(* information needed to define a case branch in a HaskProof *)
Record ProofCaseBranch {tc:TyCon}{Γ}{Δ}{lev}{branchtype : HaskType Γ ★}{avars}{sac:@StrongAltCon tc} :=
{ pcb_freevars : Tree ??(LeveledHaskType Γ ★)
-; pcb_judg := sac_Γ sac Γ > sac_Δ sac Γ avars (map weakCK' Δ)
+; pcb_judg := sac_gamma sac Γ > sac_delta sac Γ avars (map weakCK' Δ)
> (mapOptionTree weakLT' pcb_freevars),,(unleaves (map (fun t => t@@weakL' lev)
(vec2list (sac_types sac Γ avars))))
|- [weakLT' (branchtype @@ lev)]
Defined.
Lemma update_branches : forall Γ (ξ:VV -> LeveledHaskType Γ ★) lev l1 l2 q,
- update_ξ ξ lev (app l1 l2) q = update_ξ (update_ξ ξ lev l2) lev l1 q.
+ update_xi ξ lev (app l1 l2) q = update_xi (update_xi ξ lev l2) lev l1 q.
intros.
induction l1.
reflexivity.
Lemma fresh_lemma'' Γ
: forall types ξ lev,
FreshM { varstypes : _
- | mapOptionTree (update_ξ(Γ:=Γ) ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) = (types @@@ lev)
+ | mapOptionTree (update_xi(Γ:=Γ) ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) = (types @@@ lev)
/\ distinct (leaves (mapOptionTree (@fst _ _) varstypes)) }.
admit.
Defined.
Lemma fresh_lemma' Γ
: forall types vars Σ ξ lev, Σ = mapOptionTree ξ vars ->
FreshM { varstypes : _
- | mapOptionTree (update_ξ(Γ:=Γ) ξ lev (leaves varstypes)) vars = Σ
- /\ mapOptionTree (update_ξ ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) = (types @@@ lev)
+ | mapOptionTree (update_xi(Γ:=Γ) ξ lev (leaves varstypes)) vars = Σ
+ /\ mapOptionTree (update_xi ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) = (types @@@ lev)
/\ distinct (leaves (mapOptionTree (@fst _ _) varstypes)) }.
induction types.
intros; destruct a.
intros vars Σ ξ lev pf; refine (bind x2 = IHtypes2 vars Σ ξ lev pf; _).
apply FreshMon.
destruct x2 as [vt2 [pf21 [pf22 pfdist]]].
- refine (bind x1 = IHtypes1 (vars,,(mapOptionTree (@fst _ _) vt2)) (Σ,,(types2@@@lev)) (update_ξ ξ lev
+ refine (bind x1 = IHtypes1 (vars,,(mapOptionTree (@fst _ _) vt2)) (Σ,,(types2@@@lev)) (update_xi ξ lev
(leaves vt2)) _ _; return _).
apply FreshMon.
simpl.
Lemma fresh_lemma Γ ξ vars Σ Σ' lev
: Σ = mapOptionTree ξ vars ->
FreshM { vars' : _
- | mapOptionTree (update_ξ(Γ:=Γ) ξ lev ((vars',Σ')::nil)) vars = Σ
- /\ mapOptionTree (update_ξ ξ lev ((vars',Σ')::nil)) [vars'] = [Σ' @@ lev] }.
+ | mapOptionTree (update_xi(Γ:=Γ) ξ lev ((vars',Σ')::nil)) vars = Σ
+ /\ mapOptionTree (update_xi ξ lev ((vars',Σ')::nil)) [vars'] = [Σ' @@ lev] }.
intros.
set (fresh_lemma' Γ [Σ'] vars Σ ξ lev H) as q.
refine (q >>>= fun q' => return _).
prod (judg2exprType (pcb_judg (projT2 pcb))) {vars' : Tree ??VV & pcb_freevars (projT2 pcb) = mapOptionTree ξ vars'} ->
((fun sac => FreshM
{ scb : StrongCaseBranchWithVVs VV eqdec_vv tc avars sac
- & Expr (sac_Γ sac Γ) (sac_Δ sac Γ avars (weakCK'' Δ)) (scbwv_ξ scb ξ lev) (weakLT' (tbranches @@ lev)) }) (projT1 pcb)).
+ & Expr (sac_gamma sac Γ) (sac_delta sac Γ avars (weakCK'' Δ)) (scbwv_xi scb ξ lev) (weakLT' (tbranches @@ lev)) }) (projT1 pcb)).
intro pcb.
intro X.
simpl in X.
cut (distinct (vec2list localvars'')). intro H'''.
set (@Build_StrongCaseBranchWithVVs _ _ _ _ avars sac localvars'' H''') as scb.
- refine (bind q = (f (scbwv_ξ scb ξ lev) (vars,,(unleaves (vec2list (scbwv_exprvars scb)))) _) ; return _).
+ refine (bind q = (f (scbwv_xi scb ξ lev) (vars,,(unleaves (vec2list (scbwv_exprvars scb)))) _) ; return _).
apply FreshMon.
simpl.
- unfold scbwv_ξ.
+ unfold scbwv_xi.
rewrite vars_pf.
rewrite <- mapOptionTree_compose.
clear localvars_pf1.
refine (fresh_lemma _ ξ vars _ tx x H >>>= (fun pf => _)).
apply FreshMon.
destruct pf as [ vnew [ pf1 pf2 ]].
- set (update_ξ ξ x (((vnew, tx )) :: nil)) as ξ' in *.
+ set (update_xi ξ x (((vnew, tx )) :: nil)) as ξ' in *.
refine (X_ ξ' (vars,,[vnew]) _ >>>= _).
apply FreshMon.
simpl.
apply FreshMon.
destruct pf as [ vnew [ pf1 pf2 ]].
- set (update_ξ ξ p (((vnew, σ₁ )) :: nil)) as ξ' in *.
+ set (update_xi ξ p (((vnew, σ₁ )) :: nil)) as ξ' in *.
inversion X_.
apply ileaf in X.
apply ileaf in X0.
apply FreshMon.
destruct pf as [ vnew [ pf1 pf2 ]].
- set (update_ξ ξ p (((vnew, σ₁ )) :: nil)) as ξ' in *.
+ set (update_xi ξ p (((vnew, σ₁ )) :: nil)) as ξ' in *.
inversion X_.
apply ileaf in X.
apply ileaf in X0.
apply ILeaf; simpl; intros.
refine (bind ξvars = fresh_lemma' _ y _ _ _ t H; _). apply FreshMon.
destruct ξvars as [ varstypes [ pf1[ pf2 pfdist]]].
- refine (X_ ((update_ξ ξ t (leaves varstypes)))
+ refine (X_ ((update_xi ξ t (leaves varstypes)))
(vars,,(mapOptionTree (@fst _ _) varstypes)) _ >>>= fun X => return _); clear X_. apply FreshMon.
simpl.
rewrite pf2.
clear q.
destruct q' as [varstypes [pf1 [pf2 distpf]]].
exists (mapOptionTree (@fst _ _) varstypes).
- exists (update_ξ ξ l (leaves varstypes)).
+ exists (update_xi ξ l (leaves varstypes)).
symmetry; auto.
refine (return _).
exists [].
{ scbwv_exprvars : vec VV (sac_numExprVars sac)
; scbwv_exprvars_distinct : distinct (vec2list scbwv_exprvars)
; scbwv_varstypes := vec_zip scbwv_exprvars (sac_types sac Γ atypes)
- ; scbwv_ξ := fun ξ lev => update_ξ (weakLT'○ξ) (weakL' lev) (vec2list scbwv_varstypes)
+ ; scbwv_xi := fun ξ lev => update_xi (weakLT'○ξ) (weakL' lev) (vec2list scbwv_varstypes)
}.
Implicit Arguments StrongCaseBranchWithVVs [[Γ]].
| EVar : ∀ Γ Δ ξ ev, Expr Γ Δ ξ (ξ ev)
| ELit : ∀ Γ Δ ξ lit l, Expr Γ Δ ξ (literalType lit@@l)
| EApp : ∀ Γ Δ ξ t1 t2 l, Expr Γ Δ ξ (t2--->t1 @@ l) -> Expr Γ Δ ξ (t2 @@ l) -> Expr Γ Δ ξ (t1 @@ l)
- | ELam : ∀ Γ Δ ξ t1 t2 l ev, Expr Γ Δ (update_ξ ξ l ((ev,t1)::nil)) (t2@@l) -> Expr Γ Δ ξ (t1--->t2@@l)
- | ELet : ∀ Γ Δ ξ tv t l ev,Expr Γ Δ ξ (tv@@l)->Expr Γ Δ (update_ξ ξ l ((ev,tv)::nil))(t@@l) -> Expr Γ Δ ξ (t@@l)
+ | ELam : ∀ Γ Δ ξ t1 t2 l ev, Expr Γ Δ (update_xi ξ l ((ev,t1)::nil)) (t2@@l) -> Expr Γ Δ ξ (t1--->t2@@l)
+ | ELet : ∀ Γ Δ ξ tv t l ev,Expr Γ Δ ξ (tv@@l)->Expr Γ Δ (update_xi ξ l ((ev,tv)::nil))(t@@l) -> Expr Γ Δ ξ (t@@l)
| EEsc : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (<[ ec |- t ]> @@ l) -> Expr Γ Δ ξ (t @@ (ec::l))
| EBrak : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (t @@ (ec::l)) -> Expr Γ Δ ξ (<[ ec |- t ]> @@ l)
| ECast : forall Γ Δ ξ t1 t2 (γ:HaskCoercion Γ Δ (t1 ∼∼∼ t2)) l,
Expr Γ Δ ξ (caseType tc atypes @@ l) ->
Tree ??{ sac : _
& { scb : StrongCaseBranchWithVVs tc atypes sac
- & Expr (sac_Γ sac Γ)
- (sac_Δ sac Γ atypes (weakCK'' Δ))
- (scbwv_ξ scb ξ l)
+ & Expr (sac_gamma sac Γ)
+ (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l)
(weakLT' (tbranches@@l)) } } ->
Expr Γ Δ ξ (tbranches @@ l)
| ELetRec : ∀ Γ Δ ξ l τ vars,
distinct (leaves (mapOptionTree (@fst _ _) vars)) ->
- let ξ' := update_ξ ξ l (leaves vars) in
+ let ξ' := update_xi ξ l (leaves vars) in
ELetRecBindings Γ Δ ξ' l vars ->
Expr Γ Δ ξ' (τ@@l) ->
Expr Γ Δ ξ (τ@@l)
{Γ} lev
(ξ:VV -> LeveledHaskType Γ ★)
lv tree2 :
- mapOptionTree (update_ξ ξ lev lv) (stripOutVars (map (@fst _ _) lv) tree2)
+ mapOptionTree (update_xi ξ lev lv) (stripOutVars (map (@fst _ _) lv) tree2)
= mapOptionTree ξ (stripOutVars (map (@fst _ _) lv) tree2).
induction tree2.
inversion H; auto.
Qed.
-Lemma update_ξ_lemma' `{EQD_VV:EqDecidable VV} Γ ξ (lev:HaskLevel Γ)(varstypes:Tree ??(VV*_)) :
+Lemma update_xiv_lemma' `{EQD_VV:EqDecidable VV} Γ ξ (lev:HaskLevel Γ)(varstypes:Tree ??(VV*_)) :
forall v1 v2,
distinct (map (@fst _ _) (leaves (v1,,(varstypes,,v2)))) ->
- mapOptionTree (update_ξ ξ lev (leaves (v1,,(varstypes,,v2)))) (mapOptionTree (@fst _ _) varstypes) =
+ mapOptionTree (update_xi ξ lev (leaves (v1,,(varstypes,,v2)))) (mapOptionTree (@fst _ _) varstypes) =
mapOptionTree (fun t => t@@ lev) (mapOptionTree (@snd _ _) varstypes).
induction varstypes; intros.
destruct a; simpl; [ idtac | reflexivity ].
repeat rewrite ass_app in *; auto.
Qed.
-Lemma update_ξ_lemma `{EQD_VV:EqDecidable VV} Γ ξ (lev:HaskLevel Γ)(varstypes:Tree ??(VV*_)) :
+Lemma update_xiv_lemma `{EQD_VV:EqDecidable VV} Γ ξ (lev:HaskLevel Γ)(varstypes:Tree ??(VV*_)) :
distinct (map (@fst _ _) (leaves varstypes)) ->
- mapOptionTree (update_ξ ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) =
+ mapOptionTree (update_xi ξ lev (leaves varstypes)) (mapOptionTree (@fst _ _) varstypes) =
mapOptionTree (fun t => t@@ lev) (mapOptionTree (@snd _ _) varstypes).
- set (update_ξ_lemma' Γ ξ lev varstypes [] []) as q.
+ set (update_xiv_lemma' Γ ξ lev varstypes [] []) as q.
simpl in q.
rewrite <- app_nil_end in q.
apply q.
| ECase Γ Δ ξ l tc tbranches atypes e' alts =>
((fix varsfromalts (alts:
Tree ??{ sac : _ & { scb : StrongCaseBranchWithVVs _ _ tc atypes sac
- & Expr (sac_Γ sac Γ)
- (sac_Δ sac Γ atypes (weakCK'' Δ))
- (scbwv_ξ scb ξ l)
+ & Expr (sac_gamma sac Γ)
+ (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l)
(weakLT' (tbranches@@l)) } }
): Tree ??VV :=
match alts with
Definition mkProofCaseBranch {Γ}{Δ}{ξ}{l}{tc}{tbranches}{atypes}
(alt : { sac : _ & { scb : StrongCaseBranchWithVVs _ _ tc atypes sac
- & Expr (sac_Γ sac Γ)
- (sac_Δ sac Γ atypes (weakCK'' Δ))
- (scbwv_ξ scb ξ l)
+ & Expr (sac_gamma sac Γ)
+ (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l)
(weakLT' (tbranches@@l)) } })
: { sac : _ & ProofCaseBranch tc Γ Δ l tbranches atypes sac }.
destruct alt.
Defined.
Lemma updating_stripped_tree_is_inert {Γ} (ξ:VV -> LeveledHaskType Γ ★) v tree t lev :
- mapOptionTree (update_ξ ξ lev ((v,t)::nil)) (stripOutVars (v :: nil) tree)
+ mapOptionTree (update_xi ξ lev ((v,t)::nil)) (stripOutVars (v :: nil) tree)
= mapOptionTree ξ (stripOutVars (v :: nil) tree).
set (@updating_stripped_tree_is_inert' Γ lev ξ ((v,t)::nil)) as p.
rewrite p.
Lemma letRecSubproofsToND' Γ Δ ξ lev τ tree :
forall branches body (dist:distinct (leaves (mapOptionTree (@fst _ _) tree))),
- ND Rule [] [Γ > Δ > mapOptionTree (update_ξ ξ lev (leaves tree)) (expr2antecedent body) |- [τ @@ lev]] ->
- LetRecSubproofs Γ Δ (update_ξ ξ lev (leaves tree)) lev tree branches ->
+ ND Rule [] [Γ > Δ > mapOptionTree (update_xi ξ lev (leaves tree)) (expr2antecedent body) |- [τ @@ lev]] ->
+ LetRecSubproofs Γ Δ (update_xi ξ lev (leaves tree)) lev tree branches ->
ND Rule [] [Γ > Δ > mapOptionTree ξ (expr2antecedent (@ELetRec VV _ Γ Δ ξ lev τ tree dist branches body)) |- [τ @@ lev]].
(* NOTE: how we interpret stuff here affects the order-of-side-effects *)
apply disti.
rewrite mapleaves in disti'.
- set (@update_ξ_lemma _ Γ ξ lev tree disti') as ξlemma.
+ set (@update_xiv_lemma _ Γ ξ lev tree disti') as ξlemma.
rewrite <- mapOptionTree_compose in ξlemma.
- set ((update_ξ ξ lev (leaves tree))) as ξ' in *.
+ set ((update_xi ξ lev (leaves tree))) as ξ' in *.
set ((stripOutVars (leaves (mapOptionTree (@fst _ _) tree)) (eLetRecContext branches))) as ctx.
set (mapOptionTree (@fst _ _) tree) as pctx.
set (mapOptionTree ξ' pctx) as passback.
Lemma scbwv_coherent {tc}{Γ}{atypes:IList _ (HaskType Γ) _}{sac} :
forall scb:StrongCaseBranchWithVVs _ _ tc atypes sac,
forall l ξ,
- vec2list (vec_map (scbwv_ξ scb ξ l) (scbwv_exprvars scb)) =
+ vec2list (vec_map (scbwv_xi scb ξ l) (scbwv_exprvars scb)) =
vec2list (vec_map (fun t => t @@ weakL' l) (sac_types sac _ atypes)).
intros.
- unfold scbwv_ξ.
+ unfold scbwv_xi.
unfold scbwv_varstypes.
- set (@update_ξ_lemma _ _ (weakLT' ○ ξ) (weakL' l)
+ set (@update_xiv_lemma _ _ (weakLT' ○ ξ) (weakL' l)
(unleaves (vec2list (vec_zip (scbwv_exprvars scb) (sac_types sac Γ atypes))))
) as q.
rewrite <- mapleaves' in q.
(alts':Tree
??{sac : StrongAltCon &
{scb : StrongCaseBranchWithVVs VV eqd_vv tc atypes sac &
- Expr (sac_Γ sac Γ) (sac_Δ sac Γ atypes (weakCK'' Δ))
- (scbwv_ξ scb ξ l) (weakLT' (tbranches @@ l))}}),
+ Expr (sac_gamma sac Γ) (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l) (weakLT' (tbranches @@ l))}}),
(mapOptionTreeAndFlatten (fun x => pcb_freevars (projT2 x))
(mapOptionTree mkProofCaseBranch alts'))
| ELet Γ Δ ξ tv t v lev ev ebody => let case_ELet := tt in
(fun pf_let pf_body => _) (expr2proof _ _ _ _ ev) (expr2proof _ _ _ _ ebody)
| ELetRec Γ Δ ξ lev t tree disti branches ebody =>
- let ξ' := update_ξ ξ lev (leaves tree) in
+ let ξ' := update_xi ξ lev (leaves tree) in
let case_ELetRec := tt in (fun e' subproofs => _) (expr2proof _ _ _ _ ebody)
((fix subproofs Γ'' Δ'' ξ'' lev'' (tree':Tree ??(VV * HaskType Γ'' ★))
(branches':ELetRecBindings Γ'' Δ'' ξ'' lev'' tree')
let dcsp :=
((fix mkdcsp (alts:
Tree ??{ sac : _ & { scb : StrongCaseBranchWithVVs _ _ tc atypes sac
- & Expr (sac_Γ sac Γ)
- (sac_Δ sac Γ atypes (weakCK'' Δ))
- (scbwv_ξ scb ξ l)
+ & Expr (sac_gamma sac Γ)
+ (sac_delta sac Γ atypes (weakCK'' Δ))
+ (scbwv_xi scb ξ l)
(weakLT' (tbranches@@l)) } })
: ND Rule [] (mapOptionTree (fun x => pcb_judg (projT2 (mkProofCaseBranch x))) alts) :=
match alts as ALTS return ND Rule []
destruct case_ELam; intros.
unfold mapOptionTree; simpl; fold (mapOptionTree ξ).
eapply nd_comp; [ idtac | eapply nd_rule; apply RLam ].
- set (update_ξ ξ lev ((v,t1)::nil)) as ξ'.
+ set (update_xi ξ lev ((v,t1)::nil)) as ξ'.
set (factorContextRightAndWeaken Γ Δ v (expr2antecedent e) ξ') as pfx.
eapply RArrange in pfx.
unfold mapOptionTree in pfx; simpl in pfx.
unfold ξ' in pfx.
rewrite updating_stripped_tree_is_inert in pfx.
- unfold update_ξ in pfx.
+ unfold update_xi in pfx.
destruct (eqd_dec v v).
eapply nd_comp; [ idtac | apply (nd_rule pfx) ].
clear pfx.
eapply nd_comp; [ apply pf_body | idtac ].
fold (@mapOptionTree VV).
fold (mapOptionTree ξ).
- set (update_ξ ξ v ((lev,tv)::nil)) as ξ'.
+ set (update_xi ξ v ((lev,tv)::nil)) as ξ'.
set (factorContextLeftAndWeaken Γ Δ lev (expr2antecedent ebody) ξ') as n.
unfold mapOptionTree in n; simpl in n; fold (mapOptionTree ξ') in n.
unfold ξ' in n.
rewrite updating_stripped_tree_is_inert in n.
- unfold update_ξ in n.
+ unfold update_xi in n.
destruct (eqd_dec lev lev).
unfold ξ'.
- unfold update_ξ.
+ unfold update_xi.
eapply RArrange in n.
apply (nd_rule n).
assert False. apply n0; auto. inversion H.
rewrite mapleaves'.
simpl.
rewrite <- mapOptionTree_compose.
- unfold scbwv_ξ.
+ unfold scbwv_xi.
rewrite <- mapleaves'.
rewrite vec2list_map_list2vec.
- unfold sac_Γ.
+ unfold sac_gamma.
rewrite <- (scbwv_coherent scbx l ξ).
rewrite <- vec2list_map_list2vec.
rewrite mapleaves'.
set (@factorContextRightAndWeaken'') as q.
- unfold scbwv_ξ.
+ unfold scbwv_xi.
set (@updating_stripped_tree_is_inert' _ (weakL' l) (weakLT' ○ ξ) (vec2list (scbwv_varstypes scbx))) as z.
unfold scbwv_varstypes in z.
rewrite vec2list_map_list2vec in z.
replace (stripOutVars (vec2list (scbwv_exprvars scbx))) with
(stripOutVars (leaves (unleaves (vec2list (scbwv_exprvars scbx))))).
apply q.
- apply (sac_Δ sac Γ atypes (weakCK'' Δ)).
+ apply (sac_delta sac Γ atypes (weakCK'' Δ)).
rewrite leaves_unleaves.
apply (scbwv_exprvars_distinct scbx).
rewrite leaves_unleaves.
Context {VV}{eqVV:EqDecidable VV}{toStringVV:ToString VV}.
- Definition update_χ (χ:VV->???WeakExprVar)(vv:VV)(ev':WeakExprVar) : VV->???WeakExprVar :=
+ Definition update_chi (χ:VV->???WeakExprVar)(vv:VV)(ev':WeakExprVar) : VV->???WeakExprVar :=
fun vv' =>
if eqd_dec vv vv'
then OK ev'
else χ vv'.
- Fixpoint update_χ' (χ:VV->???WeakExprVar)(varsexprs:list (VV * WeakExprVar)) : VV->???WeakExprVar :=
+ Fixpoint update_chi' (χ:VV->???WeakExprVar)(varsexprs:list (VV * WeakExprVar)) : VV->???WeakExprVar :=
match varsexprs with
| nil => χ
- | (vv,wev)::rest => update_χ (update_χ' χ rest) vv wev
+ | (vv,wev)::rest => update_chi (update_chi' χ rest) vv wev
end.
Fixpoint exprToWeakExpr {Γ}{Δ}{ξ}{τ}(χ:VV->???WeakExprVar)(exp:@Expr _ eqVV Γ Δ ξ τ)
; return (fold_left (fun x y => WETyApp x y) tv' (WEVar g))
| ELam Γ' _ _ tv _ _ cv e => fun ite => bind tv' = typeToWeakType tv ite
; bind ev' = mkWeakExprVar tv'
- ; bind e' = exprToWeakExpr (update_χ χ cv ev') e ite
+ ; bind e' = exprToWeakExpr (update_chi χ cv ev') e ite
; return WELam ev' e'
| ELet Γ' _ _ t _ _ ev e1 e2 => fun ite => bind tv' = typeToWeakType t ite
; bind e1' = exprToWeakExpr χ e1 ite
; bind ev' = mkWeakExprVar tv'
- ; bind e2' = exprToWeakExpr (update_χ χ ev ev') e2 ite
+ ; bind e2' = exprToWeakExpr (update_chi χ ev ev') e2 ite
; return WELet ev' e1' e2'
| ELit _ _ _ lit _ => fun ite => return WELit lit
| EApp Γ' _ _ _ _ _ e1 e2 => fun ite => bind e1' = exprToWeakExpr χ e1 ite
; bind v' = mkWeakExprVar tleaf
; return ((fst vt),v'))
varstypes)
- ; let χ' := update_χ' χ exprvars in
+ ; let χ' := update_chi' χ exprvars in
bind e'' = exprToWeakExpr χ' e (snd evars_ite)
; return [(sac_altcon sac, vec2list (fst evars_ite), nil, (map (@snd _ _) exprvars), e'')]
| T_Branch b1 b2 => bind b1' = caseBranches b1
; bind v' = mkWeakExprVar tleaf
; return ((fst vt),v'))
(leaves vars))
- ; let χ' := update_χ' χ vars' in
+ ; let χ' := update_chi' χ vars' in
bind elrb' = exprLetRec2WeakExprLetRec χ' elrb ite
; bind e' = exprToWeakExpr χ' e ite
; return WELetRec elrb' e'
; sac_numExprVars : nat
; sac_ekinds : vec Kind sac_numExTyVars
; sac_kinds := app (tyConKind tc) (vec2list sac_ekinds)
-; sac_Γ := fun Γ => app (vec2list sac_ekinds) Γ
-; sac_coercions : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskCoercionKind (sac_Γ Γ)) sac_numCoerVars
-; sac_types : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskType (sac_Γ Γ) ★) sac_numExprVars
-; sac_Δ := fun Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)) Δ => app (vec2list (sac_coercions Γ atypes)) Δ
+; sac_gamma := fun Γ => app (vec2list sac_ekinds) Γ
+; sac_coercions : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskCoercionKind (sac_gamma Γ)) sac_numCoerVars
+; sac_types : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskType (sac_gamma Γ) ★) sac_numExprVars
+; sac_delta := fun Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)) Δ => app (vec2list (sac_coercions Γ atypes)) Δ
}.
Coercion sac_tc : StrongAltCon >-> TyCon.
Coercion sac_altcon : StrongAltCon >-> WeakAltCon.
Notation "a ∼∼∼ b" := (@mkHaskCoercionKind _ _ a b) (at level 18).
-Fixpoint update_ξ
+Fixpoint update_xi
`{EQD_VV:EqDecidable VV}{Γ}
(ξ:VV -> LeveledHaskType Γ ★)
(lev:HaskLevel Γ)
: VV -> LeveledHaskType Γ ★ :=
match vt with
| nil => ξ
- | (v,τ)::tl => fun v' => if eqd_dec v v' then τ @@ lev else (update_ξ ξ lev tl) v'
+ | (v,τ)::tl => fun v' => if eqd_dec v v' then τ @@ lev else (update_xi ξ lev tl) v'
end.
-Lemma update_ξ_lemma0 `{EQD_VV:EqDecidable VV} : forall Γ ξ (lev:HaskLevel Γ)(varstypes:list (VV*_)) v,
+Lemma update_xi_lemma0 `{EQD_VV:EqDecidable VV} : forall Γ ξ (lev:HaskLevel Γ)(varstypes:list (VV*_)) v,
not (In v (map (@fst _ _) varstypes)) ->
- (update_ξ ξ lev varstypes) v = ξ v.
+ (update_xi ξ lev varstypes) v = ξ v.
intros.
induction varstypes.
reflexivity.
Definition TyVarResolver Γ := forall wt:WeakTypeVar, ???(HaskTyVar Γ wt).
Definition CoVarResolver Γ Δ := forall wt:WeakCoerVar, ???(HaskCoVar Γ Δ).
-Definition upφ {Γ}(tv:WeakTypeVar)(φ:TyVarResolver Γ) : TyVarResolver ((tv:Kind)::Γ).
+Definition upPhi {Γ}(tv:WeakTypeVar)(φ:TyVarResolver Γ) : TyVarResolver ((tv:Kind)::Γ).
unfold TyVarResolver.
refine (fun tv' =>
if eqd_dec tv tv'
rewrite <- _H; apply fresh.
Defined.
-Definition upφ' {Γ}(tvs:list WeakTypeVar)(φ:TyVarResolver Γ)
+Definition upPhi2 {Γ}(tvs:list WeakTypeVar)(φ:TyVarResolver Γ)
: (TyVarResolver (app (map (fun tv:WeakTypeVar => tv:Kind) tvs) Γ)).
induction tvs.
apply φ.
simpl.
- apply upφ.
+ apply upPhi.
apply IHtvs.
Defined.
apply X.
Defined.
-Definition substφ {Γ:TypeEnv}(lk:list Kind)(θ:IList _ (fun κ => HaskType Γ κ) lk){κ} : HaskType (app lk Γ) κ -> HaskType Γ κ.
+Definition substphi {Γ:TypeEnv}(lk:list Kind)(θ:IList _ (fun κ => HaskType Γ κ) lk){κ} : HaskType (app lk Γ) κ -> HaskType Γ κ.
induction lk.
intro q; apply q.
simpl.
(* this is a StrongAltCon plus some stuff we know about StrongAltCons which we've built ourselves *)
Record StrongAltConPlusJunk {tc:TyCon} :=
{ sacpj_sac : @StrongAltCon tc
-; sacpj_φ : forall Γ (φ:TyVarResolver Γ ), (TyVarResolver (sac_Γ sacpj_sac Γ))
-; sacpj_ψ : forall Γ Δ atypes (ψ:CoVarResolver Γ Δ), CoVarResolver _ (sac_Δ sacpj_sac Γ atypes (weakCK'' Δ))
+; sacpj_phi : forall Γ (φ:TyVarResolver Γ ), (TyVarResolver (sac_gamma sacpj_sac Γ))
+; sacpj_psi : forall Γ Δ atypes (ψ:CoVarResolver Γ Δ), CoVarResolver _ (sac_delta sacpj_sac Γ atypes (weakCK'' Δ))
}.
Implicit Arguments StrongAltConPlusJunk [ ].
Coercion sacpj_sac : StrongAltConPlusJunk >-> StrongAltCon.
Definition mkPhi (lv:list WeakTypeVar)
: (TyVarResolver (map (fun x:WeakTypeVar => x:Kind) lv)).
- set (upφ'(Γ:=nil) lv emptyφ) as φ'.
- rewrite <- app_nil_end in φ'.
- apply φ'.
+ set (upPhi2(Γ:=nil) lv emptyφ) as φ2.
+ rewrite <- app_nil_end in φ2.
+ apply φ2.
Defined.
Definition dataConExKinds dc := vec_map (fun x:WeakTypeVar => (x:Kind)) (list2vec (dataConExTyVars dc)).
| WIParam _ ty => let case_WIParam := tt in Error "weakTypeToType: WIParam not implemented"
| WAppTy t1 t2 => let case_WAppTy := tt in weakTypeToType _ φ t1 >>= fun t1' => weakTypeToType _ φ t2 >>= fun t2' => _
| WTyVarTy v => let case_WTyVarTy := tt in φ v >>= fun v' => _
- | WForAllTy wtv t => let case_WForAllTy := tt in weakTypeToType _ (upφ wtv φ) t >>= fun t => _
+ | WForAllTy wtv t => let case_WForAllTy := tt in weakTypeToType _ (upPhi wtv φ) t >>= fun t => _
| WCodeTy ec tbody => let case_WCodeTy := tt in weakTypeToType _ φ tbody
>>= fun tbody' => φ (@fixkind ECKind ec) >>= fun ec' => _
| WCoFunTy t1 t2 t3 => let case_WCoFunTy := tt in
intro ct.
apply (addErrorMessage "weakTypeToType'").
set (ilmap (@weakT' _ (vec2list (dataConExKinds dc))) avars) as avars'.
- set (@substφ _ _ avars') as q.
- set (upφ' (tyConTyVars tc) (mkPhi (dataConExTyVars dc))) as φ'.
- set (@weakTypeToType _ φ' ct) as t.
+ set (@substphi _ _ avars') as q.
+ set (upPhi2 (tyConTyVars tc) (mkPhi (dataConExTyVars dc))) as φ2.
+ set (@weakTypeToType _ φ2 ct) as t.
destruct t as [|t]; try apply (Error error_message).
destruct t as [tk t].
matchThings tk ★ "weakTypeToType'".
Definition mkStrongAltConPlusJunk : StrongAltConPlusJunk tc.
refine
{| sacpj_sac := mkStrongAltCon
- ; sacpj_φ := fun Γ φ => (fun htv => φ htv >>= fun htv' => OK (weakV' htv'))
- ; sacpj_ψ :=
+ ; sacpj_phi := fun Γ φ => (fun htv => φ htv >>= fun htv' => OK (weakV' htv'))
+ ; sacpj_psi :=
fun Γ Δ avars ψ => (fun htv => ψ htv >>= fun htv' => OK (_ (weakCV' (vec2list (sac_ekinds mkStrongAltCon)) htv')))
|}.
intro.
- unfold sac_Γ.
+ unfold sac_gamma.
unfold HaskCoVar in *.
intros.
apply (x TV CV env).
simpl in cenv.
- unfold sac_Δ in *.
+ unfold sac_delta in *.
unfold InstantiatedCoercionEnv in *.
apply vec_chop' in cenv.
apply cenv.
; sac_altcon := WeakLitAlt h
|} |}.
intro; intro φ; apply φ.
- intro; intro; intro; intro ψ. simpl. unfold sac_Γ; simpl. unfold sac_Δ; simpl.
+ intro; intro; intro; intro ψ. simpl. unfold sac_gamma; simpl. unfold sac_delta; simpl.
rewrite weakCK'_nil_inert. apply ψ.
apply OK; refine {| sacpj_sac := {|
sac_ekinds := vec_nil ; sac_coercions := fun _ _ => vec_nil ; sac_types := fun _ _ => vec_nil
; sac_altcon := WeakDEFAULT |} |}.
intro; intro φ; apply φ.
- intro; intro; intro; intro ψ. simpl. unfold sac_Γ; simpl. unfold sac_Δ; simpl.
+ intro; intro; intro; intro ψ. simpl. unfold sac_gamma; simpl. unfold sac_delta; simpl.
rewrite weakCK'_nil_inert. apply ψ.
Defined.
Variable weakCoercionToHaskCoercion : forall Γ Δ κ, WeakCoercion -> HaskCoercion Γ Δ κ.
-Definition weakψ {Γ}{Δ:CoercionEnv Γ} {κ}(ψ:WeakCoerVar -> ???(HaskCoVar Γ Δ)) :
+Definition weakPsi {Γ}{Δ:CoercionEnv Γ} {κ}(ψ:WeakCoerVar -> ???(HaskCoVar Γ Δ)) :
WeakCoerVar -> ???(HaskCoVar Γ (κ::Δ)).
intros.
refine (ψ X >>= _).
| WELam ev ebody => weakTypeToTypeOfKind φ ev ★ >>= fun tv =>
weakTypeOfWeakExpr ebody >>= fun tbody =>
weakTypeToTypeOfKind φ tbody ★ >>= fun tbody' =>
- let ξ' := update_ξ ξ lev (((ev:CoreVar),tv)::nil) in
+ let ξ' := update_xi ξ lev (((ev:CoreVar),tv)::nil) in
let ig' := update_ig ig ((ev:CoreVar)::nil) in
weakExprToStrongExpr Γ Δ φ ψ ξ' ig' tbody' lev ebody >>= fun ebody' =>
castExpr we "WELam" (τ@@lev) (ELam Γ Δ ξ tv tbody' lev ev ebody')
| WELet v ve ebody => weakTypeToTypeOfKind φ v ★ >>= fun tv =>
weakExprToStrongExpr Γ Δ φ ψ ξ ig tv lev ve >>= fun ve' =>
- weakExprToStrongExpr Γ Δ φ ψ (update_ξ ξ lev (((v:CoreVar),tv)::nil))
+ weakExprToStrongExpr Γ Δ φ ψ (update_xi ξ lev (((v:CoreVar),tv)::nil))
(update_ig ig ((v:CoreVar)::nil)) τ lev ebody
>>= fun ebody' =>
OK (ELet _ _ _ tv _ lev (v:CoreVar) ve' ebody')
weakExprToStrongExpr Γ Δ φ ψ ξ ig (t2'--->τ) lev e1 >>= fun e1' =>
OK (EApp _ _ _ _ _ _ e1' e2')
- | WETyLam tv e => let φ' := upφ tv φ in
+ | WETyLam tv e => let φ2 := upPhi tv φ in
weakTypeOfWeakExpr e >>= fun te =>
- weakTypeToTypeOfKind φ' te ★ >>= fun τ' =>
- weakExprToStrongExpr _ (weakCE Δ) φ'
+ weakTypeToTypeOfKind φ2 te ★ >>= fun τ' =>
+ weakExprToStrongExpr _ (weakCE Δ) φ2
(fun x => (ψ x) >>= fun y => OK (weakCV y)) (weakLT○ξ) ig _ (weakL lev) e
>>= fun e' => castExpr we "WETyLam2" _ (ETyLam Γ Δ ξ tv (mkTAll' τ') lev e')
| WETyApp e t => weakTypeOfWeakExpr e >>= fun te =>
match te with
| WForAllTy wtv te' =>
- let φ' := upφ wtv φ in
- weakTypeToTypeOfKind φ' te' ★ >>= fun te'' =>
+ let φ2 := upPhi wtv φ in
+ weakTypeToTypeOfKind φ2 te' ★ >>= fun te'' =>
weakExprToStrongExpr Γ Δ φ ψ ξ ig (mkTAll te'') lev e >>= fun e' =>
weakTypeToTypeOfKind φ t (wtv:Kind) >>= fun t' =>
castExpr we "WETyApp" _ (ETyApp Γ Δ wtv (mkTAll' te'') t' ξ lev e')
weakTypeToTypeOfKind φ te ★ >>= fun te' =>
weakTypeToTypeOfKind φ t1 cv >>= fun t1' =>
weakTypeToTypeOfKind φ t2 cv >>= fun t2' =>
- weakExprToStrongExpr Γ (_ :: Δ) φ (weakψ ψ) ξ ig te' lev e >>= fun e' =>
+ weakExprToStrongExpr Γ (_ :: Δ) φ (weakPsi ψ) ξ ig te' lev e >>= fun e' =>
castExpr we "WECoLam" _ (ECoLam Γ Δ cv te' t1' t2' ξ lev e')
| WECast e co => let (t1,t2) := weakCoercionTypes co in
(ECast Γ Δ ξ t1' t2' (weakCoercionToHaskCoercion _ _ _ co) lev e')
| WELetRec rb e =>
- let ξ' := update_ξ ξ lev _ in
+ let ξ' := update_xi ξ lev _ in
let ig' := update_ig ig (map (fun x:(WeakExprVar*_) => (fst x):CoreVar) (leaves rb)) in
let binds :=
(fix binds (t:Tree ??(WeakExprVar * WeakExpr))
weakTypeToTypeOfKind φ tbranches ★ >>= fun tbranches' =>
(fix mkTree (t:Tree ??(WeakAltCon*list WeakTypeVar*list WeakCoerVar*list WeakExprVar*WeakExpr)) : ???(Tree
??{ sac : _ & {scb : StrongCaseBranchWithVVs CoreVar CoreVarEqDecidable tc avars' sac &
- Expr (sac_Γ sac Γ) (sac_Δ sac Γ avars' (weakCK'' Δ))(scbwv_ξ scb ξ lev)(weakLT' (tbranches' @@ lev))}}) :=
+ Expr (sac_gamma sac Γ) (sac_delta sac Γ avars' (weakCK'' Δ))(scbwv_xi scb ξ lev)(weakLT' (tbranches' @@ lev))}}) :=
match t with
| T_Leaf None => OK []
| T_Leaf (Some (ac,extyvars,coervars,exprvars,ebranch)) =>
>>= fun exprvars' =>
(let case_pf := tt in _) >>= fun pf =>
let scb := @Build_StrongCaseBranchWithVVs CoreVar CoreVarEqDecidable tc Γ avars' sac exprvars' pf in
- weakExprToStrongExpr (sac_Γ sac Γ) (sac_Δ sac Γ avars' (weakCK'' Δ)) (sacpj_φ sac _ φ)
- (sacpj_ψ sac _ _ avars' ψ)
- (scbwv_ξ scb ξ lev)
+ weakExprToStrongExpr (sac_gamma sac Γ) (sac_delta sac Γ avars' (weakCK'' Δ)) (sacpj_phi sac _ φ)
+ (sacpj_psi sac _ _ avars' ψ)
+ (scbwv_xi scb ξ lev)
(update_ig ig (map (@fst _ _) (vec2list (scbwv_varstypes scb))))
(weakT' tbranches') (weakL' lev) ebranch >>= fun ebranch' =>
let case_case := tt in OK [ _ ]
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