[(F#における)Modus Ponens と Cut]
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Transcript of [(F#における)Modus Ponens と Cut]
![Page 1: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/1.jpg)
[(F#における)Modus Ponensと Cut ]
Nobuhisa Koizumi
![Page 2: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/2.jpg)
Profile
• ハイパーK泉さん
• 近況:ピーナッツ
![Page 3: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/3.jpg)
[(F#における)Modus Ponensと Cut ]
Nobuhisa Koizumi
![Page 4: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/4.jpg)
Modus Ponens
![Page 5: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/5.jpg)
Modus Ponens
A → A → B → B
A A → B
B
A → (A → B) → B
(A → B) → B
※ A ⋀ A → B → B
![Page 6: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/6.jpg)
Modus Ponens
A → A → B → B
> 1 |> (fun x -> (x, x)) ;;val it : int * int = (1, 1)
![Page 7: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/7.jpg)
Modus Ponens
A → A → B → B
> 1 |> (fun x -> (x, x)) ;;val it : int * int = (1, 1)
> ( |> ) ;;val it : ('a -> ('a -> 'b) -> 'b) = <fun:it@21-2>
![Page 8: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/8.jpg)
[(F#における)Modus Ponensと Cut ]
Nobuhisa Koizumi
![Page 9: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/9.jpg)
Cut
Γ → Δ, 𝐴 𝐴, Π → ∑
Γ, Π → Δ,∑
![Page 10: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/10.jpg)
Cut
(A → B) → B → C → (A → C)
A A → B
B
(B → C) → (A → C)
※ A → B ⋀ B → C → (A → C)
Γ → Δ, 𝐴 𝐴, Π → ∑
Γ, Π → Δ,∑
B → C
C
A → C
(A → B) → (B → C) → (A → C)
![Page 11: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/11.jpg)
Cut
(A → B) → B → C → (A → C)
> (1, 2) |> (fst >> float) ;;val it : float = 1.0
![Page 12: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/12.jpg)
Cut
(A → B) → B → C → (A → C)
> (1, 2) |> (fst >> float) ;;val it : float = 1.0
> ( >> ) ;;val it : (('a -> 'b) -> ('b -> 'c) -> 'a -> 'c) = <fun:it@30-5>
![Page 13: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/13.jpg)
カリー・ハワード同型対応(Curry–Howard isomorphism)
命題論理 ↔ 型付きラムダ計算
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“37221” 事件
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F# 37221
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F# 37221
ダメ!ゼッタイ!
![Page 17: [(F#における)Modus Ponens と Cut]](https://reader030.fdocument.pub/reader030/viewer/2022020116/559e02a11a28ab1e6a8b46c1/html5/thumbnails/17.jpg)
[(F#における)Modus Ponensと Cut ]
Nobuhisa Koizumi
おしまい