A Number by Any Other Name

In 1999, NASA's Mars Climate Orbiter crashed into the red planet as it was
trying to enter orbit. The problem? Two pieces of software were using different
units in their calculations.

If you've ever calculated a wrong value because you forgot to convert seconds
into hours or because you accidentally inverted two number arguments in a
function, then you've encountered this same bug.

Join me as we leverage Elm's type system to catch these bugs, get better
error messages, and improved readability in the process. Along the way we'll
examine some assumptions we have around numbers and the operations we can do on
them.

Watch the recorded talk: https://www.youtube.com/watch?v=WnTw0z7rD3E

Transcript

1. A NUMBER BY ANY OTHER NAME
2. JOËL QUENNEVILLE
5. MARS CLIMATE ORBITER
6. WHAT HAPPENED?
7. Root Cause: Failure to use metric units in the coding of a trajectory model.
8. [...] the navigation software algorithm therefore, underestimated the effect on the spacecraft trajectory by a factor of 4.45 [...]
9. An erroneous trajectory was computed using this incorrect data.
10. I'M NOT BUILDING SPACECRAFT
11. PLAYING FAST AND LOOSE WITH NUMBERS
12. 3 KINDS OF MISTAKES 1. Argument order 2. Unit conversion 3. Invalid operation
13. ARGUMENT ORDER ERROR
14. ARGUMENT ORDER ERROR speed : Float -> Float -> Float speed distance time = distance / time
15. ARGUMENT ORDER ERROR distance = 10 time = 5 -- WHICH ONE? speed distance time speed time distance
16. HOW CAN WE MAKE FEWER OF THESE MISTAKES?
17. COMMUNICATION
18. CONFUSING Float -> Float -> Float
19. WHAT DO THESE NUMBERS REPRESENT?
20. FUNDAMENTALLY DIFFERENT QUANTITIES
21. WHAT ABOUT THIS Meter -> Second -> MeterPerSecond
22. TYPE ALIASES
23. PROVIDE ALTERNATE NAME FOR EXISTING TYPES
24. COMPILER CAN'T TELL THE DIFFERENCE Float -> Float -> Float -- SAME AS Meter -> Second -> MeterPerSecond
25. TYPE ALIASES ARE FOR HUMANS ONLY
26. [the Elm compiler] has my back when I make a dumb mistake. It brings joy into front-end programming. - Joël Quenneville
27. WHAT IF THE COMPILER COULD HELP US?
28. COMMUNICATION
29. CUSTOM TYPES type Meter = Meter Float type Second = Second Float type MetersPerSecond = MetersPerSecond Float
30. CAN'T DO MATH ON THESE
31. speed : Meter -> Second -> MetersPerSecond speed (Meter m) (Second s) = MetersPerSecond (m / s)
32. ARGUMENT ORDER ERROR - TYPED distance = Meter 10 time = Second 5 -- Wrong argument order myVal = speed time distance
33. The 1st argument to `speed` is not what I expect: 21| myVal = speed time distance ^^^^ This `time` value is a: Second But `speed` needs the 1st argument to be: Meter
34. 3 KINDS OF MISTAKES 1. Argument order 2. Unit conversion 3. Invalid operation
35. UNIT CONVERSION ERROR
36. UNIT CONVERSION ERROR minutes = 40 hours = 2 total = minutes + hours -- RETURNS 42 -- SHOULD RETURN 160 OR 2.67
37. CAN THE COMPILER HELP?
38. COMMUNICATE
39. CREATE CUSTOM ADD FUNCTION? add : Minute -> Hour -> ???
40. COMBINATORIAL EXPLOSION add : Minute -> Hour -> ??? add : Minute -> Minute -> ??? add : Hour -> Hour -> ???
41. !
42. WHAT KIND OF QUANTITIES DO THESE NUMBERS REPRESENT?
43. DIFFERENT VARIATIONS OF THE SAME QUANTITY
44. SHARE A TYPE add : Time -> Time -> Time
45. OPAQUE TYPES
46. OPAQUE TYPES module Time exposing (Time) type Time = Time Float
47. OPAQUE TYPES module Time exposing (Time, fromMinutes) -- OTHER STUFF fromMinutes : Float -> Time fromMinutes mins = Time mins
48. OPAQUE TYPES module Time exposing (Time, fromMinutes, fromHours) -- OTHER STUFF fromHours : Float -> Time fromHours hrs = Time (hrs * 60)
49. OPAQUE TYPES module Time exposing (Time, fromMinutes, fromHours, add) -- OTHER STUFF add : Time -> Time -> Time add (Time t1) (Time t2) = Time (t1 + t2)
50. OPAQUE TYPES module Time exposing (Time, fromMinutes, fromHours, add) -- OTHER STUFF inHours : Time -> Float inHours (Time t) toFloat t / 60
51. minutes = Time.fromMinutes 40 hours = Time.fromHours 2 total = Time.add hours minutes -- RETURNS `Time 160`
52. UNIT CONVERSIONS HAPPEN AUTOMATICALLY
53. SINGLE POINT OF FAILURE
54. ELM 0.19 INTRODUCES Posix TYPE
55. MONEY
56. MONEY usd = 5 eur = 10 total = usd + eur -- RETURNS 15 -- SHOULD BE ??
57. WHAT KIND OF QUANTITIES DO THESE NUMBERS REPRESENT?
58. RULES 1. Can only add currencies of the same type 2. Can convert currencies of different types given a rate
59. TWO OPAQUE TYPES
60. module Usd exposing(Usd, fromCents, add, toEur) add : Usd -> Usd -> Usd toEur : Float -> Usd -> Eur -- MORE CODE
61. module Eur exposing (Eur, fromCents, add, toUsd) add : Eur -> Eur -> Eur toUsd : Float -> Eur -> Usd -- MORE CODE
62. SUCCESS? usd = Usd.fromCents 500 eur = Eur.fromCents 1000 total = eur |> Eur.toUsd 1.14 |> Usd.add usd -- RETURNS `Usd 1640`
63. NEW CURRENCY - JPY
64. Jpy.add Jpy.toUsd Jpy.toEur Eur.toJpy Usd.toJpy
65. COMBINATORIAL EXPLOSION
66. !
67. WE WANT 1. Implement adding once 2. Implement conversion once
68. RULES 1. Can only add currencies of the same type 2. Can convert currencies of different types given a rate
69. COMMUNICATE
70. add : Currency a -> Currency a -> Currency a convert : ConversionRate from to -> Currency from -> Currency to
71. PHANTOM TYPES
72. TWO THINGS ARE DIFFERENT WHILE SHARING AN IMPLEMENTATION
73. module Currency exposing (Currency, Usd, Eur, Jpy) type Usd = Usd type Eur = Eur type Jpy = Jpy type Currency a = Currency Float
74. module Currency exposing (Currency, Usd, Eur, Jpy, add) -- OTHER CODE add : Currency a -> Currency a -> Currency a add (Currency c1) (Currency c2) = Currency (c1 + c2)
75. usd : Currency Usd usd = Currency 500 eur : Currency Eur eur = Currency 1000 total = Currency.add usd eur
76. The 2nd argument to `add` is not what I expect: 29| add usd eur ^^^ This `eur` value is a: Currency Eur But `add` needs the 2nd argument to be: Currency Usd
77. CONSTRAINT ENFORCED!
78. CONVERSION - PHANTOM TYPE X 2 type ConversionRate from to = ConversionRate Float convert : ConversionRate from to -> Currency from -> Currency to convert (ConversionRate rate) (Currency c) = Currency (rate * c)
79. -- usd AND eur DEFINITIONS HIDDEN rate : ConversionRate Eur Usd rate = ConversionRate 1.12 total = eur |> Currency.convert rate |> Currency.add usd
80. GOING ALL THE WAY addDifferent : Currency a -> ConversionRate a b -> Currency b -> Currency b
81. 3 KINDS OF MISTAKES 1. Argument order 2. Unit conversion 3. Invalid operation
82. INVALID OPERATION
83. MAKE NO SENSE IN YOUR DOMAIN
84. INVALID OPERATION total : Float -> Float -> Float total subTotal tax = subTotal * tax
85. total : Dollar -> Dollar -> DollarSquared total subTotal tax = subTotal |> Dollar.times tax
86. WHAT DOES A NUMBER REPRESENT
87. DON'T TRY TO IMPLEMENT EVERY MATH FUNCTION
88. No code has no bugs
89. UNITS GUIDE US ON WHAT CODE NOT TO WRITE
90. CASE STUDY: MIT SPRING
91. UNIX TIMESTAMPS
92. VIDEO TIMESTAMPS
93. VIDEO OFFSET
94. REFACTORING BY INTRODUCING A TYPE
95. toUnix : VideoEpoch -> VideoTime -> UnixTime
96. GRADUALLY
97. CASE STUDY: GAMEDEV COORDINATE SPACES
98. SOME OF THE WORLD MAY BE OFFSCREEN
99. CUSTOM TYPES type alias Point = (Int, Int) type WorldSpace = WorldSpace Point type ScreenSpace = ScreenSpace Point
100. CONVERTING BETWEEN THE TWO - VIEWPORT type alias Viewport = { position : WorldSpace , width : GameDistance , height : GameDistance }
101. renderCharacter : Viewport -> Character -> Svg a renderCharacter vp character = character.position |> toScreenCoords vp |> renderSpriteAt "character.png"
102. 3 KINDS OF MISTAKES 1. Argument order 2. Unit conversion 3. Invalid operation
103. COMMUNICATE!
104. WHAT QUANTITY DOES THIS REPRESENT?
105. ENFORCE CONSTRAINTS WITH OPAQUE TYPES
106. SHARE IMPLEMENTATIONS WITH PHANTOM TYPES
107. ianmackenzie/elm- units
108. F#