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| Original file line number | Diff line number | Diff line change |
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| @@ -1,8 +1,24 @@ | ||
| import DeBruijnSSA.BinSyntax.Rewrite.Region.Structural.Gloop | ||
| import DeBruijnSSA.BinSyntax.Rewrite.Region.Structural.Letc | ||
| import DeBruijnSSA.BinSyntax.Rewrite.Region.Structural.Sum | ||
| import DeBruijnSSA.BinSyntax.Rewrite.Region.Compose.Elgot | ||
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| namespace BinSyntax | ||
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| variable [Φ: EffInstSet φ (Ty α) ε] [PartialOrder α] [SemilatticeSup ε] [OrderBot ε] | ||
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| namespace Region | ||
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| def Eqv.fixpoint_def' {A B : Ty α} {Γ : Ctx α ε} {L : LCtx α} (f : Eqv φ (⟨A, ⊥⟩::Γ) ((B.coprod A)::L)) | ||
| : Eqv φ (⟨A, ⊥⟩::Γ) (B::L) := letc A nil (f.vwk1.lwk1 ;; left_exit) | ||
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| theorem Eqv.letc_to_vwk1 {Γ : Ctx α ε} {L : LCtx α} {A : Ty α} {β : Eqv φ ((B, ⊥)::Γ) (A::L)} {G} | ||
| : letc A β G = letc (B.prod A) | ||
| (ret Term.Eqv.split ;; _ ⋊ β) | ||
| ((ret Term.Eqv.split ⋉ _ ;; assoc ;; _ ⋊ (let2 (Term.Eqv.var 0 Ctx.Var.shead) G.vwk2)).vwk1) | ||
| := by | ||
| sorry | ||
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| theorem Eqv.letc_vwk1_den {Γ : Ctx α ε} | ||
| {A B : Ty α} {β : Eqv φ ((X, ⊥)::Γ) [A, B]} {G : Eqv φ ((A, ⊥)::Γ) [A, B]} | ||
| : letc A β G.vwk1 = β.packed_out ;; fixpoint (coprod (coprod zero inj_l) (G.packed_out ;; inj_r)) | ||
| := sorry |
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DeBruijnSSA/BinSyntax/Rewrite/Region/Structural/Gloop.lean
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DeBruijnSSA/BinSyntax/Rewrite/Region/Structural/Letc.lean
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,102 @@ | ||
| import DeBruijnSSA.BinSyntax.Rewrite.Region.Compose.Seq | ||
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| namespace BinSyntax | ||
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| variable [Φ: EffInstSet φ (Ty α) ε] [PartialOrder α] [SemilatticeSup ε] [OrderBot ε] | ||
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| namespace Region | ||
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| def Eqv.letc {Γ : Ctx α ε} {L : LCtx α} | ||
| (A : Ty α) (β : Eqv φ Γ (A::L)) (G : Eqv φ ((A, ⊥)::Γ) (A::L)) : Eqv φ Γ L | ||
| := Eqv.cfg [A] β (Fin.elim1 G) | ||
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| theorem Eqv.cfg_eq_letc {Γ : Ctx α ε} {L : LCtx α} {A : Ty α} {β : Eqv φ Γ (A::L)} {G} | ||
| : Eqv.cfg [A] β G = β.letc A (G (0 : Fin 1)) := rfl | ||
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| @[simp] | ||
| theorem Eqv.vwk_letc {Γ Δ : Ctx α ε} {L : LCtx α} | ||
| {A : Ty α} {β : Eqv φ Δ (A::L)} {G : Eqv φ ((A, ⊥)::Δ) (A::L)} {ρ : Γ.InS Δ} | ||
| : (β.letc A G).vwk ρ = (β.vwk ρ).letc A (G.vwk ρ.slift) | ||
| := by rw [letc, vwk_cfg]; rfl | ||
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| @[simp] | ||
| theorem Eqv.vsubst_letc {Γ Δ : Ctx α ε} {L : LCtx α} | ||
| {A : Ty α} {β : Eqv φ Δ (A::L)} {G : Eqv φ ((A, ⊥)::Δ) (A::L)} {σ : Term.Subst.Eqv φ Γ Δ} | ||
| : (β.letc A G).vsubst σ = (β.vsubst σ).letc A (G.vsubst (σ.lift (le_refl _))) | ||
| := by rw [letc, vsubst_cfg]; rfl | ||
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| @[simp] | ||
| theorem Eqv.lwk_letc {Γ : Ctx α ε} {L K : LCtx α} | ||
| {A : Ty α} {β : Eqv φ Γ (A::L)} {G : Eqv φ ((A, ⊥)::Γ) (A::L)} {ρ : L.InS K} | ||
| : (β.letc A G).lwk ρ = (β.lwk ρ.slift).letc A (G.lwk ρ.slift) := by | ||
| rw [letc, lwk_cfg] | ||
| congr | ||
| · ext k; simp [Nat.liftnWk_one] | ||
| · ext i; cases i using Fin.elim1 | ||
| simp only [Fin.elim1_zero] | ||
| congr; ext k; simp [Nat.liftnWk_one] | ||
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| @[simp] | ||
| theorem Eqv.lsubst_letc {Γ : Ctx α ε} {L K : LCtx α} | ||
| {A : Ty α} {β : Eqv φ Γ (A::L)} {G : Eqv φ ((A, ⊥)::Γ) (A::L)} {σ : Subst.Eqv φ Γ L K} | ||
| : (β.letc A G).lsubst σ = (β.lsubst σ.slift).letc A (G.lsubst σ.slift.vlift) | ||
| := by rw [letc, lsubst_cfg, Subst.Eqv.liftn_append_singleton]; rfl | ||
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| theorem Eqv.dinaturality_from_letc {Γ : Ctx α ε} {R L : LCtx α} | ||
| {σ : Subst.Eqv φ Γ R ([B] ++ L)} {β : Eqv φ Γ (R ++ L)} | ||
| {G : Eqv φ (⟨B, ⊥⟩::Γ) (R ++ L)} | ||
| : letc B (β.lsubst σ.extend_in) (G.lsubst σ.extend_in.vlift) | ||
| = cfg R β (λi => (σ.get i).lsubst (Subst.Eqv.fromFCFG_append (L := [B]) (Fin.elim1 G)).vlift) | ||
| := dinaturality (Γ := Γ) (R := R) (R' := [B]) (L := L) (σ := σ) (β := β) (G := Fin.elim1 G) | ||
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| theorem Eqv.dinaturality_from_letc_rec {Γ : Ctx α ε} {R L : LCtx α} | ||
| {σ : Subst.Eqv φ Γ R [B]} {β : Eqv φ Γ (R ++ L)} | ||
| {G : Eqv φ (⟨B, ⊥⟩::Γ) (R ++ L)} | ||
| : letc B (β.lsubst σ.extend) (G.lsubst σ.extend.vlift) | ||
| = cfg R β (λi => (σ.get i).lsubst (Subst.Eqv.fromFCFG (Fin.elim1 G)).vlift) | ||
| := dinaturality_rec (Γ := Γ) (R := R) (R' := [B]) (L := L) (σ := σ) (β := β) (G := Fin.elim1 G) | ||
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| theorem Eqv.dinaturality_to_letc {Γ : Ctx α ε} {R' L : LCtx α} | ||
| {σ : Subst.Eqv φ Γ [A] (R' ++ L)} {β : Eqv φ Γ (A::L)} | ||
| {G : (i : Fin R'.length) → Eqv φ (⟨R'.get i, ⊥⟩::Γ) ([A] ++ L)} | ||
| : cfg R' (β.lsubst σ.extend_in) (λi => (G i).lsubst σ.extend_in.vlift) | ||
| = letc A β ((σ.get (0 : Fin 1)).lsubst (Subst.Eqv.fromFCFG_append G).vlift) | ||
| := dinaturality (Γ := Γ) (R := [A]) (R' := R') (L := L) (σ := σ) (β := β) (G := G) | ||
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| theorem Eqv.dinaturality_to_letc_rec {Γ : Ctx α ε} {R' L : LCtx α} | ||
| {σ : Subst.Eqv φ Γ [A] R'} {β : Eqv φ Γ (A::L)} | ||
| {G : (i : Fin R'.length) → Eqv φ (⟨R'.get i, ⊥⟩::Γ) ([A] ++ L)} | ||
| : cfg R' (β.lsubst σ.extend) (λi => (G i).lsubst σ.extend.vlift) | ||
| = letc A β ((σ.get (0 : Fin 1)).lsubst (Subst.Eqv.fromFCFG G).vlift) | ||
| := dinaturality_rec (Γ := Γ) (R := [A]) (R' := R') (L := L) (σ := σ) (β := β) (G := G) | ||
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| theorem Eqv.dinaturality_letc {Γ : Ctx α ε} {L : LCtx α} | ||
| {σ : Subst.Eqv φ Γ [A] ([B] ++ L)} {β : Eqv φ Γ (A::L)} | ||
| {G : Eqv φ (⟨B, ⊥⟩::Γ) (A::L)} | ||
| : letc B (β.lsubst σ.extend_in) (G.lsubst σ.extend_in.vlift) | ||
| = letc A β ((σ.get (0 : Fin 1)).lsubst | ||
| (Subst.Eqv.fromFCFG_append (K := [A]) (Fin.elim1 G)).vlift) | ||
| := dinaturality (Γ := Γ) (R := [A]) (R' := [B]) (L := L) (σ := σ) (β := β) (G := Fin.elim1 G) | ||
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| theorem Eqv.uniform_letc {Γ : Ctx α ε} {L : LCtx α} | ||
| {β : Eqv φ Γ (A::L)} {e : Term.Eqv φ ((A, ⊥)::Γ) (B, ⊥)} | ||
| {r : Eqv φ ((B, ⊥)::Γ) (B::L)} {s : Eqv φ ((A, ⊥)::Γ) (A::L)} | ||
| (hrs : (ret e) ;; r = s ;; (ret e)) : letc B (β.wrseq (ret e)) r = letc A β s := Eqv.uniform hrs | ||
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| theorem Eqv.wrseq_letc_vwk1 {B C : Ty α} {Γ : Ctx α ε} {L : LCtx α} | ||
| {f : Eqv φ Γ (B::L)} {g : Eqv φ (⟨B, ⊥⟩::Γ) (C::D::L)} | ||
| {h : Eqv φ (⟨C, ⊥⟩::Γ) (C::D::L)} | ||
| : f.wrseq (letc C g h.vwk1) = letc C (f.lwk1.wrseq g) h | ||
| := wrseq_cont f g h | ||
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| theorem Eqv.seq_letc_vwk1 {A B C : Ty α} {Γ : Ctx α ε} {L : LCtx α} | ||
| {f : Eqv φ (⟨A, ⊥⟩::Γ) (B::L)} {g : Eqv φ (⟨B, ⊥⟩::Γ) (C::D::L)} | ||
| {h : Eqv φ (⟨C, ⊥⟩::Γ) (C::D::L)} | ||
| : f ;; letc C g h.vwk1 = letc C (f.lwk1 ;; g) h.vwk1 | ||
| := seq_cont f g h | ||
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| theorem Eqv.seq_ret_letc_vwk1 {A B C : Ty α} {Γ : Ctx α ε} {L : LCtx α} | ||
| {f : Term.Eqv φ (⟨A, ⊥⟩::Γ) (B, ⊥)} {g : Eqv φ (⟨B, ⊥⟩::Γ) (C::D::L)} | ||
| {h : Eqv φ (⟨C, ⊥⟩::Γ) (C::D::L)} | ||
| : ret f ;; letc C g h.vwk1 = letc C (ret f ;; g) h.vwk1 | ||
| := by rw [seq_letc_vwk1, lwk1_ret] |
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