# HG changeset patch # User Shinji KONO # Date 1615703516 -32400 # Node ID 0e87089e5de464a8e8e4b9cef15949727c50a6a5 # Parent 6835096cfa3aa79a2f82738d70ae3d555d5cc427 ..` diff -r 6835096cfa3a -r 0e87089e5de4 agda/halt.agda --- a/agda/halt.agda Sun Mar 14 08:27:05 2021 +0900 +++ b/agda/halt.agda Sun Mar 14 15:31:56 2021 +0900 @@ -42,12 +42,12 @@ -- ¬ A = A → ⊥ -diag : (b : Bijection ( ℕ → Bool ) ℕ) → ℕ → Bool +diag : {S : Set } (b : Bijection ( S → Bool ) S) → S → Bool diag b n = not (fun← b n n) -diagonal : ¬ Bijection ( ℕ → Bool ) ℕ -diagonal b = diagn1 (fun→ b (diag b) ) refl where - diagn1 : (n : ℕ ) → ¬ (fun→ b (diag b) ≡ n ) +diagonal : { S : Set } → ¬ Bijection ( S → Bool ) S +diagonal {S} b = diagn1 (fun→ b (diag b) ) refl where + diagn1 : (n : S ) → ¬ (fun→ b (diag b) ≡ n ) diagn1 n dn = ¬t=f (diag b n ) ( begin not (diag b n) ≡⟨⟩ @@ -172,8 +172,8 @@ lbisor [] = refl lbisor (false ∷ []) = refl lbisor (true ∷ []) = refl - lbisor (false ∷ true ∷ t) = ? - lbisor (false ∷ false ∷ t) = ? + lbisor (false ∷ true ∷ t) = {!!} + lbisor (false ∷ false ∷ t) = {!!} lbisor (true ∷ x ∷ t) = {!!} @@ -204,7 +204,7 @@ tmb1 x with is-tm x | inspect is-tm x ... | refl | record { eq = refl } = tm-cong (is-tm x) refl refl -TNℕ : Bijection TM ℕ +TNℕ : Halt → Bijection (TM → Bool) TM TNℕ = {!!} -- Halt1 (Halt2 x) ≡ x