*)
Section HaskFlattener.
-
Ltac eqd_dec_refl' :=
match goal with
| [ |- context[@eqd_dec ?T ?V ?X ?X] ] =>
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.
; 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).
apply precompose.
Defined.
+
+
+
(* useful for cutting down on the pretty-printed noise
Notation "` x" := (take_lev _ x) (at level 20).
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 | 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.
| 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 _
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'.
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").
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