X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FHaskFlattener.v;h=c7625b8874b57ac96cde6ae035274f2ae249f2fa;hp=1bb35c6579faec1e2020809f4547df7ae2340dd5;hb=489b12c6c491b96c37839610d33fbdf666ee527f;hpb=1a2754d2e135ef3c5fd7ef817e1129af93b533a5

diff --git a/src/HaskFlattener.v b/src/HaskFlattener.v
index 1bb35c6..c7625b8 100644
--- a/src/HaskFlattener.v
+++ b/src/HaskFlattener.v
@@ -46,7 +46,6 @@ Set Printing Width 130.
  *)
 Section HaskFlattener.
 
-
   Ltac eqd_dec_refl' :=
     match goal with
       | [ |- context[@eqd_dec ?T ?V ?X ?X] ] =>
@@ -161,9 +160,6 @@ Section HaskFlattener.
   (*******************************************************************************)
 
 
-  Context (hetmet_flatten : WeakExprVar).
-  Context (hetmet_unflatten : WeakExprVar).
-  Context (hetmet_id      : WeakExprVar).
   Context {unitTy : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★                                          }.
   Context {prodTy : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★  -> RawHaskType TV ★ -> RawHaskType TV ★ }.
   Context {gaTy   : forall TV, RawHaskType TV ECKind  -> RawHaskType TV ★ -> RawHaskType TV ★  -> RawHaskType TV ★ }.
@@ -235,12 +231,12 @@ Section HaskFlattener.
     flatten_type  (HaskTAll κ σ) = HaskTAll κ (fun TV ite v => flatten_rawtype (σ TV ite v)).
 
   Axiom flatten_commutes_with_HaskTApp :
-    forall  κ Γ (Δ:CoercionEnv Γ) (σ:∀ TV, InstantiatedTypeEnv TV Γ → TV κ → RawHaskType TV ★),
-    flatten_type  (HaskTApp (weakF σ) (FreshHaskTyVar κ)) =
-    HaskTApp (weakF (fun TV ite v => flatten_rawtype  (σ TV ite v))) (FreshHaskTyVar κ).
+    forall n κ Γ (Δ:CoercionEnv Γ) (σ:∀ TV, InstantiatedTypeEnv TV Γ → TV κ → RawHaskType TV ★),
+    flatten_type  (HaskTApp (weakF_ σ) (FreshHaskTyVar_ κ)) =
+    HaskTApp (weakF_ (fun TV ite v => flatten_rawtype  (σ TV ite v))) (FreshHaskTyVar_(n:=n) κ).
 
-  Axiom flatten_commutes_with_weakLT : forall (Γ:TypeEnv) κ  t,
-    flatten_leveled_type  (weakLT(Γ:=Γ)(κ:=κ) t) = weakLT(Γ:=Γ)(κ:=κ) (flatten_leveled_type  t).
+  Axiom flatten_commutes_with_weakLT : forall n (Γ:TypeEnv) κ t,
+    flatten_leveled_type  (weakLT_(n:=n)(Γ:=Γ)(κ:=κ) t) = weakLT_(n:=n)(Γ:=Γ)(κ:=κ) (flatten_leveled_type  t).
 
   Axiom globals_do_not_have_code_types : forall (Γ:TypeEnv) (g:Global Γ) v,
     flatten_type (g v) = g v.
@@ -272,12 +268,14 @@ Section HaskFlattener.
   ; ga_second    : ∀ Γ Δ ec l a b x, ND Rule [] [Γ > Δ >      [@ga_mk Γ ec a b @@l] |- [@ga_mk Γ ec (x,,a) (x,,b) ]@l ]
   ; ga_lit       : ∀ Γ Δ ec l lit  , ND Rule [] [Γ > Δ >                          [] |- [@ga_mk Γ ec [] [literalType lit] ]@l ]
   ; ga_curry     : ∀ Γ Δ ec l a b c, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (a,,[b]) [c] @@ l] |- [@ga_mk Γ ec a [b ---> c] ]@ l ]
+  ; ga_loopl     : ∀ Γ Δ ec l x y z, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (z,,x) (z,,y) @@ l] |- [@ga_mk Γ ec x y ]@ l ]
+  ; ga_loopr     : ∀ Γ Δ ec l x y z, ND Rule [] [Γ > Δ > [@ga_mk Γ ec (x,,z) (y,,z) @@ l] |- [@ga_mk Γ ec x y ]@ l ]
   ; ga_comp      : ∀ Γ Δ ec l a b c, ND Rule [] [Γ > Δ > [@ga_mk Γ ec a b @@ l],,[@ga_mk Γ ec b c @@ l] |- [@ga_mk Γ ec a c ]@l ] 
   ; ga_apply     : ∀ Γ Δ ec l a a' b c,
                  ND Rule [] [Γ > Δ > [@ga_mk Γ ec a [b ---> c] @@ l],,[@ga_mk Γ ec a' [b] @@ l] |- [@ga_mk Γ ec (a,,a') [c] ]@l ]
-  ; ga_kappa     : ∀ Γ Δ ec l a b Σ, ND Rule
-  [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec [] b ]@l ]
-  [Γ > Δ > Σ          |- [@ga_mk Γ ec a  b ]@l ]
+  ; ga_kappa     : ∀ Γ Δ ec l a b c Σ, ND Rule
+  [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec b c      ]@l ]
+  [Γ > Δ > Σ                          |- [@ga_mk Γ ec (a,,b) c ]@l ]
   }.
   Context `(gar:garrow).
 
@@ -288,7 +286,7 @@ Section HaskFlattener.
     ND Rule [ Γ > Δ > ant |- [x]@lev ] [ Γ > Δ > ant      |- [y]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -304,7 +302,7 @@ Section HaskFlattener.
       [ Γ > Δ > a                           |- [@ga_mk _ ec y z ]@lev ]
       [ Γ > Δ > a,,[@ga_mk _ ec x y @@ lev] |- [@ga_mk _ ec x z ]@lev ].
     intros.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -327,7 +325,7 @@ Section HaskFlattener.
       [ Γ > Δ > a                           |- [@ga_mk _ ec x y ]@lev ]
       [ Γ > Δ > a,,[@ga_mk _ ec y z @@ lev] |- [@ga_mk _ ec x z ]@lev ].
     intros.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -348,7 +346,7 @@ Section HaskFlattener.
             [ Γ > Δ > Σ                    |- [@ga_mk Γ ec (a,,c) (b,,c) ]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -371,7 +369,7 @@ Section HaskFlattener.
      [ Γ > Δ > Σ                    |- [@ga_mk Γ ec (c,,a) (c,,b) ]@lev ].
     intros.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanR ].
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+    eapply nd_comp; [ idtac | apply RLet ].
     eapply nd_comp; [ apply nd_rlecnac | idtac ].
     apply nd_prod.
     apply nd_id.
@@ -394,12 +392,12 @@ Section HaskFlattener.
      [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec x       b ]@l ].
      intros.
      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
-     eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+     eapply nd_comp; [ idtac | eapply RLet ].
      eapply nd_comp; [ apply nd_llecnac | idtac ].
      apply nd_prod.
      apply ga_first.
 
-     eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+     eapply nd_comp; [ idtac | eapply RLet ].
      eapply nd_comp; [ apply nd_llecnac | idtac ].
      apply nd_prod.
      apply postcompose.
@@ -408,6 +406,9 @@ Section HaskFlattener.
      apply precompose.
      Defined.
 
+
+
+
   (* useful for cutting down on the pretty-printed noise
   
   Notation "`  x" := (take_lev _ x) (at level 20).
@@ -450,14 +451,14 @@ Section HaskFlattener.
           set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) b)) as b' in *.
           set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) c)) as c' in *.
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-          eapply nd_comp; [ idtac | eapply nd_rule; apply
+          eapply nd_comp; [ idtac | apply
              (@RLet Γ Δ [] [] (@ga_mk _ (v2t ec) a' b') (@ga_mk _ (v2t ec) a' c')) ].
           eapply nd_comp; [ apply nd_llecnac | idtac ].
           apply nd_prod.
           apply r2'.
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
           eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-          eapply nd_comp; [ idtac | eapply nd_rule;  apply RLet ].
+          eapply nd_comp; [ idtac | apply RLet ].
           eapply nd_comp; [ apply nd_llecnac | idtac ].
           eapply nd_prod.
           apply r1'.
@@ -537,13 +538,13 @@ Section HaskFlattener.
     intro pfb.
     apply secondify with (c:=a)  in pfb.
     apply firstify  with (c:=[])  in pfa.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ eapply nd_llecnac | idtac ].
     apply nd_prod.
     apply pfa.
     clear pfa.
 
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     eapply nd_comp; [ apply nd_llecnac | idtac ].
     apply nd_prod.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
@@ -576,7 +577,7 @@ Section HaskFlattener.
     eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch ].
     simpl.
     eapply nd_comp; [ apply nd_llecnac | idtac ].
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+    eapply nd_comp; [ idtac | eapply RLet ].
     apply nd_prod.
     Focus 2.
     apply nd_id.
@@ -637,66 +638,109 @@ Section HaskFlattener.
     clear y q.
 
     set (mapOptionTree flatten_leveled_type (dropT (mkFlags (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ))) as q.
-    destruct (decide_tree_empty q); [ idtac | apply (Prelude_error "escapifying open code not yet supported") ].
-    destruct s.
+    destruct (decide_tree_empty q).
 
-    simpl.
-    eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AExch ].
-    set (fun z z' => @RLet Γ Δ z (mapOptionTree flatten_leveled_type q') t z' nil) as q''.
-    eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
-    clear q''.
-    eapply nd_comp; [ apply nd_rlecnac | idtac ].
-    apply nd_prod.
-    apply nd_rule.
-    apply RArrange.
-    eapply AComp; [ idtac | apply ACanR ].
-    apply ALeft.
-    apply (@arrangeCancelEmptyTree _ _ _ _ e).
-   
-    eapply nd_comp.
-      eapply nd_rule.
-      eapply (@RVar Γ Δ t nil).
-    apply nd_rule.
+      destruct s.
+      simpl.
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AExch ].
+      set (fun z z' => @RLet Γ Δ z (mapOptionTree flatten_leveled_type q') t z' nil) as q''.
+      eapply nd_comp; [ idtac | apply RLet ].
+      clear q''.
+      eapply nd_comp; [ apply nd_rlecnac | idtac ].
+      apply nd_prod.
+      apply nd_rule.
       apply RArrange.
-      eapply AComp.
-      apply AuCanR.
+      eapply AComp; [ idtac | apply ACanR ].
       apply ALeft.
-      apply AWeak.
-(*
-    eapply decide_tree_empty.
-
-    simpl.
-    set (dropT (mkFlags (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ)) as escapified.
-    destruct (decide_tree_empty escapified).
+      apply (@arrangeCancelEmptyTree _ _ _ _ e).
+   
+      eapply nd_comp.
+        eapply nd_rule.
+        eapply (@RVar Γ Δ t nil).
+      apply nd_rule.
+        apply RArrange.
+        eapply AComp.
+        apply AuCanR.
+        apply ALeft.
+        apply AWeak.
 
-    induction succ.
-    destruct a.
-      unfold drop_lev.
-      destruct l.
       simpl.
-      unfold mkDropFlags; simpl.
+      clear q.
+      unfold q'.
+      clear q'.
+      apply nd_rule.
+      apply RArrange.
+      induction succ.
+      destruct a.
+      destruct l as [t' l']. 
+      simpl.
+      Transparent drop_lev.
+      simpl.
       unfold take_lev.
       unfold mkTakeFlags.
       simpl.
-      destruct (General.list_eq_dec h0 (ec :: nil)).
-        simpl.
-        rewrite e.
-        apply nd_id.
-        simpl.
-        apply nd_rule.
-        apply RArrange.
-        apply ALeft.
-        apply AWeak.
+      unfold drop_lev.
       simpl.
-        apply nd_rule.
-        unfold take_lev.
-        simpl.
-        apply RArrange.
-        apply ALeft.
-        apply AWeak.
-      apply (Prelude_error "escapifying code with multi-leaf antecedents is not supported").
-*)
-      Defined.
+      unfold mkDropFlags.
+      simpl.
+      unfold flatten_leveled_type.
+      destruct (General.list_eq_dec l' (ec :: nil)); simpl.
+      rewrite e.
+      unfold levels_to_tcode.
+      eapply AComp.
+      apply ACanL.
+      apply AuCanR.
+      eapply AComp.
+      apply ACanR.
+      eapply AComp.
+      apply AuCanL.
+      apply ARight.
+      apply AWeak.
+      
+      simpl.
+      apply ARight.
+      apply AWeak.
+      
+      drop_simplify.
+      simpl.
+      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ2)) as d2 in *.
+      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ1)) as d1 in *.
+      set (mapOptionTree flatten_leveled_type (dropT (mkFlags
+        (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ1))) as s1 in *.
+      set (mapOptionTree flatten_leveled_type (dropT (mkFlags
+        (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ2))) as s2 in *.
+      set (mapOptionTree (flatten_type ○ unlev) (dropT (mkFlags
+        (liftBoolFunc true (bnot ○ levelMatch (ec :: nil))) succ1))) as s1' in *.
+      set (mapOptionTree (flatten_type ○ unlev) (dropT (mkFlags
+        (liftBoolFunc true (bnot ○ levelMatch (ec :: nil))) succ2))) as s2' in *.
+
+      eapply AComp.
+      apply arrangeSwapMiddle.
+      
+      eapply AComp.
+      eapply ALeft.
+      apply IHsucc2.
+      
+      eapply AComp.
+      eapply ARight.
+      apply IHsucc1.
+      
+      eapply AComp.
+      apply arrangeSwapMiddle.
+      apply ARight.
+      unfold take_lev.
+      unfold mkTakeFlags.
+      
+      unfold s1'.
+      unfold s2'.
+      clear s1' s2'.
+      set (mapOptionTree (flatten_type ○ unlev) (dropT (mkFlags
+        (liftBoolFunc true (bnot ○ levelMatch (ec :: nil))) succ1))) as s1' in *.
+      set (mapOptionTree (flatten_type ○ unlev) (dropT (mkFlags
+        (liftBoolFunc true (bnot ○ levelMatch (ec :: nil))) succ2))) as s2' in *.
+      
+      apply (Prelude_error "almost there!").
+    Defined.
 
   Lemma unlev_relev : forall {Γ}(t:Tree ??(HaskType Γ ★)) lev, mapOptionTree unlev (t @@@ lev) = t.
     intros.
@@ -775,16 +819,28 @@ Section HaskFlattener.
                  (fun TV : Kind → Type => take_arg_types ○ t TV))))).
     reflexivity.
     unfold flatten_type.
-    clear hetmet_flatten.
-    clear hetmet_unflatten.
-    clear hetmet_id.
     clear gar.
     set (t tv ite) as x.
     admit.
     admit.
     Qed.
 
-  Definition flatten_proof :
+  Lemma drop_to_nothing : forall (Γ:TypeEnv) Σ (lev:HaskLevel Γ),
+    drop_lev lev (Σ @@@ lev) = mapTree (fun _ => None) (mapTree (fun _ => tt) Σ).
+    intros.
+    induction Σ.
+    destruct a; simpl.
+    drop_simplify.
+    auto.
+    drop_simplify.
+    auto.
+    simpl.
+    rewrite <- IHΣ1.
+    rewrite <- IHΣ2.
+    reflexivity.
+    Qed.
+
+  Definition flatten_skolemized_proof :
     forall  {h}{c},
       ND SRule h c ->
       ND  Rule (mapOptionTree (flatten_judgment ) h) (mapOptionTree (flatten_judgment ) c).
@@ -810,14 +866,14 @@ Section HaskFlattener.
       | RGlobal  Γ Δ σ l wev           => let case_RGlobal := tt       in _
       | RLam     Γ Δ Σ tx te     lev   => let case_RLam := tt          in _
       | RCast    Γ Δ Σ σ τ lev γ       => let case_RCast := tt         in _
-      | RAbsT    Γ Δ Σ κ σ lev         => let case_RAbsT := tt         in _
+      | RAbsT    Γ Δ Σ κ σ lev n       => let case_RAbsT := tt         in _
       | RAppT    Γ Δ Σ κ σ τ     lev   => let case_RAppT := tt         in _
       | RAppCo   Γ Δ Σ κ σ₁ σ₂ γ σ lev => let case_RAppCo := tt        in _
       | RAbsCo   Γ Δ Σ κ σ  σ₁ σ₂  lev => let case_RAbsCo := tt        in _
       | RApp     Γ Δ Σ₁ Σ₂ tx te lev   => let case_RApp := tt          in _
-      | RLet     Γ Δ Σ₁ Σ₂ σ₁ σ₂ lev   => let case_RLet := tt          in _
-      | RWhere   Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ lev   => let case_RWhere := tt          in _
-      | RJoin    Γ p lri m x q l       => let case_RJoin := tt in _
+      | RCut     Γ Δ Σ Σ₁ Σ₁₂ Σ₂ Σ₃ l  => let case_RCut := tt          in _
+      | RLeft    Γ Δ Σ₁ Σ₂  Σ     l    => let case_RLeft := tt in _
+      | RRight   Γ Δ Σ₁ Σ₂  Σ     l    => let case_RRight := tt in _
       | RVoid    _ _       l           => let case_RVoid := tt   in _
       | RBrak    Γ Δ t ec succ lev           => let case_RBrak := tt         in _
       | REsc     Γ Δ t ec succ lev           => let case_REsc := tt          in _
@@ -871,6 +927,7 @@ Section HaskFlattener.
       rename l into g.
       rename σ into l.
       destruct l as [|ec lev]; simpl. 
+        (*
         destruct (eqd_dec (g:CoreVar) (hetmet_flatten:CoreVar)).
           set (flatten_type (g wev)) as t.
           set (RGlobal _ Δ nil (mkGlobal Γ t hetmet_id)) as q.
@@ -885,6 +942,7 @@ Section HaskFlattener.
           apply nd_rule.
           apply q.
           apply INil.
+          *)
         unfold flatten_leveled_type. simpl.
           apply nd_rule; rewrite globals_do_not_have_code_types.
           apply RGlobal.
@@ -913,12 +971,6 @@ Section HaskFlattener.
       apply flatten_coercion; auto.
       apply (Prelude_error "RCast at level >0; casting inside of code brackets is currently not supported").
 
-    destruct case_RJoin.
-      simpl.
-      destruct l;
-        [ apply nd_rule; apply RJoin | idtac ];
-        apply (Prelude_error "RJoin at depth >0").
-
     destruct case_RApp.
       simpl.
 
@@ -947,65 +999,151 @@ Section HaskFlattener.
   Notation "!<[@]> x" := (mapOptionTree flatten_leveled_type x) (at level 1).
 *)
 
-    destruct case_RLet.
+    destruct case_RCut.
       simpl.
-      destruct lev as [|ec lev]; simpl; [ apply nd_rule; apply RLet; auto | idtac ].
-      repeat drop_simplify.
-      repeat take_simplify.
+      destruct l as [|ec lev]; simpl.
+        apply nd_rule.
+        replace (mapOptionTree flatten_leveled_type (Σ₁₂ @@@ nil)) with (mapOptionTree flatten_type Σ₁₂ @@@ nil).
+        apply RCut.
+        induction Σ₁₂; try destruct a; auto.
+        simpl.
+        rewrite <- IHΣ₁₂1.
+        rewrite <- IHΣ₁₂2.
+        reflexivity.
+      simpl; repeat drop_simplify.
+      simpl; repeat take_simplify.
       simpl.
-
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as Σ₁'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as Σ₂'.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₁)) as Σ₁''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as Σ₂''.
-
-      eapply nd_comp.
-      eapply nd_prod; [ idtac | apply nd_id ].
-      eapply boost.
-      apply (ga_first _ _ _ _ _ _ Σ₂').
-
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+      set (drop_lev (ec :: lev) (Σ₁₂ @@@ (ec :: lev))) as x1.
+      rewrite take_lemma'.
+      rewrite mapOptionTree_compose.
+      rewrite mapOptionTree_compose.
+      rewrite mapOptionTree_compose.
+      rewrite mapOptionTree_compose.
+      rewrite unlev_relev.
+      rewrite <- mapOptionTree_compose.
+      rewrite <- mapOptionTree_compose.
+      rewrite <- mapOptionTree_compose.
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ]. 
       apply nd_prod.
       apply nd_id.
-      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ACanL | idtac ].
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AExch (* okay *)].
+      eapply nd_comp.
+      eapply nd_rule.
+      eapply RArrange.
+      eapply ALeft.
+      eapply ARight.
+      unfold x1.
+      rewrite drop_to_nothing.
+      apply arrangeCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ₁₂)).
+        induction Σ₁₂; try destruct a; auto.
+        simpl.
+        rewrite <- IHΣ₁₂1 at 2.
+        rewrite <- IHΣ₁₂2 at 2.
+        reflexivity.
+      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply ALeft; eapply ACanL | idtac ].
+      set (mapOptionTree flatten_type Σ₁₂) as a.
+      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as b.
+      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as c.
+      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as d.
+      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ)) as e.
+      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ)) as f.
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+      eapply nd_comp; [ apply nd_llecnac | idtac ].
+      apply nd_prod.
+      simpl.
+      eapply secondify.
+      apply ga_first.
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ALeft; eapply AExch ].
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuAssoc ].
+      simpl.
       apply precompose.
 
-    destruct case_RWhere.
+    destruct case_RLeft.
       simpl.
-      destruct lev as [|ec lev]; simpl; [ apply nd_rule; apply RWhere; auto | idtac ].
-      repeat take_simplify.
+      destruct l as [|ec lev].
+      simpl.
+        replace (mapOptionTree flatten_leveled_type (Σ @@@ nil)) with (mapOptionTree flatten_type Σ @@@ nil).
+        apply nd_rule.
+        apply RLeft.
+        induction Σ; try destruct a; auto.
+        simpl.
+        rewrite <- IHΣ1.
+        rewrite <- IHΣ2.
+        reflexivity.
       repeat drop_simplify.
+        rewrite drop_to_nothing.
+        simpl.
+        eapply nd_comp.
+        Focus 2.
+        eapply nd_rule.
+        eapply RArrange.
+        eapply ARight.
+        apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
+          induction Σ; try destruct a; auto.
+          simpl.
+          rewrite <- IHΣ1 at 2.
+          rewrite <- IHΣ2 at 2.
+          reflexivity.
+        idtac.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanL ].
+        apply boost.
+        take_simplify.
+        simpl.
+        replace (take_lev (ec :: lev) (Σ @@@ (ec :: lev))) with (Σ @@@ (ec::lev)).
+        rewrite mapOptionTree_compose.
+        rewrite mapOptionTree_compose.
+        rewrite unlev_relev.
+        apply ga_second.
+      rewrite take_lemma'.
+      reflexivity.
+        
+    destruct case_RRight.
       simpl.
-
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as Σ₁'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as Σ₂'.
-      set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₃)) as Σ₃'.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₁)) as Σ₁''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as Σ₂''.
-      set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₃)) as Σ₃''.
-
-      eapply nd_comp.
-      eapply nd_prod; [ eapply nd_id | idtac ].
-      eapply (first_nd _ _ _ _ _ _ Σ₃').
-      eapply nd_comp.
-      eapply nd_prod; [ eapply nd_id | idtac ].
-      eapply (second_nd _ _ _ _ _ _ Σ₁').
-
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RWhere ].
-      apply nd_prod; [ idtac | apply nd_id ].
-      eapply nd_comp; [ idtac | eapply precompose' ].
-      apply nd_rule.
-      apply RArrange.
-      apply ALeft.
-      apply ACanL.
+      destruct l as [|ec lev].
+      simpl.
+        replace (mapOptionTree flatten_leveled_type (Σ @@@ nil)) with (mapOptionTree flatten_type Σ @@@ nil).
+        apply nd_rule.
+        apply RRight.
+        induction Σ; try destruct a; auto.
+        simpl.
+        rewrite <- IHΣ1.
+        rewrite <- IHΣ2.
+        reflexivity.
+      repeat drop_simplify.
+        rewrite drop_to_nothing.
+        simpl.
+        eapply nd_comp.
+        Focus 2.
+        eapply nd_rule.
+        eapply RArrange.
+        eapply ALeft.
+        apply arrangeUnCancelEmptyTree with (q:=(mapTree (fun _ : ??(HaskType Γ ★) => tt) Σ)).
+          induction Σ; try destruct a; auto.
+          simpl.
+          rewrite <- IHΣ1 at 2.
+          rewrite <- IHΣ2 at 2.
+          reflexivity.
+        idtac.
+        eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
+        apply boost.
+        take_simplify.
+        simpl.
+        replace (take_lev (ec :: lev) (Σ @@@ (ec :: lev))) with (Σ @@@ (ec::lev)).
+        rewrite mapOptionTree_compose.
+        rewrite mapOptionTree_compose.
+        rewrite unlev_relev.
+        apply ga_first.
+      rewrite take_lemma'.
+      reflexivity.
 
     destruct case_RVoid.
       simpl.
-      apply nd_rule.
       destruct l.
+      apply nd_rule.
       apply RVoid.
-      apply (Prelude_error "RVoid at level >0").
+      drop_simplify.
+      take_simplify.
+      simpl.
+      apply ga_id.
         
     destruct case_RAppT.
       simpl. destruct lev; simpl.
@@ -1025,8 +1163,8 @@ Section HaskFlattener.
       rewrite flatten_commutes_with_HaskTApp.
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RAbsT ].
       simpl.
-      set (mapOptionTree (flatten_leveled_type ) (mapOptionTree (weakLT(κ:=κ)) Σ)) as a.
-      set (mapOptionTree (weakLT(κ:=κ)) (mapOptionTree (flatten_leveled_type ) Σ)) as q'.
+      set (mapOptionTree (flatten_leveled_type ) (mapOptionTree (weakLT_(n:=n)(κ:=κ)) Σ)) as a.
+      set (mapOptionTree (weakLT_(n:=n)(κ:=κ)) (mapOptionTree (flatten_leveled_type ) Σ)) as q'.
       assert (a=q').
         unfold a.
         unfold q'.
@@ -1076,11 +1214,53 @@ Section HaskFlattener.
         rewrite IHy1.
         rewrite IHy2.
         reflexivity.
-      apply (Prelude_error "LetRec not supported inside brackets yet (FIXME)").
+      repeat drop_simplify.
+      repeat take_simplify.
+      simpl.
+      rewrite drop_to_nothing.
+      eapply nd_comp.
+        eapply nd_rule.
+        eapply RArrange.
+        eapply AComp.
+        eapply ARight.
+        apply arrangeCancelEmptyTree with (q:=y).
+          induction y; try destruct a; auto.
+          simpl.
+          rewrite <- IHy1.
+          rewrite <- IHy2.
+          reflexivity.
+        apply ACanL.
+        rewrite take_lemma'.
+        set (mapOptionTree (flatten_type ○ unlev) (take_lev (h :: lev) lri)) as lri'.
+        set (mapOptionTree flatten_leveled_type (drop_lev (h :: lev) lri)) as lri''.
+        replace (mapOptionTree (flatten_type ○ unlev) (y @@@ (h :: lev))) with (mapOptionTree flatten_type y).
+        apply boost.
+        apply ga_loopl.
+        rewrite <- mapOptionTree_compose.
+        simpl.
+        reflexivity.
 
     destruct case_RCase.
-      simpl.
-      apply (Prelude_error "Case not supported (BIG FIXME)").
+      destruct lev; [ idtac | apply (Prelude_error "case at depth >0") ]; simpl.
+      apply nd_rule.
+      rewrite <- mapOptionTree_compose.
+      replace (mapOptionTree
+        (fun x  => flatten_judgment (pcb_judg (snd x)))
+        alts,, [Γ > Δ > mapOptionTree flatten_leveled_type Σ |- [flatten_type (caseType tc avars)] @ nil])
+      with
+        (mapOptionTree
+           (fun x  => @pcb_judg tc Γ Δ nil (flatten_type tbranches) avars (fst x) (snd x))
+           alts,,
+           [Γ > Δ > mapOptionTree flatten_leveled_type Σ |- [caseType tc avars] @ nil]).
+      replace (mapOptionTree flatten_leveled_type
+        (mapOptionTreeAndFlatten
+           (fun x  => (snd x)) alts))
+      with (mapOptionTreeAndFlatten
+           (fun x =>
+            (snd x)) alts).
+      apply RCase.
+      admit.
+      admit.
 
     destruct case_SBrak.
       simpl.
@@ -1142,7 +1322,7 @@ Section HaskFlattener.
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply AuCanR ].
       eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply ACanL ].
-      eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+      eapply nd_comp; [ idtac | eapply RLet ].
       eapply nd_comp; [ apply nd_llecnac | idtac ].
       apply nd_prod; [ idtac | eapply boost ].
       induction x.
@@ -1171,13 +1351,49 @@ Section HaskFlattener.
         apply secondify.
         apply IHx2.
 
-      (* environment has non-empty leaves *)
-      apply (Prelude_error "ga_kappa not supported yet (BIG FIXME)").
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
+      eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply AuCanR ].
+
+      replace (mapOptionTree (fun ht => levels_to_tcode (unlev ht) (getlev ht) @@  nil) (drop_lev (ec :: nil) succ))
+        with (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ)).
+      eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply AExch | idtac ].
+      apply ga_kappa.
+      induction succ.
+        destruct a.
+        destruct l.
+        Transparent drop_lev.
+        simpl.
+        unfold drop_lev.
+        Opaque drop_lev.
+        unfold mkDropFlags.
+        simpl.
+        destruct (General.list_eq_dec h1 (ec :: nil)).
+        simpl.
+        auto.
+        simpl.
+        unfold flatten_leveled_type.
+        simpl.
+        auto.
+        simpl.
+        auto.
+        simpl.
+        drop_simplify.
+        simpl.
+        rewrite IHsucc1.
+        rewrite IHsucc2.
+        reflexivity.
 
       (* nesting too deep *)
       apply (Prelude_error "found Esc at depth >0 indicating 3-level code; only two-level code is currently supported").
       Defined.
 
+  Definition flatten_proof :
+    forall  {h}{c},
+      ND  Rule h c ->
+      ND  Rule h c.
+    apply (Prelude_error "sorry, non-skolemized flattening isn't implemented").
+    Defined.
+
   Definition skolemize_and_flatten_proof :
     forall  {h}{c},
       ND  Rule h c ->
@@ -1187,7 +1403,7 @@ Section HaskFlattener.
     intros.
     rewrite mapOptionTree_compose.
     rewrite mapOptionTree_compose.
-    apply flatten_proof.
+    apply flatten_skolemized_proof.
     apply skolemize_proof.
     apply X.
     Defined.