PLT-A3 Maybe Monad

Transcript

1. pineapple.cc ۚ୩Ұ࿕ʢ௕࡚େֶ৘ใσʔλՊֶ෦ʣ ʲิʳ.BZCFϞφυ ϓϩάϥϛϯάݴޠ࿦
2. pineapple.cc Value Func Value’ x′  = fx
3. pineapple.cc Value Func Value’ Func3 Func2 Func1 • • x′  = (h ∙ g ∙ f)x
4. pineapple.cc Value Func Value’ x′  = fx Float
5. pineapple.cc 1 0 = ?
7. pineapple.cc θϩআࢉ΁ͷରԠ w ϓϩάϥϜΛҟৗऴྃͤ͞Δʢྫ֎Λൃੜͤ͞Δʣ
   w ༗ཧ਺શମɼ࣮਺શମΑΓ΋ʮ޿͍ʯू߹Λ࢖͏
   w *O fi OJUZͱ͍͏஋ʹ͢Δ
   w /B/
   /PU
   B
   /VNCFS ͱ͍͏஋ʹ͢Δ
   w ൚༻తͳ࿮૊ΈΛ࢖͏
8. pineapple.cc 1 0 = ?
9. pineapple.cc fx ≡ 1/x
10. pineapple.cc f :: Float -> Float f x = 1.0/x
11. pineapple.cc fx ≡ { 1/x if x ≠ 0 ∅ otherwise
12. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise
13. pineapple.cc f :: Float -> Float f x = 1/x f :: Float -> Maybe Float f x = if x /= 0 then Just (1/x) else Nothing
14. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise
15. pineapple.cc fx ≡ { [1/x] if x ≠ 0 [] otherwise
16. pineapple.cc f :: Float -> Maybe Float f x = if x /= 0 then Just (1/x) else Nothing f :: Float -> [Float] f x = if x /= 0 then [1/x] else []
17. pineapple.cc Value Func Value’ x′  = fx Maybe Float Float
18. pineapple.cc Value Func’ Value’ x′  = f′  x Maybe Float Maybe Float
19. pineapple.cc f′  x ≡ { ⟨1/x⟩ if x ≠ ∅ and x ≠ 0 ∅ otherwise
20. pineapple.cc Value Func Value’ Func3 Func2 Func1 • • x′  = (h ∙ g ∙ f)x
21. pineapple.cc Value Func’ Value’ Func3 Func2 Func1 • • x′  = (h ∘ g ∘ f)x
22. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise
23. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise gx ≡ 2.0 × x
24. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise gx ≡ 2.0 × x g′  x ≡ ⟨gx⟩
25. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise gx ≡ 2.0 × x g′  x ≡ ⟨gx⟩ x′  ≡ (g′  ∘ f)x
26. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ 0 ∅ otherwise gx ≡ 2.0 × x g′  x ≡ ⟨gx⟩ x′  ≡ ⟨x⟩ ↣ f ↣ g′ 
27. pineapple.cc f :: Float -> Maybe Float f x = if x /= 0 then Just (1/x) else Nothing g :: Float -> Float g x = 2.0*x g’ :: Float -> Maybe Float g’ x = Just (g x) x’ = Just 2 >>= f >>= g’
28. pineapple.cc f :: Float -> Maybe Float f x = if x /= 0 then Just (1/x) else Nothing g :: Float -> Float g x = 2.0*x x’ = (liftM g . f) x ผղ
29. pineapple.cc fx ≡ { ⟨1/x⟩ if x ≠ ∅ and x ≠ 0 ∅ otherwise gx ≡ 2.0 × x x′  ≡ (g* ∙ f)x ผղ