X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FHaskProofToStrong.v;h=b6e8efee00b3730606325935a866162a67bb9ffa;hp=6f75235f42e9b7ea04ea87dd7fb1b352cf1fef51;hb=93ac0d63048027161f816c451a7954fb8a6470c0;hpb=539d675a181f178e24c15b2a6ad3c990492eed79 diff --git a/src/HaskProofToStrong.v b/src/HaskProofToStrong.v index 6f75235..b6e8efe 100644 --- a/src/HaskProofToStrong.v +++ b/src/HaskProofToStrong.v @@ -25,12 +25,6 @@ Section HaskProofToStrong. Definition ExprVarResolver Γ := VV -> LeveledHaskType Γ ★. - Definition ujudg2exprType {Γ}{Δ}(ξ:ExprVarResolver Γ)(j:UJudg Γ Δ) : Type := - match j with - mkUJudg Σ τ => forall vars, Σ = mapOptionTree ξ vars -> - FreshM (ITree _ (fun t => Expr Γ Δ ξ t) τ) - end. - Definition judg2exprType (j:Judg) : Type := match j with (Γ > Δ > Σ |- τ) => forall (ξ:ExprVarResolver Γ) vars, Σ = mapOptionTree ξ vars -> @@ -125,6 +119,14 @@ Section HaskProofToStrong. reflexivity. Qed. + Lemma fresh_lemma'' Γ + : forall types ξ lev, + FreshM { varstypes : _ + | mapOptionTree (update_ξ(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 : _ @@ -220,172 +222,136 @@ Section HaskProofToStrong. inversion pf2. Defined. - Definition urule2expr : forall Γ Δ h j (r:@URule Γ Δ h j) (ξ:VV -> LeveledHaskType Γ ★), - ITree _ (ujudg2exprType ξ) h -> ITree _ (ujudg2exprType ξ) j. - - refine (fix urule2expr Γ Δ h j (r:@URule Γ Δ h j) ξ {struct r} : - ITree _ (ujudg2exprType ξ) h -> ITree _ (ujudg2exprType ξ) j := - match r as R in URule H C return ITree _ (ujudg2exprType ξ) H -> ITree _ (ujudg2exprType ξ) C with - | RLeft h c ctx r => let case_RLeft := tt in (fun e => _) (urule2expr _ _ _ _ r) - | RRight h c ctx r => let case_RRight := tt in (fun e => _) (urule2expr _ _ _ _ r) - | RCanL t a => let case_RCanL := tt in _ - | RCanR t a => let case_RCanR := tt in _ - | RuCanL t a => let case_RuCanL := tt in _ - | RuCanR t a => let case_RuCanR := tt in _ - | RAssoc t a b c => let case_RAssoc := tt in _ - | RCossa t a b c => let case_RCossa := tt in _ - | RExch t a b => let case_RExch := tt in _ - | RWeak t a => let case_RWeak := tt in _ - | RCont t a => let case_RCont := tt in _ + Definition ujudg2exprType Γ (ξ:ExprVarResolver Γ)(Δ:CoercionEnv Γ) Σ τ : Type := + forall vars, Σ = mapOptionTree ξ vars -> FreshM (ITree _ (fun t => Expr Γ Δ ξ t) τ). + + Definition urule2expr : forall Γ Δ h j t (r:@Arrange _ h j) (ξ:VV -> LeveledHaskType Γ ★), + ujudg2exprType Γ ξ Δ h t -> + ujudg2exprType Γ ξ Δ j t + . + intros Γ Δ. + refine (fix urule2expr h j t (r:@Arrange _ h j) ξ {struct r} : + ujudg2exprType Γ ξ Δ h t -> + ujudg2exprType Γ ξ Δ j t := + match r as R in Arrange H C return + ujudg2exprType Γ ξ Δ H t -> + ujudg2exprType Γ ξ Δ C t + with + | RLeft h c ctx r => let case_RLeft := tt in (fun e => _) (urule2expr _ _ _ r) + | RRight h c ctx r => let case_RRight := tt in (fun e => _) (urule2expr _ _ _ r) + | RId a => let case_RId := tt in _ + | RCanL a => let case_RCanL := tt in _ + | RCanR a => let case_RCanR := tt in _ + | RuCanL a => let case_RuCanL := tt in _ + | RuCanR a => let case_RuCanR := tt in _ + | RAssoc a b c => let case_RAssoc := tt in _ + | RCossa a b c => let case_RCossa := tt in _ + | RExch a b => let case_RExch := tt in _ + | RWeak a => let case_RWeak := tt in _ + | RCont a => let case_RCont := tt in _ + | RComp a b c f g => let case_RComp := tt in (fun e1 e2 => _) (urule2expr _ _ _ f) (urule2expr _ _ _ g) end); clear urule2expr; intros. + destruct case_RId. + apply X. + destruct case_RCanL. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. - apply (X0 ([],,vars)). + simpl; unfold ujudg2exprType; intros. + simpl in X. + apply (X ([],,vars)). simpl; rewrite <- H; auto. destruct case_RCanR. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. - apply (X0 (vars,,[])). + simpl; unfold ujudg2exprType; intros. + simpl in X. + apply (X (vars,,[])). simpl; rewrite <- H; auto. destruct case_RuCanL. - apply ILeaf; simpl; intros. + simpl; unfold ujudg2exprType; intros. destruct vars; try destruct o; inversion H. - inversion X. - simpl in X0. - apply (X0 vars2); auto. + simpl in X. + apply (X vars2); auto. destruct case_RuCanR. - apply ILeaf; simpl; intros. + simpl; unfold ujudg2exprType; intros. destruct vars; try destruct o; inversion H. - inversion X. - simpl in X0. - apply (X0 vars1); auto. + simpl in X. + apply (X vars1); auto. destruct case_RAssoc. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. + simpl; unfold ujudg2exprType; intros. + simpl in X. destruct vars; try destruct o; inversion H. destruct vars1; try destruct o; inversion H. - apply (X0 (vars1_1,,(vars1_2,,vars2))). + apply (X (vars1_1,,(vars1_2,,vars2))). subst; auto. destruct case_RCossa. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. + simpl; unfold ujudg2exprType; intros. + simpl in X. destruct vars; try destruct o; inversion H. destruct vars2; try destruct o; inversion H. - apply (X0 ((vars1,,vars2_1),,vars2_2)). + apply (X ((vars1,,vars2_1),,vars2_2)). subst; auto. + destruct case_RExch. + simpl; unfold ujudg2exprType ; intros. + simpl in X. + destruct vars; try destruct o; inversion H. + apply (X (vars2,,vars1)). + inversion H; subst; auto. + + destruct case_RWeak. + simpl; unfold ujudg2exprType; intros. + simpl in X. + apply (X []). + auto. + + destruct case_RCont. + simpl; unfold ujudg2exprType ; intros. + simpl in X. + apply (X (vars,,vars)). + simpl. + rewrite <- H. + auto. + destruct case_RLeft. - destruct c; [ idtac | apply no_urules_with_multiple_conclusions in r0; inversion r0; exists c1; exists c2; auto ]. - destruct o; [ idtac | apply INone ]. - destruct u; simpl in *. - apply ILeaf; simpl; intros. + intro vars; unfold ujudg2exprType; intro H. destruct vars; try destruct o; inversion H. - set (fun q => ileaf (e ξ q)) as r'. - simpl in r'. - apply r' with (vars:=vars2). - clear r' e. - clear r0. - induction h0. - destruct a. - destruct u. + apply (fun q => e ξ q vars2 H2). + clear r0 e H2. simpl in X. - apply ileaf in X. - apply ILeaf. simpl. - simpl in X. + unfold ujudg2exprType. intros. apply X with (vars:=vars1,,vars). - simpl. rewrite H0. rewrite H1. + simpl. reflexivity. - apply INone. - apply IBranch. - apply IHh0_1. inversion X; auto. - apply IHh0_2. inversion X; auto. - auto. - + destruct case_RRight. - destruct c; [ idtac | apply no_urules_with_multiple_conclusions in r0; inversion r0; exists c1; exists c2; auto ]. - destruct o; [ idtac | apply INone ]. - destruct u; simpl in *. - apply ILeaf; simpl; intros. + intro vars; unfold ujudg2exprType; intro H. destruct vars; try destruct o; inversion H. - set (fun q => ileaf (e ξ q)) as r'. - simpl in r'. - apply r' with (vars:=vars1). - clear r' e. - clear r0. - induction h0. - destruct a. - destruct u. + apply (fun q => e ξ q vars1 H1). + clear r0 e H2. simpl in X. - apply ileaf in X. - apply ILeaf. simpl. - simpl in X. + unfold ujudg2exprType. intros. apply X with (vars:=vars,,vars2). - simpl. rewrite H0. - rewrite H2. + inversion H. + simpl. reflexivity. - apply INone. - apply IBranch. - apply IHh0_1. inversion X; auto. - apply IHh0_2. inversion X; auto. - auto. - destruct case_RExch. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. - destruct vars; try destruct o; inversion H. - apply (X0 (vars2,,vars1)). - inversion H; subst; auto. - - destruct case_RWeak. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. - apply (X0 []). - auto. - - destruct case_RCont. - apply ILeaf; simpl; intros. - inversion X. - simpl in X0. - apply (X0 (vars,,vars)). - simpl. - rewrite <- H. - auto. + destruct case_RComp. + apply e2. + apply e1. + apply X. Defined. - Definition bridge Γ Δ (c:Tree ??(UJudg Γ Δ)) ξ : - ITree Judg judg2exprType (mapOptionTree UJudg2judg c) -> ITree (UJudg Γ Δ) (ujudg2exprType ξ) c. - intro it. - induction c. - destruct a. - destruct u; simpl in *. - apply ileaf in it. - apply ILeaf. - simpl in *. - intros; apply it with (vars:=vars); auto. - apply INone. - apply IBranch; [ apply IHc1 | apply IHc2 ]; inversion it; auto. - Defined. - Definition letrec_helper Γ Δ l (varstypes:Tree ??(VV * HaskType Γ ★)) ξ' : ITree (LeveledHaskType Γ ★) (fun t : LeveledHaskType Γ ★ => Expr Γ Δ ξ' t) @@ -415,100 +381,137 @@ Section HaskProofToStrong. apply IHvarstypes2; inversion X; auto. Defined. - Definition case_helper tc Γ Δ lev tbranches avars ξ (Σ:Tree ??VV) : - forall pcb : ProofCaseBranch tc Γ Δ lev tbranches avars, - judg2exprType (pcb_judg pcb) -> - (pcb_freevars pcb) = mapOptionTree ξ Σ -> - FreshM - {scb : StrongCaseBranchWithVVs VV eqdec_vv tc avars & - Expr (sac_Γ scb Γ) (sac_Δ scb Γ avars (weakCK'' Δ)) - (scbwv_ξ scb ξ lev) (weakLT' (tbranches @@ lev))}. + Definition unindex_tree {V}{F} : forall {t:Tree ??V}, ITree V F t -> Tree ??{ v:V & F v }. + refine (fix rec t it := match it as IT return Tree ??{ v:V & F v } with + | INone => T_Leaf None + | ILeaf x y => T_Leaf (Some _) + | IBranch _ _ b1 b2 => (rec _ b1),,(rec _ b2) + end). + exists x; auto. + Defined. + + Definition fix_indexing X (F:X->Type)(J:X->Type)(t:Tree ??{ x:X & F x }) + : ITree { x:X & F x } (fun x => J (projT1 x)) t + -> ITree X (fun x:X => J x) (mapOptionTree (@projT1 _ _) t). + intro it. + induction it; simpl in *. + apply INone. + apply ILeaf. + apply f. + simpl; apply IBranch; auto. + Defined. - intros. + Definition fix2 {X}{F} : Tree ??{ x:X & FreshM (F x) } -> Tree ??(FreshM { x:X & F x }). + refine (fix rec t := match t with + | T_Leaf None => T_Leaf None + | T_Leaf (Some x) => T_Leaf (Some _) + | T_Branch b1 b2 => T_Branch (rec b1) (rec b2) + end). + destruct x as [x fx]. + refine (bind fx' = fx ; return _). + apply FreshMon. + exists x. + apply fx'. + Defined. + + Definition case_helper tc Γ Δ lev tbranches avars ξ : + forall pcb:{sac : StrongAltCon & ProofCaseBranch tc Γ Δ lev tbranches avars sac}, + 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)). + intro pcb. + intro X. simpl in X. - destruct pcb. + simpl. + destruct pcb as [sac pcb]. simpl in *. - set (sac_types pcb_scb _ avars) as boundvars. - refine (fresh_lemma' _ (unleaves (vec2list boundvars)) Σ (mapOptionTree weakLT' pcb_freevars) (weakLT' ○ ξ) (weakL' lev) _ - >>>= fun ξvars => _). apply FreshMon. - rewrite H. - rewrite <- mapOptionTree_compose. - reflexivity. - destruct ξvars as [ exprvars [pf1 [pf2 pfdistinct]]]. - set (list2vec (leaves (mapOptionTree (@fst _ _) exprvars))) as exprvars'. - - assert (distinct (vec2list exprvars')) as pfdistinct'. - unfold exprvars'. - rewrite vec2list_list2vec. - apply pfdistinct. - - assert (sac_numExprVars pcb_scb = Datatypes.length (leaves (mapOptionTree (@fst _ _) exprvars))) as H'. - rewrite <- mapOptionTree_compose in pf2. - simpl in pf2. - rewrite mapleaves. - rewrite <- map_preserves_length. - rewrite map_preserves_length with (f:= - (@update_ξ VV eqdec_vv (@sac_Γ tc pcb_scb Γ) - (@weakLT' Γ (@vec2list (@sac_numExTyVars tc pcb_scb) Kind (@sac_ekinds tc pcb_scb)) ★ ○ ξ) - (@weakL' Γ (@vec2list (@sac_numExTyVars tc pcb_scb) Kind (@sac_ekinds tc pcb_scb)) lev) - (@leaves (VV * HaskType (@sac_Γ tc pcb_scb Γ) ★) exprvars) ○ @fst VV (HaskType (@sac_Γ tc pcb_scb Γ) ★))). - rewrite <- mapleaves. - rewrite pf2. - rewrite <- mapleaves'. - rewrite leaves_unleaves. - rewrite vec2list_map_list2vec. - rewrite vec2list_len. - reflexivity. - - clear pfdistinct'. - rewrite <- H' in exprvars'. - clear H'. - assert (distinct (vec2list exprvars')) as pfdistinct'. - admit. - - set (@Build_StrongCaseBranchWithVVs VV _ tc _ avars pcb_scb exprvars' pfdistinct') as scb. - set (scbwv_ξ scb ξ lev) as ξ'. - refine (X ξ' (Σ,,(unleaves (vec2list exprvars'))) _ >>>= fun X' => return _). apply FreshMon. + + destruct X. + destruct s as [vars vars_pf]. + + refine (bind localvars = fresh_lemma' _ (unleaves (vec2list (sac_types sac _ avars))) vars + (mapOptionTree weakLT' (pcb_freevars pcb)) (weakLT' ○ ξ) (weakL' lev) _ ; _). + apply FreshMon. + rewrite vars_pf. + rewrite <- mapOptionTree_compose. + reflexivity. + destruct localvars as [localvars [localvars_pf1 [localvars_pf2 localvars_dist ]]]. + set (mapOptionTree (@fst _ _) localvars) as localvars'. + + set (list2vec (leaves localvars')) as localvars''. + cut (length (leaves localvars') = sac_numExprVars sac). intro H''. + rewrite H'' in localvars''. + 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 _). + apply FreshMon. simpl. - unfold ξ'. unfold scbwv_ξ. + rewrite vars_pf. + rewrite <- mapOptionTree_compose. + clear localvars_pf1. simpl. - admit. - - apply ileaf in X'. - simpl in X'. - exists scb. - unfold weakCK''. - unfold ξ' in X'. - apply X'. - Defined. + rewrite mapleaves'. - Fixpoint treeM {T}(t:Tree ??(FreshM T)) : FreshM (Tree ??T) := - match t with - | T_Leaf None => return [] - | T_Leaf (Some x) => bind x' = x ; return [x'] - | T_Branch b1 b2 => bind b1' = treeM b1 ; bind b2' = treeM b2 ; return (b1',,b2') - end. + admit. + + exists scb. + apply ileaf in q. + apply q. - Lemma itree_mapOptionTree : forall T T' F (f:T->T') t, - ITree _ F (mapOptionTree f t) -> - ITree _ (F ○ f) t. + admit. + admit. + Defined. + + Definition gather_branch_variables + Γ Δ (ξ:VV -> LeveledHaskType Γ ★) tc avars tbranches lev (alts:Tree ?? {sac : StrongAltCon & + ProofCaseBranch tc Γ Δ lev tbranches avars sac}) + : + forall vars, + mapOptionTreeAndFlatten (fun x => pcb_freevars(Γ:=Γ) (projT2 x)) alts = mapOptionTree ξ vars + -> ITree Judg judg2exprType (mapOptionTree (fun x => pcb_judg (projT2 x)) alts) + -> ITree _ (fun q => prod (judg2exprType (pcb_judg (projT2 q))) + { vars' : _ & pcb_freevars (projT2 q) = mapOptionTree ξ vars' }) + alts. + induction alts; + intro vars; + intro pf; + intro source. + destruct a; [ idtac | apply INone ]. + simpl in *. + apply ileaf in source. + apply ILeaf. + destruct s as [sac pcb]. + simpl in *. + split. intros. - induction t; try destruct a; simpl in *. - apply ILeaf. - inversion X; auto. - apply INone. - apply IBranch. - apply IHt1; inversion X; auto. - apply IHt2; inversion X; auto. - Defined. + eapply source. + apply H. + clear source. + + exists vars. + auto. + + simpl in pf. + destruct vars; try destruct o; simpl in pf; inversion pf. + simpl in source. + inversion source. + subst. + apply IBranch. + apply (IHalts1 vars1 H0 X); auto. + apply (IHalts2 vars2 H1 X0); auto. + + Defined. + Definition rule2expr : forall h j (r:Rule h j), ITree _ judg2exprType h -> ITree _ judg2exprType j. intros h j r. refine (match r as R in Rule H C return ITree _ judg2exprType H -> ITree _ judg2exprType C with - | RURule a b c d e => let case_RURule := tt in _ + | RArrange a b c d e r => let case_RURule := tt in _ | RNote Γ Δ Σ τ l n => let case_RNote := tt in _ | RLit Γ Δ l _ => let case_RLit := tt in _ | RVar Γ Δ σ p => let case_RVar := tt in _ @@ -521,27 +524,26 @@ Section HaskProofToStrong. | RAbsCo Γ Δ Σ κ σ σ₁ σ₂ y => let case_RAbsCo := tt in _ | RApp Γ Δ Σ₁ Σ₂ tx te p => let case_RApp := tt in _ | RLet Γ Δ Σ₁ Σ₂ σ₁ σ₂ p => let case_RLet := tt in _ - | RBindingGroup Γ p lri m x q => let case_RBindingGroup := tt in _ - | REmptyGroup _ _ => let case_REmptyGroup := tt in _ + | RJoin Γ p lri m x q => let case_RJoin := tt in _ + | RVoid _ _ => let case_RVoid := tt in _ | RBrak Σ a b c n m => let case_RBrak := tt in _ | REsc Σ a b c n m => let case_REsc := tt in _ | RCase Γ Δ lev tc Σ avars tbranches alts => let case_RCase := tt in _ | RLetRec Γ Δ lri x y t => let case_RLetRec := tt in _ end); intro X_; try apply ileaf in X_; simpl in X_. - destruct case_RURule. - destruct d; try destruct o. - apply ILeaf; destruct u; simpl; intros. - set (@urule2expr a b _ _ e ξ) as q. - set (fun z => ileaf (q z)) as q'. + destruct case_RURule. + apply ILeaf. simpl. intros. + set (@urule2expr a b _ _ e r0 ξ) as q. + set (fun z => q z) as q'. simpl in q'. apply q' with (vars:=vars). clear q' q. - apply bridge. - apply X_. + unfold ujudg2exprType. + intros. + apply X_ with (vars:=vars0). + auto. auto. - apply no_urules_with_empty_conclusion in e; inversion e; auto. - apply no_urules_with_multiple_conclusions in e; inversion e; auto; exists d1; exists d2; auto. destruct case_RBrak. apply ILeaf; simpl; intros; refine (X_ ξ vars H >>>= fun X => return ILeaf _ _). apply FreshMon. @@ -571,7 +573,6 @@ Section HaskProofToStrong. destruct case_RGlobal. apply ILeaf; simpl; intros; refine (return ILeaf _ _). apply EGlobal. - apply wev. destruct case_RLam. apply ILeaf. @@ -579,7 +580,7 @@ Section HaskProofToStrong. 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_ξ ξ x (((vnew, tx )) :: nil)) as ξ' in *. refine (X_ ξ' (vars,,[vnew]) _ >>>= _). apply FreshMon. simpl. @@ -603,7 +604,7 @@ Section HaskProofToStrong. apply ileaf in X. simpl in X. apply X. - destruct case_RBindingGroup. + destruct case_RJoin. apply ILeaf; simpl; intros. inversion X_. apply ileaf in X. @@ -635,7 +636,7 @@ Section HaskProofToStrong. apply ileaf in q1'. apply ileaf in q2'. simpl in *. - apply (EApp _ _ _ _ _ _ q1' q2'). + apply (EApp _ _ _ _ _ _ q2' q1'). destruct case_RLet. apply ILeaf. @@ -644,15 +645,16 @@ Section HaskProofToStrong. refine (fresh_lemma _ ξ vars1 _ σ₂ p H1 >>>= (fun pf => _)). apply FreshMon. destruct pf as [ vnew [ pf1 pf2 ]]. - set (update_ξ ξ p ((⟨vnew, σ₂ ⟩) :: nil)) as ξ' in *. + set (update_ξ ξ p (((vnew, σ₂ )) :: nil)) as ξ' in *. inversion X_. apply ileaf in X. apply ileaf in X0. simpl in *. - refine (X0 ξ vars2 _ >>>= fun X0' => _). + refine (X ξ vars2 _ >>>= fun X0' => _). apply FreshMon. auto. - refine (X ξ' (vars1,,[vnew]) _ >>>= fun X1' => _). + + refine (X0 ξ' (vars1,,[vnew]) _ >>>= fun X1' => _). apply FreshMon. rewrite H1. simpl. @@ -660,6 +662,7 @@ Section HaskProofToStrong. rewrite pf1. rewrite H1. reflexivity. + refine (return _). apply ILeaf. apply ileaf in X0'. @@ -669,7 +672,7 @@ Section HaskProofToStrong. apply X0'. apply X1'. - destruct case_REmptyGroup. + destruct case_RVoid. apply ILeaf; simpl; intros. refine (return _). apply INone. @@ -715,6 +718,7 @@ Section HaskProofToStrong. inversion X; subst; clear X. apply (@ELetRec _ _ _ _ _ _ _ varstypes). + auto. apply (@letrec_helper Γ Δ t varstypes). rewrite <- pf2 in X1. rewrite mapOptionTree_compose. @@ -729,38 +733,41 @@ Section HaskProofToStrong. subst. apply ileaf in X0. simpl in X0. - set (mapOptionTreeAndFlatten pcb_freevars alts) as Σalts in *. - refine (bind ξvars = fresh_lemma' _ (mapOptionTree unlev (Σalts,,Σ)) _ _ _ lev H ; _). - apply FreshMon. - destruct vars; try destruct o; inversion H; clear H. - rename vars1 into varsalts. - rename vars2 into varsΣ. - refine ( _ >>>= fun Y => X0 ξ varsΣ _ >>>= fun X => return ILeaf _ (@ECase _ _ _ _ _ _ _ _ _ (ileaf X) Y)); auto. + (* body_freevars and alts_freevars are the types of variables in the body and alternatives (respectively) which are free + * from the viewpoint just outside the case block -- i.e. not bound by any of the branches *) + rename Σ into body_freevars_types. + rename vars into all_freevars. + rename X0 into body_expr. + rename X into alts_exprs. + + destruct all_freevars; try destruct o; inversion H. + rename all_freevars2 into body_freevars. + rename all_freevars1 into alts_freevars. + + set (gather_branch_variables _ _ _ _ _ _ _ _ _ H1 alts_exprs) as q. + set (itmap (fun pcb alt_expr => case_helper tc Γ Δ lev tbranches avars ξ pcb alt_expr) q) as alts_exprs'. + apply fix_indexing in alts_exprs'. + simpl in alts_exprs'. + apply unindex_tree in alts_exprs'. + simpl in alts_exprs'. + apply fix2 in alts_exprs'. + apply treeM in alts_exprs'. + + refine ( alts_exprs' >>>= fun Y => + body_expr ξ _ _ + >>>= fun X => return ILeaf _ (@ECase _ _ _ _ _ _ _ _ _ (ileaf X) Y)); auto. apply FreshMon. - destruct ξvars as [varstypes [pf1 pf2]]. - - apply treeM. - apply itree_mapOptionTree in X. - refine (itree_to_tree (itmap _ X)). - intros. - eapply case_helper. - apply X1. - instantiate (1:=varsΣ). - rewrite <- H2. - admit. apply FreshMon. + apply H2. Defined. - Definition closed2expr : forall c (pn:@ClosedND _ Rule c), ITree _ judg2exprType c. - refine (( - fix closed2expr' j (pn:@ClosedND _ Rule j) {struct pn} : ITree _ judg2exprType j := - match pn in @ClosedND _ _ J return ITree _ judg2exprType J with - | cnd_weak => let case_nil := tt in INone _ _ - | cnd_rule h c cnd' r => let case_rule := tt in rule2expr _ _ r (closed2expr' _ cnd') - | cnd_branch _ _ c1 c2 => let case_branch := tt in IBranch _ _ (closed2expr' _ c1) (closed2expr' _ c2) - end)); clear closed2expr'; intros; subst. - Defined. + Fixpoint closed2expr h j (pn:@SIND _ Rule h j) {struct pn} : ITree _ judg2exprType h -> ITree _ judg2exprType j := + match pn in @SIND _ _ H J return ITree _ judg2exprType H -> ITree _ judg2exprType J with + | scnd_weak _ => let case_nil := tt in fun _ => INone _ _ + | scnd_comp x h c cnd' r => let case_rule := tt in fun q => rule2expr _ _ r (closed2expr _ _ cnd' q) + | scnd_branch _ _ _ c1 c2 => let case_branch := tt in fun q => IBranch _ _ (closed2expr _ _ c1 q) (closed2expr _ _ c2 q) + end. Lemma manyFresh : forall Γ Σ (ξ0:VV -> LeveledHaskType Γ ★), FreshM { vars : _ & { ξ : VV -> LeveledHaskType Γ ★ & Σ = mapOptionTree ξ vars } }. @@ -798,7 +805,7 @@ Section HaskProofToStrong. {zz:ToString VV} : ND Rule [] [Γ > Δ > Σ |- [τ]] -> FreshM (???{ ξ : _ & Expr Γ Δ ξ τ}). intro pf. - set (closedFromSCND _ _ (mkSCND systemfc_all_rules_one_conclusion _ _ _ pf (scnd_weak [])) cnd_weak) as cnd. + set (mkSIND systemfc_all_rules_one_conclusion _ _ _ pf (scnd_weak [])) as cnd. apply closed2expr in cnd. apply ileaf in cnd. simpl in *. @@ -813,6 +820,7 @@ Section HaskProofToStrong. refine (return OK _). exists ξ. apply (ileaf it). + apply INone. Defined. End HaskProofToStrong.