PLT-X1 Division by Zero and Maybe

Transcript

1. pineapple.cc ۚ୩Ұ࿕ʢ௕࡚େֶ৘ใσʔλՊֶ෦ʣ θϩআࢉͱ.BZCF ϓϩάϥϛϯάݴޠ࿦
2. pineapple.cc 1 0 = ?
4. 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࢖͏
5. pineapple.cc 1 0 = ?
6. pineapple.cc a ∈ ℤ b ∈ ℚ a = user_input b = 1 a
7. pineapple.cc b⋆ ∈ {∅} ∪ ℚ
8. pineapple.cc a ∈ ℤ b⋆ ∈ {∅} ∪ ℚ a = user_input b⋆ = { 1 a where a ≠ 0 ∅ otherwise
9. pineapple.cc M 𝔸 ≜ {∅} ∪ 𝔸
10. pineapple.cc a ∈ ℤ b⋆ ∈ M ℚ a = user_input b⋆ = { 1 a where a ≠ 0 ∅ otherwise
11. pineapple.cc b⋆, c⋆ ∈ M ℚ b⋆ + c⋆ = { b + c where b⋆ ≠ ∅ ∧ c⋆ ≠ ∅ ∅ otherwise
12. pineapple.cc b⋆, c⋆ ∈ M ℚ b⋆ + c⋆ = { b + c where b⋆ ≠ ∅ ∧ c⋆ ≠ ∅ ∅ otherwise M ℚ ℚ
13. pineapple.cc x ∈ 𝔸 Jx ∈ M 𝔸 Jx = x b⋆, c⋆ ∈ M ℚ b⋆ + c⋆ = { J(b + c) where b⋆ ≠ ∅ ∧ c⋆ ≠ ∅ ∅ otherwise ܕίϯετϥΫλ ஋ίϯετϥΫλ
14. pineapple.cc x0 = 0 x1 = 1 x2 = 2 x′  = [x0 , x1 , x2]
15. pineapple.cc xi ∈ ℝ x′  ∈ [ℝ]
16. pineapple.cc xi ∈ ℝ x′  ∈ [ℝ] = L ℝ = [] ℝ ܕίϯετϥΫλ ܕίϯετϥΫλ
17. pineapple.cc x′  = [x0 , x1 , x2] y′  = [y0 , y1 , y2 , y3] z′  = x′  #y′  = [x0 , x1 , x2 , y0 , y1 , y2 , y3] ஋ίϯετϥΫλ
18. pineapple.cc x′  = [x0 , x1 , x2] y′  = [ ] z′  = x′  #y′  = [x0 , x1 , x2] ஋ίϯετϥΫλ
19. pineapple.cc Maybe/Optional ഑ྻ ҰൠԽ جຊܕ A A A ܕ {∅}∪A [A] *1 ܕίϯετϥΫλ M A Maybe A L A List A, [] A, [A] F A F A ஋ίϯετϥΫλ J x, ∅ Just x, Nothing [x], [ ] [x], [] V x V x *1 Functor Lawʹै͏೚ҙͷܕ