| TCoerc _ t1 t2 t => TCoerc (flatten_rawtype t1) (flatten_rawtype t2) (flatten_rawtype t)
| TArrow => TArrow
| TCode ec e => let e' := flatten_rawtype e
- in ga_mk_raw ec (unleaves (take_arg_types e')) [drop_arg_types e']
+ in ga_mk_raw ec (unleaves_ (take_arg_types e')) [drop_arg_types e']
| TyFunApp tfc kl k lt => TyFunApp tfc kl k (flatten_rawtype_list _ lt)
end
with flatten_rawtype_list {TV}(lk:list Kind)(exp:@RawHaskTypeList TV lk) : @RawHaskTypeList TV lk :=
ND Rule [] [ Γ > Δ > [x@@lev] |- [y@@lev] ] ->
ND Rule [ Γ > Δ > ant |- [x@@lev] ] [ Γ > Δ > ant |- [y@@lev] ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
- eapply nd_comp; [ idtac | eapply nd_rule; apply (@RLet Γ Δ [] ant y x lev) ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply nd_id.
apply X.
eapply nd_rule.
eapply RArrange.
- apply RuCanL.
- Defined.
-
- Definition postcompose' : ∀ Γ Δ ec lev a b c Σ,
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ] ->
- ND Rule [] [ Γ > Δ > Σ,,[@ga_mk Γ ec b c @@ lev] |- [@ga_mk Γ ec a c @@ lev] ].
- intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
- eapply nd_comp; [ idtac
- | eapply nd_rule; apply (@RLet Γ Δ [@ga_mk _ ec b c @@lev] Σ (@ga_mk _ ec a c) (@ga_mk _ ec a b) lev) ].
- eapply nd_comp; [ apply nd_llecnac | idtac ].
- apply nd_prod.
- apply X.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RExch ].
- apply ga_comp.
- Defined.
+ apply RuCanR.
+ Defined.
Definition precompose Γ Δ ec : forall a x y z lev,
ND Rule
[ 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.
- apply nd_rlecnac.
- eapply nd_comp.
- eapply nd_prod.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+ eapply nd_comp; [ apply nd_rlecnac | idtac ].
+ apply nd_prod.
apply nd_id.
- eapply ga_comp.
-
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RExch ].
-
- apply nd_rule.
- apply RLet.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ apply ga_comp.
Defined.
- Definition precompose' : ∀ Γ Δ ec lev a b c Σ,
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec b c @@ lev] ] ->
- ND Rule [] [ Γ > Δ > Σ,,[@ga_mk Γ ec a b @@ lev] |- [@ga_mk Γ ec a c @@ lev] ].
- intros.
- eapply nd_comp.
- apply X.
- apply precompose.
- Defined.
+ Definition precompose' Γ Δ ec : forall a b x y z lev,
+ ND Rule
+ [ Γ > Δ > a,,b |- [@ga_mk _ ec y z @@ lev] ]
+ [ Γ > Δ > a,,([@ga_mk _ ec x y @@ lev],,b) |- [@ga_mk _ ec x z @@ lev] ].
+ intros.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RLeft; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCossa ].
+ apply precompose.
+ Defined.
- Definition postcompose : ∀ Γ Δ ec lev a b c,
- ND Rule [] [ Γ > Δ > [] |- [@ga_mk Γ ec a b @@ lev] ] ->
- ND Rule [] [ Γ > Δ > [@ga_mk Γ ec b c @@ lev] |- [@ga_mk Γ ec a c @@ lev] ].
- intros.
- eapply nd_comp.
- apply postcompose'.
- apply X.
- apply nd_rule.
- apply RArrange.
- apply RCanL.
- Defined.
+ Definition postcompose_ Γ Δ ec : forall a x y z lev,
+ ND Rule
+ [ 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; [ apply nd_rlecnac | idtac ].
+ apply nd_prod.
+ apply nd_id.
+ apply ga_comp.
+ Defined.
- Definition firstify : ∀ Γ Δ ec lev a b c Σ,
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ] ->
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec (a,,c) (b,,c) @@ lev] ].
+ Definition postcompose Γ Δ ec : forall x y z lev,
+ ND Rule [] [ Γ > Δ > [] |- [@ga_mk _ ec x y @@ lev] ] ->
+ ND Rule [] [ Γ > Δ > [@ga_mk _ ec y z @@ lev] |- [@ga_mk _ ec x z @@ lev] ].
intros.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
- eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
- eapply nd_comp; [ apply nd_llecnac | idtac ].
- apply nd_prod.
+ eapply nd_comp; [ idtac | eapply postcompose_ ].
apply X.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanL ].
- apply ga_first.
Defined.
- Definition secondify : ∀ Γ Δ ec lev a b c Σ,
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ] ->
- ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec (c,,a) (c,,b) @@ lev] ].
+ Definition first_nd : ∀ Γ Δ ec lev a b c Σ,
+ ND Rule [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ]
+ [ Γ > Δ > Σ |- [@ga_mk Γ ec (a,,c) (b,,c) @@ lev] ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
- eapply nd_comp; [ apply nd_llecnac | idtac ].
+ eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
- apply X.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanL ].
- apply ga_second.
+ apply nd_id.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanR ].
+ apply ga_first.
Defined.
- Lemma ga_unkappa : ∀ Γ Δ ec l z a b Σ,
- ND Rule
- [Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ l] ]
- [Γ > Δ > Σ,,[@ga_mk Γ ec z a @@ l] |- [@ga_mk Γ ec z b @@ l] ].
+ Definition firstify : ∀ Γ Δ ec lev a b c Σ,
+ ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ] ->
+ ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec (a,,c) (b,,c) @@ lev] ].
intros.
- set (ga_comp Γ Δ ec l z a b) as q.
-
- set (@RLet Γ Δ) as q'.
- set (@RLet Γ Δ [@ga_mk _ ec z a @@ l] Σ (@ga_mk _ ec z b) (@ga_mk _ ec a b) l) as q''.
eapply nd_comp.
- Focus 2.
- eapply nd_rule.
- eapply RArrange.
- apply RExch.
-
- eapply nd_comp.
- Focus 2.
- eapply nd_rule.
- apply q''.
+ apply X.
+ apply first_nd.
+ Defined.
- idtac.
- clear q'' q'.
- eapply nd_comp.
- apply nd_rlecnac.
+ Definition second_nd : ∀ Γ Δ ec lev a b c Σ,
+ ND Rule
+ [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ]
+ [ Γ > Δ > Σ |- [@ga_mk Γ ec (c,,a) (c,,b) @@ lev] ].
+ intros.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
+ eapply nd_comp; [ apply nd_rlecnac | idtac ].
apply nd_prod.
apply nd_id.
- apply q.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RuCanR ].
+ apply ga_second.
Defined.
- Lemma ga_unkappa' : ∀ Γ Δ ec l a b Σ x,
- ND Rule
- [Γ > Δ > Σ |- [@ga_mk Γ ec (a,,x) b @@ l] ]
- [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec x b @@ l] ].
+ Definition secondify : ∀ Γ Δ ec lev a b c Σ,
+ ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec a b @@ lev] ] ->
+ ND Rule [] [ Γ > Δ > Σ |- [@ga_mk Γ ec (c,,a) (c,,b) @@ lev] ].
intros.
- eapply nd_comp; [ idtac | eapply nd_rule; 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; [ apply nd_llecnac | idtac ].
- apply nd_prod.
- apply postcompose.
- apply ga_uncancell.
- apply precompose.
+ eapply nd_comp.
+ apply X.
+ apply second_nd.
Defined.
- Lemma ga_kappa' : ∀ Γ Δ ec l a b Σ x,
- ND Rule
- [Γ > Δ > Σ,,[@ga_mk Γ ec [] a @@ l] |- [@ga_mk Γ ec x b @@ l] ]
- [Γ > Δ > Σ |- [@ga_mk Γ ec (a,,x) b @@ l] ].
- apply (Prelude_error "ga_kappa not supported yet (BIG FIXME)").
- Defined.
+ Lemma ga_unkappa : ∀ Γ Δ ec l a b Σ x,
+ ND Rule
+ [Γ > Δ > Σ |- [@ga_mk Γ ec (a,,x) b @@ l] ]
+ [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 RExch ].
+ eapply nd_comp; [ idtac | eapply nd_rule; 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; [ apply nd_llecnac | idtac ].
+ apply nd_prod.
+ apply postcompose.
+ apply ga_uncancell.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ apply precompose.
+ Defined.
(* useful for cutting down on the pretty-printed noise
(mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) B))
(mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) A)) @@ nil]]
with
+ | RId a => let case_RId := tt in ga_id _ _ _ _ _
| RCanL a => let case_RCanL := tt in ga_uncancell _ _ _ _ _
| RCanR a => let case_RCanR := tt in ga_uncancelr _ _ _ _ _
| RuCanL a => let case_RuCanL := tt in ga_cancell _ _ _ _ _
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) c)) as c' in *.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
eapply nd_comp; [ idtac | eapply nd_rule; apply
- (@RLet Γ Δ [] [] (@ga_mk _ (v2t ec) a' c') (@ga_mk _ (v2t ec) a' b')) ].
+ (@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 RuCanL ].
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanR ].
- eapply nd_comp; [ idtac | eapply nd_rule; apply
- (@RLet Γ Δ [@ga_mk _ (v2t ec) a' b' @@ _] [] (@ga_mk _ (v2t ec) a' c') (@ga_mk _ (v2t ec) b' c'))].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
+ eapply nd_comp; [ idtac | eapply nd_rule; apply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
eapply nd_prod.
apply r1'.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
apply ga_comp.
Defined.
match r as R in Arrange A B return
Arrange (mapOptionTree (flatten_leveled_type ) (drop_lev _ A))
(mapOptionTree (flatten_leveled_type ) (drop_lev _ B)) with
+ | RId a => let case_RId := tt in RId _
| RCanL a => let case_RCanL := tt in RCanL _
| RCanR a => let case_RCanR := tt in RCanR _
| RuCanL a => let case_RuCanL := tt in RuCanL _
apply nd_rule.
apply RArrange.
induction r; simpl.
+ apply RId.
apply RCanL.
apply RCanR.
apply RuCanL.
apply RuCanR.
apply RAssoc.
apply RCossa.
- apply RExch.
+ apply RExch. (* TO DO: check for all-leaf trees here *)
apply RWeak.
apply RCont.
apply RLeft; auto.
intro pfa.
intro pfb.
apply secondify with (c:=a) in pfb.
- eapply nd_comp.
- Focus 2.
+ apply firstify with (c:=[]) in pfa.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
eapply nd_comp; [ eapply nd_llecnac | idtac ].
- eapply nd_prod.
- apply pfb.
- clear pfb.
- apply postcompose'.
- eapply nd_comp.
+ apply nd_prod.
apply pfa.
clear pfa.
- apply boost.
+
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+ eapply nd_comp; [ apply nd_llecnac | idtac ].
+ apply nd_prod.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
- apply precompose'.
+ eapply nd_comp; [ idtac | eapply postcompose_ ].
apply ga_uncancelr.
- apply nd_id.
+
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
+ eapply nd_comp; [ idtac | eapply precompose ].
+ apply pfb.
Defined.
Definition arrange_brak : forall Γ Δ ec succ t,
ND Rule
- [Γ > Δ > mapOptionTree (flatten_leveled_type ) (drop_lev (ec :: nil) succ),,
- [(@ga_mk _ (v2t ec) [] (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: nil) succ))) @@ nil] |- [t @@ nil]]
+ [Γ > Δ >
+ [(@ga_mk _ (v2t ec) [] (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: nil) succ))) @@ nil],,
+ mapOptionTree (flatten_leveled_type ) (drop_lev (ec :: nil) succ) |- [t @@ nil]]
[Γ > Δ > mapOptionTree (flatten_leveled_type ) succ |- [t @@ nil]].
+
intros.
unfold drop_lev.
set (@arrange' _ succ (levelMatch (ec::nil))) as q.
apply y.
idtac.
clear y q.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch ].
simpl.
eapply nd_comp; [ apply nd_llecnac | idtac ].
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
apply IHsucc2.
Defined.
+ Definition arrange_empty_tree : forall {T}{A}(q:Tree A)(t:Tree ??T),
+ t = mapTree (fun _:A => None) q ->
+ Arrange t [].
+ intros T A q.
+ induction q; intros.
+ simpl in H.
+ rewrite H.
+ apply RId.
+ simpl in *.
+ destruct t; try destruct o; inversion H.
+ set (IHq1 _ H1) as x1.
+ set (IHq2 _ H2) as x2.
+ eapply RComp.
+ eapply RRight.
+ rewrite <- H1.
+ apply x1.
+ eapply RComp.
+ apply RCanL.
+ rewrite <- H2.
+ apply x2.
+ Defined.
+
+(* Definition unarrange_empty_tree : forall {T}{A}(t:Tree ??T)(q:Tree A),
+ t = mapTree (fun _:A => None) q ->
+ Arrange [] t.
+ Defined.*)
+
+ Definition decide_tree_empty : forall {T:Type}(t:Tree ??T),
+ sum { q:Tree unit & t = mapTree (fun _ => None) q } unit.
+ intro T.
+ refine (fix foo t :=
+ match t with
+ | T_Leaf x => _
+ | T_Branch b1 b2 => let b1' := foo b1 in let b2' := foo b2 in _
+ end).
+ intros.
+ destruct x.
+ right; apply tt.
+ left.
+ exists (T_Leaf tt).
+ auto.
+ destruct b1'.
+ destruct b2'.
+ destruct s.
+ destruct s0.
+ subst.
+ left.
+ exists (x,,x0).
+ reflexivity.
+ right; auto.
+ right; auto.
+ Defined.
+
Definition arrange_esc : forall Γ Δ ec succ t,
ND Rule
[Γ > Δ > mapOptionTree (flatten_leveled_type ) succ |- [t @@ nil]]
- [Γ > Δ > mapOptionTree (flatten_leveled_type ) (drop_lev (ec :: nil) succ),,
- [(@ga_mk _ (v2t ec) [] (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: nil) succ))) @@ nil] |- [t @@ nil]].
+ [Γ > Δ >
+ [(@ga_mk _ (v2t ec) [] (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: nil) succ))) @@ nil],,
+ mapOptionTree (flatten_leveled_type ) (drop_lev (ec :: nil) succ) |- [t @@ nil]].
intros.
- unfold drop_lev.
set (@arrange _ succ (levelMatch (ec::nil))) as q.
+ set (@drop_lev Γ (ec::nil) succ) as q'.
+ assert (@drop_lev Γ (ec::nil) succ=q') as H.
+ reflexivity.
+ unfold drop_lev in H.
+ unfold mkDropFlags in H.
+ rewrite H in q.
+ clear H.
set (arrangeMap _ _ flatten_leveled_type q) as y.
eapply nd_comp.
eapply nd_rule.
eapply RArrange.
apply y.
- idtac.
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.
+
+ simpl.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RExch ].
+ 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 RComp; [ idtac | apply RCanR ].
+ apply RLeft.
+ apply (@arrange_empty_tree _ _ _ _ e).
+
+ eapply nd_comp.
+ eapply nd_rule.
+ eapply (@RVar Γ Δ t nil).
+ apply nd_rule.
+ apply RArrange.
+ eapply RComp.
+ apply RuCanR.
+ apply RLeft.
+ apply RWeak.
+(*
+ eapply decide_tree_empty.
+
+ simpl.
+ set (dropT (mkFlags (liftBoolFunc false (bnot ○ levelMatch (ec :: nil))) succ)) as escapified.
+ destruct (decide_tree_empty escapified).
+
induction succ.
destruct a.
+ unfold drop_lev.
destruct l.
simpl.
unfold mkDropFlags; simpl.
apply RLeft.
apply RWeak.
apply (Prelude_error "escapifying code with multi-leaf antecedents is not supported").
+*)
Defined.
Lemma mapOptionTree_distributes
reflexivity.
Qed.
- Definition decide_tree_empty : forall {T:Type}(t:Tree ??T),
- sum { q:Tree unit & t = mapTree (fun _ => None) q } unit.
- intro T.
- refine (fix foo t :=
- match t with
- | T_Leaf x => _
- | T_Branch b1 b2 => let b1' := foo b1 in let b2' := foo b2 in _
- end).
- intros.
- destruct x.
- right; apply tt.
- left.
- exists (T_Leaf tt).
- auto.
- destruct b1'.
- destruct b2'.
- destruct s.
- destruct s0.
- subst.
- left.
- exists (x,,x0).
- reflexivity.
- right; auto.
- right; auto.
- Defined.
-
Lemma unlev_relev : forall {Γ}(t:Tree ??(HaskType Γ ★)) lev, mapOptionTree unlev (t @@@ lev) = t.
intros.
induction t.
reflexivity.
Qed.
- Lemma tree_of_nothing : forall Γ ec t a,
- Arrange (a,,mapOptionTree flatten_leveled_type (drop_lev(Γ:=Γ) (ec :: nil) (t @@@ (ec :: nil)))) a.
+ Lemma tree_of_nothing : forall Γ ec t,
+ Arrange (mapOptionTree flatten_leveled_type (drop_lev(Γ:=Γ) (ec :: nil) (t @@@ (ec :: nil)))) [].
intros.
- induction t; try destruct o; try destruct a0.
+ induction t; try destruct o; try destruct a.
simpl.
drop_simplify.
simpl.
- apply RCanR.
+ apply RId.
simpl.
- apply RCanR.
+ apply RId.
+ eapply RComp; [ idtac | apply RCanL ].
+ eapply RComp; [ idtac | eapply RLeft; apply IHt2 ].
Opaque drop_lev.
simpl.
Transparent drop_lev.
+ idtac.
drop_simplify.
- simpl.
- eapply RComp.
- eapply RComp.
- eapply RAssoc.
- eapply RRight.
+ apply RRight.
apply IHt1.
- apply IHt2.
Defined.
- Lemma tree_of_nothing' : forall Γ ec t a,
- Arrange a (a,,mapOptionTree flatten_leveled_type (drop_lev(Γ:=Γ) (ec :: nil) (t @@@ (ec :: nil)))).
+ Lemma tree_of_nothing' : forall Γ ec t,
+ Arrange [] (mapOptionTree flatten_leveled_type (drop_lev(Γ:=Γ) (ec :: nil) (t @@@ (ec :: nil)))).
intros.
- induction t; try destruct o; try destruct a0.
+ induction t; try destruct o; try destruct a.
simpl.
drop_simplify.
simpl.
- apply RuCanR.
+ apply RId.
simpl.
- apply RuCanR.
+ apply RId.
+ eapply RComp; [ apply RuCanL | idtac ].
+ eapply RComp; [ eapply RRight; apply IHt1 | idtac ].
Opaque drop_lev.
simpl.
Transparent drop_lev.
+ idtac.
drop_simplify.
- simpl.
- eapply RComp.
- Focus 2.
- eapply RComp.
- Focus 2.
- eapply RCossa.
- Focus 2.
- eapply RRight.
- apply IHt1.
+ apply RLeft.
apply IHt2.
Defined.
- Axiom extensionality : forall Γ Q (f g:forall TV, InstantiatedTypeEnv TV Γ -> Q TV),
- (forall tv ite, f tv ite = g tv ite) -> f=g.
-
Lemma krunk : forall Γ (ec:HaskTyVar Γ ECKind) t,
flatten_type (<[ ec |- t ]>)
= @ga_mk Γ (v2t ec)
unfold flatten_type at 1.
simpl.
unfold ga_mk.
- apply extensionality.
+ apply phoas_extensionality.
intros.
unfold v2t.
unfold ga_mk_raw.
simpl.
replace (flatten_type (drop_arg_types_as_tree t) tv ite)
with (drop_arg_types (flatten_rawtype (t tv ite))).
- replace (unleaves (take_arg_types (flatten_rawtype (t tv ite))))
+ replace (unleaves_ (take_arg_types (flatten_rawtype (t tv ite))))
with ((mapOptionTree (fun x : HaskType Γ ★ => flatten_type x tv ite)
- (unleaves
+ (unleaves_
(take_trustme (count_arg_types (t (fun _ : Kind => unit) (ite_unit Γ)))
(fun TV : Kind → Type => take_arg_types ○ t TV))))).
reflexivity.
| 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 => let case_RJoin := tt in _
| RVoid _ _ => let case_RVoid := tt in _
| RBrak Γ Δ t ec succ lev => let case_RBrak := tt in _
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_second.
+ apply (ga_first _ _ _ _ _ _ Σ₂').
- eapply nd_comp.
- eapply nd_prod.
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
+ apply nd_prod.
apply nd_id.
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RCanL | idtac ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RExch (* okay *)].
+ apply precompose.
+
+ destruct case_RWhere.
+ simpl.
+ destruct lev as [|ec lev]; simpl; [ apply nd_rule; apply RWhere; auto | idtac ].
+ repeat take_simplify.
+ repeat drop_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_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_rule.
- eapply RArrange.
- apply RCanR.
- eapply precompose.
+ 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 RLet.
+ apply RArrange.
+ apply RLeft.
+ apply RCanL.
destruct case_RVoid.
simpl.
destruct case_RLetRec.
rename t into lev.
+ simpl. destruct lev; simpl.
+ replace (getjlev (y @@@ nil)) with (nil: (HaskLevel Γ)).
+ replace (mapOptionTree flatten_leveled_type (y @@@ nil))
+ with ((mapOptionTree flatten_type y) @@@ nil).
+ unfold flatten_leveled_type at 2.
+ simpl.
+ unfold flatten_leveled_type at 3.
simpl.
- apply (Prelude_error "LetRec not supported (FIXME)").
+ apply nd_rule.
+ set (@RLetRec Γ Δ (mapOptionTree flatten_leveled_type lri) (flatten_type x) (mapOptionTree flatten_type y) nil) as q.
+ simpl in q.
+ apply q.
+ induction y; try destruct a; auto.
+ simpl.
+ rewrite IHy1.
+ rewrite IHy2.
+ reflexivity.
+ induction y; try destruct a; auto.
+ simpl.
+ rewrite <- IHy1.
+ rewrite <- IHy2.
+ reflexivity.
+ apply (Prelude_error "LetRec not supported inside brackets yet (FIXME)").
destruct case_RCase.
simpl.
set (mapOptionTree (flatten_type ○ unlev)(take_lev (ec :: nil) succ)) as succ_guest.
set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
unfold empty_tree.
- eapply nd_comp; [ eapply nd_rule; eapply RArrange; apply tree_of_nothing | idtac ].
- refine (ga_unkappa' Γ Δ (v2t ec) nil _ _ _ _ ;; _).
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RLeft; apply tree_of_nothing | idtac ].
+ eapply nd_comp; [ eapply nd_rule; eapply RArrange; eapply RCanR | idtac ].
+ refine (ga_unkappa Γ Δ (v2t ec) nil _ _ _ _ ;; _).
+ eapply nd_comp; [ idtac | eapply arrange_brak ].
unfold succ_host.
unfold succ_guest.
- apply arrange_brak.
+ eapply nd_rule.
+ eapply RArrange.
+ apply RExch.
apply (Prelude_error "found Brak at depth >0 indicating 3-level code; only two-level code is currently supported").
destruct case_SEsc.
take_simplify.
drop_simplify.
simpl.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply tree_of_nothing' ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RLeft; apply tree_of_nothing' ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
simpl.
rewrite take_lemma'.
rewrite unlev_relev.
set (mapOptionTree flatten_leveled_type (drop_lev (ec :: nil) succ)) as succ_host.
set (mapOptionTree flatten_type (take_arg_types_as_tree t)) as succ_args.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RuCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; apply RCanL ].
eapply nd_comp; [ idtac | eapply nd_rule; eapply RLet ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod; [ idtac | eapply boost ].
induction x.
apply ga_id.
- eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanR ].
+ eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply RCanL ].
simpl.
apply ga_join.
apply IHx1.
apply IHx2.
(* environment has non-empty leaves *)
- apply ga_kappa'.
+ apply (Prelude_error "ga_kappa not supported yet (BIG FIXME)").
(* nesting too deep *)
apply (Prelude_error "found Esc at depth >0 indicating 3-level code; only two-level code is currently supported").
projects / coq-hetmet.git / blobdiff