4) 'expression null)
+   #:when (free-identifier=? #'m/d #'f)
+   ------------
+   [≻ (match/nat . args)]]
+  [(_ e_fn e_arg ...) ≫
+   #:do[(when debug?
+          (displayln "TYPECHECKING")
+          (pretty-print (stx->datum this-syntax)))]
+;   #:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn))]
+;   [⊢ e_fn ≫ (~and e_fn- (_ (x:id ...) e ~!)) ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
+   [⊢ e_fn ≫ e_fn- ⇒ (~Π ([X : τ_in] ...) τ_out)]
+;   #:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn-))]
+   #:fail-unless (stx-length=? #'[τ_in ...] #'[e_arg ...])
+                 (num-args-fail-msg #'e_fn #'[τ_in ...] #'[e_arg ...])
+   [⊢ e_arg ≫ e_arg- ⇐ τ_in] ... ; typechecking args
+   -----------------------------
+   [⊢ (app/eval e_fn- e_arg- ...) ⇒ #,(substs #'(e_arg- ...) #'(X ...) #'τ_out)]])
+   
+#;(define-typed-syntax #%app
+  [(_ e_fn e_arg ...) ≫ ; apply lambda
+   #:do[(printf "applying (1) ~a\n" (stx->datum #'e_fn))]
+   [⊢ e_fn ≫ (~and e_fn- (_ (x:id ...) e ~!)) ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
+   #:do[(printf "e_fn-: ~a\n" (stx->datum #'e_fn-))
+        (printf "args: ~a\n" (stx->datum #'(e_arg ...)))]
+   #:fail-unless (stx-length=? #'[τ_inX ...] #'[e_arg ...])
+                 (num-args-fail-msg #'e_fn #'[τ_inX ...] #'[e_arg ...])
+   [⊢ e_arg ≫ e_argX- ⇒ ty-argX] ... ; typechecking args must be fold; do in 2 steps
+   #:do[(define (ev e)
+          (syntax-parse e
+;            [_ #:do[(printf "eval: ~a\n" (stx->datum e))] #:when #f #'(void)]
+            [(~or _:id
+;                  ((~literal #%plain-lambda) . _)
+                  (~= _ _)
+                  ~Nat
+                  ((~literal quote) _))
+             e]
+            ;; handle nums
+            [((~literal #%plain-app)
+              (~and op (~or (~literal +-) (~literal zero?-)))
+              . args:nats)
+             #`#,(delta #'op #'args.vals)]
+            [((~literal #%plain-app) (~and f ((~literal #%plain-lambda) . b)) . rst)
+             (expand/df #`(#%app f . #,(stx-map ev #'rst)))]
+            [(x ...)
+             ;; #:do[(printf "t before: ~a\n" (typeof e))
+             ;;      (printf "t after: ~a\n" (typeof #`#,(stx-map ev #'(x ...))))]
+             (syntax-property #`#,(stx-map ev #'(x ...)) ': (typeof e))]
+            [_  e] ; other literals
+            #;[es (stx-map L #'es)]))]
+   #:with (ty-arg ...)
+          (stx-map
+           (λ (t) (ev (substs #'(e_argX- ...) #'(X ...) t)))
+           #'(ty-argX ...))
+   #:with (e_arg- ...) (stx-map (λ (e t) (assign-type e t)) #'(e_argX- ...) #'(ty-arg ...))
+   #:with (τ_in ... τ_out)
+          (stx-map
+           (λ (t) (ev (substs #'(e_arg- ...) #'(X ...) t)))
+           #'(τ_inX ... τ_outX))
+;   #:do[(printf "vars: ~a\n" #'(X ...))]
+;   #:when (stx-andmap (λ (t1 t2)(displayln (stx->datum t1)) (displayln (stx->datum t2)) (displayln (typecheck? t1 t2)) #;(typecheck? t1 t2)) #'(ty-arg ...) #'(τ_in ...))
+   ;; #:do[(stx-map
+   ;;       (λ (tx t) (printf "ty_in inst: \n~a\n~a\n" (stx->datum tx) (stx->datum t)))
+   ;;       #'(τ_inX ...)          #'(τ_in ...))]
+;   [⊢ e_arg- ≫ _ ⇐ τ_in] ...
+    #:do[(printf "res e =\n~a\n" (stx->datum (substs #'(e_arg- ...) #'(x ...) #'e)))
+         (printf "res t = ~a\n" (stx->datum (substs #'(e_arg- ...) #'(X ...) #'τ_out)))]
+   #:with res-e (let L ([e (substs #'(e_arg- ...) #'(x ...) #'e)]) ; eval
+                  (syntax-parse e
+                    [(~or _:id
+                          ((~literal #%plain-lambda) . _)
+                          (~Π ([_ : _] ...) _)
+                          (~= _ _)
+                          ~Nat)
+                     e]
+                    ;; handle nums
+                    [((~literal #%plain-app)
+                      (~and op (~or (~literal +-) (~literal zero?-)))
+                      . args:nats)
+                     #`#,(delta #'op #'args.vals)]
+                    [((~literal #%plain-app) . rst)
+                     (expand/df #`(#%app . #,(stx-map L #'rst)))]
+                    [_ e] ; other literals
+                    #;[es (stx-map L #'es)]))
+   ;; #:with res-ty (syntax-parse (substs #'(e_arg- ...) #'(X ...) #'τ_out)
+   ;;                 [((~literal #%plain-app) . rst) (expand/df #'(#%app . rst))]
+   ;;                 [other-ty #'other-ty])
+   --------
+   [⊢ res-e #;#,(substs #'(e_arg- ...) #'(x ...) #'e) ⇒ τ_out
+            #;#,(substs #'(e_arg- ...) #'(X ...) #'τ_out)]]
+  [(_ e_fn e_arg ... ~!) ≫ ; apply var
+;   #:do[(printf "applying (2) ~a\n" (stx->datum #'e_fn))]
+   [⊢ e_fn ≫ e_fn- ⇒ ty-fn]
+;   #:do[(printf "e_fn- ty: ~a\n" (stx->datum #'ty-fn))]
+   [⊢ e_fn ≫ _ ⇒ (~Π ([X : τ_inX] ...) τ_outX)]
+;   #:do[(printf "e_fn- no: ~a\n" (stx->datum #'e_fn-))
+;        (printf "args: ~a\n" (stx->datum #'(e_arg ...)))]
+   ;; #:with e_fn- (syntax-parse #'e_fn*
+   ;;                [((~literal #%plain-app) . rst) (expand/df #'(#%app . rst))]
+   ;;                [other #'other])
+   #:fail-unless (stx-length=? #'[τ_inX ...] #'[e_arg ...])
+                 (num-args-fail-msg #'e_fn #'[τ_inX ...] #'[e_arg ...])
+   [⊢ e_arg ≫ e_argX- ⇒ ty-argX] ... ; typechecking args must be fold; do in 2 steps
+   #:do[(define (ev e)
+          (syntax-parse e
+;            [_ #:do[(printf "eval: ~a\n" (stx->datum e))] #:when #f #'(void)]
+            [(~or _:id
+;                  ((~literal #%plain-lambda) . _)
+                  (~= _ _)
+                  ~Nat
+                  ((~literal quote) _))
+             e]
+            ;; handle nums
+            [((~literal #%plain-app)
+              (~and op (~or (~literal +-) (~literal zero?-)))
+              . args:nats)
+             #`#,(delta #'op #'args.vals)]
+            [((~literal #%plain-app) (~and f ((~literal #%plain-lambda) . b)) . rst)
+             (expand/df #`(#%app f . #,(stx-map ev #'rst)))]
+            [(x ...)
+             ;; #:do[(printf "t before: ~a\n" (typeof e))
+             ;;      (printf "t after: ~a\n" (typeof #`#,(stx-map ev #'(x ...))))]
+             (syntax-property #`#,(stx-map ev #'(x ...)) ': (typeof e))]
+            [_  e] ; other literals
+            #;[es (stx-map L #'es)]))]
+   #:with (ty-arg ...)
+          (stx-map
+           (λ (t) (ev (substs #'(e_argX- ...) #'(X ...) t)))
+           #'(ty-argX ...))
+   #:with (e_arg- ...) (stx-map (λ (e t) (assign-type e t)) #'(e_argX- ...) #'(ty-arg ...))
+   #:with (τ_in ... τ_out)
+          (stx-map
+           (λ (t) (ev (substs #'(e_arg- ...) #'(X ...) t)))
+           #'(τ_inX ... τ_outX))
+   ;; #:do[(printf "vars: ~a\n" #'(X ...))]
+;  #:when (stx-andmap (λ (e t1 t2)(displayln (stx->datum e))(displayln (stx->datum t1)) (displayln (stx->datum t2)) (displayln (typecheck? t1 t2)) #;(typecheck? t1 t2)) #'(e_arg ...)#'(ty-arg ...) #'(τ_in ...))
+   ;; #:do[(stx-map
+   ;;       (λ (tx t) (printf "ty_in inst: \n~a\n~a\n" (stx->datum tx) (stx->datum t)))
+   ;;       #'(τ_inX ...)          #'(τ_in ...))]
+;   [⊢ e_arg ≫ _ ⇐ τ_in] ...
+;  #:do[(printf "res e2 =\n~a\n" (stx->datum #'(#%app- e_fn- e_arg- ...)))
+;       (printf "res t2 = ~a\n" (stx->datum (substs #'(e_arg- ...) #'(X ...) #'τ_out)))]
+   ;; #:with res-e (syntax-parse #'e_fn-
+   ;;                [((~literal #%plain-lambda) . _) (expand/df #'(#%app e_fn- e_arg- ...))]
+   ;;                [other #'(#%app- e_fn- e_arg- ...)])
+   --------
+   [⊢ (#%app- e_fn- e_arg- ...) ⇒ τ_out
+      #;#,(expand/df (substs #'(e_arg- ...) #'(X ...) #'τ_out))]])
+
+(define-typed-syntax (ann e (~datum :) τ) ≫
+  [⊢ e ≫ e- ⇐ τ]
+  --------
+  [⊢ e- ⇒ τ])
+
+;; (define-typed-syntax (if e1 e2 e3) ≫
+;;   [⊢ e1 ≫ e1- ⇒ _]
+;;   [⊢ e2 ≫ e2- ⇒ ty]
+;;   [⊢ e3 ≫ e3- ⇒ _]
+;;   #:do[(displayln #'(e1 e2 e3))]
+;;   --------------
+;;   [⊢ (#%app- void-) ⇒ ty])
+
+;; top-level ------------------------------------------------------------------
+;; TODO: shouldnt need define-type-alias, should be same as define
+(define-syntax define-type-alias
+  (syntax-parser
+    [(_ alias:id τ);τ:any-type)
+     #'(define-syntax- alias
+         (make-variable-like-transformer #'τ))]
+    #;[(_ (f:id x:id ...) ty)
+     #'(define-syntax- (f stx)
+         (syntax-parse stx
+           [(_ x ...)
+            #:with τ:any-type #'ty
+            #'τ.norm]))]))
+
+(define-typed-syntax define
+  [(_ x:id (~datum :) τ e:expr) ≫
+   [⊢ e ≫ e- ⇐ τ]
+   #:with y (generate-temporary #'x)
+   #:with y+props (transfer-props #'e- #'y #:except '(origin))
+   --------
+   [≻ (begin-
+        (define-syntax x (make-rename-transformer #'y+props))
+        (define- y e-))]]
+  [(_ x:id e) ≫
+   ;This won't work with mutually recursive definitions
+   [⊢ e ≫ e- ⇒ _]
+   #:with y (generate-temporary #'x)
+   #:with y+props (transfer-props #'e- #'y #:except '(origin))
+   --------
+   [≻ (begin-
+        (define-syntax x (make-rename-transformer #'y+props))
+        (define- y e-))]]
+  #;[(_ (f [x (~datum :) ty] ... (~or (~datum →) (~datum ->)) ty_out) e ...+) ≫
+   #:with f- (add-orig (generate-temporary #'f) #'f)
+   --------
+   [≻ (begin-
+        (define-syntax- f
+          (make-rename-transformer (⊢ f- : (→ ty ... ty_out))))
+        (define- f-
+          (stlc+lit:λ ([x : ty] ...)
+            (stlc+lit:ann (begin e ...) : ty_out))))]])
+
+
+;; peano nums -----------------------------------------------------------------
+(define-base-type Nat)
+
+(struct Z () #:transparent)
+(struct S (n) #:transparent)
+
+(define-typed-syntax Zero
+  [_:id ≫ --- [⊢ (Z) ⇒ Nat]])
+
+(define-typed-syntax (Succ n) ≫
+  [⊢ n ≫ n- ⇐ Nat]
+  -----------
+  [⊢ (S n-) ⇒ Nat])
+#;(define-typed-syntax (sub1 n) ≫
+  [⊢ n ≫ n- ⇐ Nat]
+  #:do[(displayln #'n-)]
+  -----------
+  [⊢ (#%app- -- n- 1) ⇒ Nat])
+
+;; generalized recursor over natural nums
+;; (cases dispatched in #%app)
+;; (define- (nat-ind- P z s n) (#%app- void))
+;; (define-syntax nat-ind
+;;   (make-variable-like-transformer
+;;    (assign-type 
+;;     #'nat-ind-
+;;     #'(Π ([P : (→ Nat #%type)]
+;;           [z : (app P Zero)]
+;;           [s : (Π ([k : Nat]) (→ (app P k) (app P (Succ k))))]
+;;           [n : Nat])
+;;          (app P n)))))
+
+#;(define-type-alias nat-ind
+  (λ ([P : (→ Nat #%type)]
+      [z : (P Z)]
+      [s : (Π ([k : Nat]) (→ (P k) (P (S k))))]
+      [n : Nat])
+    #'(#%app- nat-ind- P z s n)))
+(struct match/delayed (n P zc sc))
+#;(define-syntax match/eval
+  (syntax-parser
+    [(_ n zc sc) #:do[(printf "matching: ~a\n" (stx->datum #'n))] #:when #f #'(void)]
+    [(_ ((~literal #%plain-app) z0:id) zc sc) 
+     #:with (_ z1) (local-expand #'(Z) 'expression null)
+     #:when (free-identifier=? #'z0 #'z1)
+     #'zc]
+    [(_ ((~literal #%plain-app) s0:id m) zc sc)
+     #:with (_ s1 . _) (local-expand #'(S 'dont-care) 'expression null)
+     #:when (free-identifier=? #'s0 #'s1)
+     #:when (displayln 2)
+     #`(app sc (nat-rec #,(typeof #'zc) zc sc m))]
+    [(_ n zc sc) #'(match/delayed n zc sc)]))
+
+;; this is an "eval" form; should not do any more type checking
+;; otherwise, will get type errs some some subexprs may still have uninst tys
+;; eg, zc and sc were typechecked with paramaterized P instead of inst'ed P
+(define-syntax match/nat
+  (syntax-parser
+    [(_ n P zc sc)
+     #:do[(when debug-match?
+            (printf "match/nating: ~a\n" (stx->datum #'(n P zc sc)))
+            #;(printf "zc ty: ~a\n" (stx->datum (typeof #'zc)))
+            #;(printf "sc ty: ~a\n" (stx->datum (typeof #'sc))))]
+     #:when #f #'(void)]
+    [(_ (~and n ((~literal #%plain-app) z0:id)) P zc sc)
+     #:with (_ z1) (local-expand #'(#%app Z) 'expression null)
+     #:when (free-identifier=? #'z0 #'z1)
+     #:do [(when debug-match? (displayln 'zc))]
+     ;; #:when (printf "match eval res zero ety: ~a\n" (stx->datum (typeof this-syntax)))
+     ;; #:when (printf "match eval res zero ty: ~a\n" (stx->datum (typeof #'zc)))
+     (assign-type #'zc #'(app/eval P n))]
+    [(_ (~and n ((~literal #%plain-app) s0:id m)) P zc sc)
+     #:with (_ s1 . _) (local-expand #'(#%app S 'dont-care) 'expression null)
+     #:when (free-identifier=? #'s0 #'s1)
+     #:with (~Π ([_ : _] ...) τ_out) (typeof #'sc)
+     #:do[(when debug-match? (displayln 'sc))]
+     ;; #:when (printf "match eval res succ ety: ~a\n" (stx->datum (typeof this-syntax)))
+     ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'sc)))
+     ;; #:when (printf "match eval res succ ty: ~a\n" (stx->datum (typeof #'(app/eval (app/eval sc m) (match/nat m P zc sc)))))
+;     #`(app sc m (nat-rec #,(typeof #'zc) zc sc m))]
+;     #:with ty (typeof this-syntax)
+     (assign-type
+      #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc))
+      #'(app/eval P n))
+  ;   #'res
+ ;    (if (syntax-e #'ty) (assign-type #'res #'ty) #'res)
+     #;(assign-type #`(app/eval #,(assign-type #'(app/eval sc m) #'τ_out) (match/nat m P zc sc)) (typeof this-syntax))]
+    [(_ n P zc sc)
+     #:do[(when debug-match?  (displayln "delay match"))]
+     (assign-type #'(#%app match/delayed n P zc sc) #'(app/eval P n))]))
+#;(define-typed-syntax (nat-rec ty zc sc n) ≫
+  [⊢ ty ≫ ty- ⇐ #%type]
+  [⊢ zc ≫ zc- ⇐ ty-] ; zero case
+  [⊢ sc ≫ sc- ⇐ (→ ty- ty-)] ; succ case
+  [⊢ n ≫ n- ⇐ Nat]
+  ;; #:with res
+  ;;   (syntax-parse #'n-
+  ;;    [aaa #:do[(printf "matching: ~a\n" (stx->datum #'aaa))] #:when #f #'(void)]
+  ;;    [((~literal #%plain-app) (~literal Z)) #'zc-]
+  ;;    [((~literal #%plain-app) (~literal S) m) #'(app sc- (nat-rec zc- sc- m))])
+  --------------------
+;  [⊢ (match/eval n- zc- sc-) ⇒ ty-])
+  [⊢ (match/nat n-
+                zc-
+                (λ ([n-1 : Nat][rec : ty-])
+                  (sc- rec)))
+     ⇒ ty-])
+  
+(define-typed-syntax (nat-ind P z s n) ≫
+  [⊢ P ≫ P- ⇐ (→ Nat #%type)]
+  [⊢ z ≫ z- ⇐ (app P- Zero)] ; zero 
+  [⊢ s ≫ s- ⇐ (Π ([k : Nat]) (→ (app P- k) (app P- (Succ k))))] ; succ
+  [⊢ n ≫ n- ⇐ Nat]
+  ;; #:with res (if (typecheck? #'n- (expand/df #'Z))
+  ;;                #'z-
+  ;;                #'(s- (nat-ind P- z- s- (sub1 n-))))
+  ----------------
+  [⊢ (match/nat n-
+                P-
+                z-
+                s-
+                #;(λ ([n-1 : Nat][rec : (app P- n-)])
+                  (app s- n-1 rec #;(nat-ind P- z- s- n-1))))
+     ⇒ (app P- n-)])
+;  [≻ (P- d-)])
+
+;; proof assistant
+
+(provide prove ? refine)
+
+(struct ?? ())
+(define-for-syntax ?+ (stx-cadr (local-expand #'(??) 'expression null)))
+
+(define-typed-syntax ?
+  [(_ ty) ≫
+   #:with x (generate-temporary)
+   #:do[(current-hole #'x)]
+   -----
+   [⊢ #,?+ ⇒ ty]]
+  [_:id ⇐ ty ≫
+   #:with x (generate-temporary)
+   #:do[(current-hole #'x)]
+   -----
+   [⊢ #,?+]])
+
+(begin-for-syntax
+  (define current-ty (make-parameter #f))
+  (define current-hole (make-parameter #f))
+  (define current-expr (make-parameter #f))
+  (define (update-expr e)
+    (set-expr (subst e ?+ (current-expr) free-identifier=?)))
+  (define (set-expr e)
+    (current-expr e)
+    (printf "current proof: ~a\n" (stx->datum (current-expr))))
+  (define (mk-hole)
+    (current-hole (generate-temporary))
+    (current-hole)))
+
+
+(define-syntax prove
+  (syntax-parser
+    [(_ ty)
+     #:do[(current-ty ((current-type-eval) #'ty))]
+     #:when (local-expand #'(? ty) 'expression null)
+     #:do[(set-expr #'?)] 
+     #'(void)]))
+
+(define-typed-syntax refine
+  [(_ e) ≫
+   #:do[(printf "refining with: ~a\n" (stx->datum #'e))]
+   #:with ty (current-ty)
+   #:with e0 (subst #'e #'? (current-expr) free-identifier=?)
+   [⊢ e0 ≫ e0- ⇐ ty]
+   #:do [(displayln "ok.")
+         (set-expr #'e0)
+         (let ([x (generate-temporary)])
+           (when ((current-type=?) #'e0 (subst #'x #'? #'e0 free-identifier=?))
+               (displayln "qed.")))]
+   -------
+   [⊢ (void) ⇒ ty]])
diff --git a/turnstile/examples/tests/dep2-assist-tests.rkt b/turnstile/examples/tests/dep2-assist-tests.rkt
new file mode 100644
index 0000000..44cf678
--- /dev/null
+++ b/turnstile/examples/tests/dep2-assist-tests.rkt
@@ -0,0 +1,295 @@
+#lang s-exp "../dep2-assist.rkt"
+(require "rackunit-typechecking.rkt")
+
+; Π → λ ∀ ≻ ⊢ ≫ ⇒
+
+;; examples from Prabhakar's Proust paper
+
+(prove (∀ (A B C) (→ (→ A B) (→ B C) (→ A C))))
+
+(refine (λ (a b c) ?))
+(refine (λ (f g) ?))
+(refine (λ (x) ?))
+; (refine (f ?)) ; wrong, g first
+(refine (g ?))
+(refine (f ?))
+(refine x)
+
+;; ;; the following examples to not require type-level eval
+;; (check-type (λ ([x : *]) x) : (Π ([x : *]) *))
+
+;; (typecheck-fail ((λ ([x : *]) x) (λ ([x : *]) x))
+;;  #:verb-msg "expected *, given (Π ([x : *]) *)")
+
+;; (check-type (λ ([A : *][B : *])
+;;               (λ ([x : A])
+;;                 (λ ([y : (→ A B)])
+;;                   (y x))))
+;;             : (∀ (A B) (→ A (→ (→ A B) B))))
+
+;; ;; check alpha equiv
+;; ;; TODO: is this correct behavior?
+;; (check-type (λ ([A : *][B : *])
+;;               (λ ([x : A])
+;;                 (λ ([y : (→ A B)])
+;;                   (y x))))
+;;             : (∀ (Y Z) (→ Y (→ (→ Y Z) Z))))
+;; (check-type (λ ([Y : *][Z : *])
+;;               (λ ([x : Y])
+;;                 (λ ([y : (→ Y Z)])
+;;                   (y x))))
+;;             : (∀ (A B) (→ A (→ (→ A B) B))))
+;; ;; check infer direction
+;; (check-type (λ (A B) (λ (x) (λ (y) (y x))))
+;;             : (∀ (A B) (→ A (→ (→ A B) B))))
+;; (check-type (λ (A B) (λ (x) (λ (y) (y x))))
+;;             : (∀ (X Y) (→ X (→ (→ X Y) Y))))
+
+;; ;; transitivity of implication --------------------
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ ([f : (→ B C)])
+;;                 (λ ([g : (→ A B)])
+;;                   (λ ([x : A])
+;;                     (f (g x))))))
+;;             : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
+;; ;; less currying
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ ([f : (→ B C)][g : (→ A B)])
+;;                 (λ ([x : A])
+;;                   (f (g x)))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;; ;; infer direction (no annotations)
+;; (check-type (λ (A B C) (λ (f) (λ (g) (λ (x) (f (g x))))))
+;;             : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
+;; ;; less currying
+;; (check-type (λ (A B C) (λ (f g) (λ (x) (f (g x)))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;; (check-type (λ (A B C) (λ (f g x) (f (g x))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) A C)))
+;; (check-type (λ (A B C f g x) (f (g x)))
+;;             : (Π ([A : *][B : *][C : *][f : (→ B C)][g : (→ A B)][x : A]) C))
+;; (check-type (λ (A B C f g x) (f (g x)))
+;;             : (Π ([X : *][Y : *][Z : *][a : (→ Y Z)][b : (→ X Y)][c : X]) Z))
+
+;; ;; partial annotations - outer lam with no annotations
+;; (check-type (λ (A B C)
+;;               (λ (f g)
+;;                 (λ ([x : A])
+;;                   (f (g x)))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;; (check-type (λ (A B C)
+;;               (λ ([f : (→ B C)][g : (→ A B)])
+;;                 (λ ([x : A])
+;;                   (f (g x)))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;; (typecheck-fail (ann
+;;                  (λ (A B C)
+;;                    (λ (f g)
+;;                      (λ ([x : C])
+;;                        (f (g x)))))
+;;                  : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;;  #:with-msg "expected A, given C")
+;; ;; partial annotations - inner lam with no annotations
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ (f g)
+;;                 (λ (x)
+;;                   (f (g x)))))
+;;             : (∀ (A B C) (→ (→ B C) (→ A B) (→ A C))))
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ ([f : (→ B C)])
+;;                 (λ (g)
+;;                   (λ (x)
+;;                     (f (g x))))))
+;;             : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ ([f : (→ B C)])
+;;                 (λ (g)
+;;                   (λ ([x : A])
+;;                     (f (g x))))))
+;;             : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
+;; (check-type (λ ([A : *][B : *][C : *])
+;;               (λ ([f : (→ B C)])
+;;                 (λ ([g : (→ A B)])
+;;                   (λ (x)
+;;                     (f (g x))))))
+;;             : (∀ (A B C) (→ (→ B C) (→ (→ A B) (→ A C)))))
+
+;; ;; Peirce's Law (doesnt work)
+;; (typecheck-fail (ann
+;;                  (λ ([A : *][B : *][C : *])
+;;                    (λ ([f : (→ (→ A B) A)])
+;;                      (λ ([g : (→ A B)]) ; need concrete (→ A B) (not in type)
+;;                        (f g))))
+;;                  : (∀ (A B C) (→ (→ (→ A B) A) A)))
+;;  #:verb-msg "expected (∀ (A B C) (→ (→ (→ A B) A) A)), given (Π ((A : *) (B : *) (C : *)) (Π ((f : (→ (→ A B) A))) (Π ((g : (→ A B))) A)))")
+
+;; ;; booleans -------------------------------------------------------------------
+
+;; ;; Bool base type
+;; ;; TODO: use define instead of define-type-alias
+;; (define-type-alias Bool (∀ (A) (→ A A A)))
+;; (check-type Bool : *)
+
+;; ;; Bool terms
+;; (define T (λ ([A : *]) (λ ([x : A][y : A]) x)))
+;; (define F (λ ([A : *]) (λ ([x : A][y : A]) y)))
+;; (check-type T : Bool)
+;; (check-type F : Bool)
+;; ;; check infer case
+;; (define T2 (λ ([abool : *]) (λ ([x : abool][y : abool]) x)))
+;; (define F2 (λ ([abool : *]) (λ ([x : abool][y : abool]) y)))
+;; (check-type T2 : Bool)
+;; (check-type F2 : Bool)
+;; (define T3 : Bool (λ (abool) (λ (x y) x)))
+;; (define F3 : Bool (λ (abool) (λ (x y) y)))
+;; (check-type T3 : Bool)
+;; (check-type F3 : Bool)
+
+;; ;; defining `and` requires instantiating polymorphic types
+;; (define and (λ ([x : Bool][y : Bool]) ((x Bool) y F)))
+;; (check-type and : (→ Bool Bool Bool))
+;; (define or (λ ([x : Bool][y : Bool]) ((x Bool) T y)))
+;; (check-type or : (→ Bool Bool Bool))
+;; (define not (λ ([x : Bool]) ((x Bool) F T)))
+;; (check-type not : (→ Bool Bool))
+
+;; ;; `And` type constructor, ie type-level fn
+;; (define-type-alias And
+;;   (λ ([P : *][Q : *])
+;;     (∀ (C) (→ (→ P Q C) C))))
+;; (check-type And : (→ * * *))
+
+;; ;; And type intro (logical conj)
+;; (define ∧
+;;   (λ ([P : *][Q : *])
+;;     (λ ([p : P][q : Q])
+;;       (λ ([C : *])
+;;         (λ ([f : (→ P Q C)])
+;;           (f p q))))))
+;; (check-type ∧ : (∀ (P Q) (→ P Q (And P Q))))
+
+;; ;; `And` type elim
+;; (define proj1
+;;   (λ ([P : *][Q : *])
+;;     (λ ([e : (And P Q)])
+;;       ((e P) (λ ([x : P][y : Q]) x)))))
+;; (define proj2
+;;   (λ ([P : *][Q : *])
+;;     (λ ([e : (And P Q)])
+;;       ((e Q) (λ ([x : P][y : Q]) y)))))
+;; ;; bad proj2: (e A) should be (e B)
+;; (typecheck-fail
+;;  (λ ([P : *][Q : *])
+;;    (λ ([e : (And P Q)])
+;;      ((e P) (λ ([x : P][y : Q]) y))))
+;;  #:verb-msg
+;;  "expected (→ P Q C), given (Π ((x : P) (y : Q)) Q)")
+;; (check-type proj1 : (∀ (P Q) (→ (And P Q) P)))
+;; (check-type proj2 : (∀ (P Q) (→ (And P Q) Q)))
+
+;; ;; proj1, no annotations
+;; (check-type (λ (P Q) (λ (e) ((e P) (λ (x y) x))))
+;;             : (∀ (P Q) (→ (And P Q) P)))
+;; ;; proj2, no annotations
+;; (check-type (λ (P Q) (λ (e) ((e Q) (λ (x y) y))))
+;;             : (∀ (P Q) (→ (And P Q) Q)))
+;; (typecheck-fail (ann (λ (P Q) (λ (e) ((e Q) (λ (x y) x))))
+;;                      : (∀ (P Q) (→ (And P Q) Q)))
+;;  #:with-msg "expected C, given P") ; TODO: err msg, fix orig
+;; (typecheck-fail (ann (λ (P Q) (λ (e) ((e P) (λ (x y) y))))
+;;                      : (∀ (P Q) (→ (And P Q) Q)))
+;;  #:with-msg "expected C, given Q") ; TODO: err msg
+
+;; ;((((conj q) p) (((proj2 p) q) a)) (((proj1 p) q) a)))))
+;; (define and-commutes
+;;   (λ ([A : *][B : *])
+;;     (λ ([e : (And A B)])
+;;       ((∧ B A) ((proj2 A B) e) ((proj1 A B) e)))))
+;; ;; bad and-commutes, dont flip A and B: (→ (And A B) (And A B))
+;; (typecheck-fail
+;;  (λ ([A : *][B : *])
+;;    (λ ([e : (And A B)])
+;;      ((∧ A B) ((proj2 A B) e) ((proj1 A B) e))))
+;;  #:verb-msg
+;;  "#%app: type mismatch: expected P, given C") ; TODO: err msg
+;; (check-type and-commutes : (∀ (A B) (→ (And A B) (And B A))))
+
+;; ;; nats -----------------------------------------------------------------------
+;; (define-type-alias nat (∀ (A) (→ A (→ A A) A)))
+;; (check-type nat : *)
+
+;; (define-type-alias z (λ ([Ty : *]) (λ ([zero : Ty][succ : (→ Ty Ty)]) zero)))
+;; (define-type-alias s (λ ([n : nat])
+;;                        (λ ([Ty : *])
+;;                          (λ ([zero : Ty][succ : (→ Ty Ty)])
+;;                            (succ ((n Ty) zero succ))))))
+;; (check-type z : nat)
+;; (check-type s : (→ nat nat))
+
+;; (define-type-alias one (s z))
+;; (define-type-alias two (s (s z)))
+;; (check-type one : nat)
+;; (check-type two : nat)
+
+;; (define-type-alias plus
+;;   (λ ([x : nat][y : nat])
+;;     ((x nat) y s)))
+;; (check-type plus : (→ nat nat nat))
+;; (check-type (λ (x y) ((x nat) y s)) : (→ nat nat nat))
+
+;; ;; equality -------------------------------------------------------------------
+;; (check-type (eq-refl one) : (= one one))
+;; (typecheck-fail (ann (eq-refl one) : (= two one))
+;;  #:verb-msg "expected (= two one), given (= one one)")
+;; (check-type (ann (eq-refl one) : (= one one)) : (= one one))
+;; (check-type (eq-refl one) : (= (s z) one))
+;; (check-type (eq-refl two) : (= (s (s z)) two))
+;; (check-type (eq-refl two) : (= (s one) two))
+;; (check-type (eq-refl two) : (= two (s one)))
+;; (check-type (eq-refl two) : (= (s (s z)) (s one)))
+;; ;; the following example requires recursive expansion after eval/app
+;; (check-type (eq-refl two) : (= (plus one one) two))
+;; (check-not-type (eq-refl two) : (= (plus one one) one))
+
+;; ;; symmetry of =
+;; (check-type (∀ (A B) (→ (= A B) (= B A))) : *)
+;; (check-type
+;;  (λ ([A : *][B : *])
+;;    (λ ([e : (= A B)])
+;;      (eq-elim A (λ ([W : *]) (= W A)) (eq-refl A) B e)))
+;;  : (∀ (A B) (→ (= A B) (= B A))))
+
+;; (check-type
+;;   (λ (A B)
+;;     (λ (e)
+;;       (eq-elim A (λ (W) (= W A)) (eq-refl A) B e)))
+;;  : (∀ (A B) (→ (= A B) (= B A))))
+
+;; (check-not-type
+;;  (λ ([A : *][B : *])
+;;    (λ ([e : (= A B)])
+;;      (eq-elim A (λ ([W : *]) (= W A)) (eq-refl A) B e)))
+;;  : (∀ (A B) (→ (= A B) (= A B))))
+
+;; ;; transitivity of =
+;; (check-type
+;;  (λ ([X : *][Y : *][Z : *])
+;;    (λ ([e1 : (= X Y)][e2 : (= Y Z)])
+;;      (eq-elim Y (λ ([W : *]) (= X W)) e1 Z e2)))
+;;  : (∀ (A B C) (→ (= A B) (= B C) (= A C))))
+;; (check-type
+;;  (λ (X Y Z)
+;;    (λ (e1 e2)
+;;      (eq-elim Y (λ (W) (= X W)) e1 Z e2)))
+;;  : (∀ (A B C) (→ (= A B) (= B C) (= A C))))
+
+;; ;; general tests that app/eval is properly applied recursively
+;; (check-type ((λ ([f : (→ * *)][x : *]) (f x))
+;;              (λ ([x : *]) x)
+;;              *)
+;;             : *)
+
+;; (check-type (((λ ([f : (→ (→ * *) * *)]) f) (λ ([g : (→ * *)][x : *]) (g x)))
+;;              (λ ([y : *]) *)
+;;              *)
+;;             : *)