The document discusses various aspects of type systems in computer science, including static and dynamic typing, type checking, and the relevant theories and practices. It emphasizes the nuances between sound and unsound typing, along with examples of code and potential errors that can arise. Additionally, several sources for further reading are provided to enhance understanding of the subject matter.

1. T E N TY P TA K M A
O S Y S T E M A C H T Y P Ó W N A P R Z Y K Ł A D Z I E
T Y P E S C R I P T ’ A
A R T U R S KO W R O Ń S K I

2. T H E R E A R E T W O H A R D T H I N G S
I N C O M P U T E R S C I E N C E :
P H I L K A R LT O N
C A C H E I N VA L I D AT I O N
N A M I N G T H I N G S

3. T H E R E A R E T W O H A R D T H I N G S
I N C O M P U T E R S C I E N C E :
P H I L K A R LT O N
C A C H E I N VA L I D AT I O N
N A M I N G T H I N G S

4. N A M I N G T H I N G S

5. O N T O L O G Y

6. O N T O L O G Y
" O N T O " O Z N A C Z A „ T O , C O J E S T ” , „ C O K O LW I E K ”

7. I N T O W H AT C AT E G O R I E S , I F A N Y, C A N W E S O R T
E X I S T I N G T H I N G S ?

9. T Y P E S T H E O RY

10. INTEGER
SET OF
VALUES
SET OF
OPERATIONS
TYPES

11. INTEGER
SET OF
VALUES
SET OF
OPERATIONS
1, 2, 3, 4, 5,
6, 7, 8, 9, 10…
NO IMPOSSIBLE VALUES

12. INTEGER
TYPES
SET OF
VALUES
SET OF
OPERATIONS

13. INTEGER
NO IMPOSSIBLE OPERATIONS
SET OF
OPERATIONS
+, -, /, *
SET OF
VALUES

14. DIVISION ON INTEGER?
SET OF
OPERATIONS
INTEGER
+, -, /, *
SET OF
VALUES

15. W E A K & S T R O N G T Y P I N G

16. L I G H T W E I G H T T E C H N O L O G Y

17. S TAT I C & D Y N A M I C T Y P I N G

18. S TAT I C T Y P I N G

19. ASSEMBLER

20. HOW CAN WE PROVE THAT THIS PROGRAM WORKS?

21. RICE’S THEOREM (1957)
KAŻDA NIETRYWIALNA WŁASNOŚĆ JĘZYKÓW REKURENCYJNIE PRZELICZALNYCH JEST NIEROZSTRZYGALNA

22. S E T O F R U L E S

23. F O R T R A N ( 1 9 5 7 )

24. D ATA A R E A N N O TAT E D W I T H T Y P E I N F O

25. S E L F - D O C U M E N TAT I O N

26. F O R H U M A N S

27. F O R M A C H I N E S

28. A N Y F O O L C A N W R I T E C O D E
T H AT A C O M P U T E R C A N
U N D E R S TA N D . G O O D
P R O G R A M M E R S W R I T E C O D E
T H AT H U M A N S C A N
U N D E R S TA N D .
M A R T I N F O W L E R

29. S TAT I C F I L E C H E C K I N G D O N E O N C O M P I L AT I O N T I M E
SOURCE
CODE
TYPE CHECKER

30. TYPE CHECKER
T Y P E C H E C K E R P R O V E S C H O S E N P R O P E R T I E S
“PROVEN”
CODE

31. TYPE CHECKER
D O N ’ T N E E D T O B E I N C O R R E C T
?

32. PERFECTLY VALID PROGRAM…
let stringValue: unknown = "Value";
stringValue.trim();

33. …STILL WILL FAIL
let stringValue: unknown = "Value";
stringValue.trim();

34. …STILL WILL FAIL
let stringValue: unknown = "Value";
stringValue.trim();

35. L O W E R B O N D O F C O R R E C T N E S S

36. T R A D E O F F : E A S Y T O U S E / C O R R E C T

37. DIVISION ON INTEGER?
SET OF
VALUES
SET OF
OPERATIONS
SUPER-STRICT-INTEGER
+, -, /, *

38. N O T Y P E S I N R U N T I M E

39. S TAT I C & D Y N A M I C T Y P I N G

40. D Y N A M I C T Y P I N G

41. HOW CAN WE PROVE THAT THIS PROGRAM WORKS?

42. P R O B L E M - N O I N F O A B O U T T Y P E S I N R U N T I M E

43. VA R I A B L E I N C O D E
int variable = 1
RUNTIME

44. RUNTIME
D E C O R AT E D W I T H T Y P E O N R U N T I M E
value = 1
type = int
variable

45. E V E RY T H I N G I S C O R R E C T
RUNTIME
Math.abs()
value = 1
type = int
variable

46. R U N T I M E E X C E P T I O N
value = 1
type = int
variable
String.trim()
RUNTIME

47. P E R F O R M A N C E

48. G R A D U A L T Y P I N G

49. S TAT I C C O R E

50. D Y N A M I C N E W C O D E ( W I T H A N Y )

51. I N T E R O P E R A B I L I T Y W I T H J AVA S C R I P T

52. T Y P E E R A S U R E

53. S T R U C T U R A L T Y P I N G

54. N O M I N A L T Y P I N G
class Foo {
method(input: string): number { ... }
}
class Bar {
method(input: string): number { ... }
}
let foo: Foo = new Bar();

55. N O M I N A L T Y P I N G
class Foo {
method(input: string): number { ... }
}
class Bar {
method(input: string): number { ... }
}
let foo: Foo = new Bar();

56. N O M I N A L T Y P I N G
class Foo {
method(input: string): number { ... }
}
class Bar {
method(input: string): number { ... }
}
let foo: Foo = new Bar();

57. S T R U C T U R A L T Y P I N G
class Foo {
method(input: string): number { ... }
}
class Bar {
method(input: string): number { ... }
}
let foo: Foo = new Bar();

58. S T R U C T U R A L T Y P I N G
class Foo {
method(input: string): number { ... }
}
class Bar {
method(input: string): number { ... }
}
let foo: Foo = new Bar();

59. E X P L I C I T T Y P I N G
let foo: Foo = new Foo();let foo: Foo = new Foo();

60. M L & H I N D L E Y – M I L N E R M E T H O D
T Y P E I N F E R E N C E

61. IMPLICIT TYPING
let foo = new Foo();

62. WHAT-A-TYPE?
let a = 'x'
let b = true
let c = 3

63. WHAT-A-TYPE?
let a = 'x' //string
let b = true //boolean
let c = 3 //number

64. WHAT-A-TYPE?
const a = 'x'
const b = true
const c = 3

65. WHAT-A-TYPE?
const a = 'x' // ‘x’
const b = true // true
const c = 3 // 3

66. WITHOUT TYPE OF GUARD
let stringValue: unknown =
"Value";
stringValue.trim()

67. TYPE OF GUARD
function withTypeGuards(value: unknown) {
if (typeof value === "string") {
return value.trim();
}
}

68. TYPE OF GUARD
function withTypeGuards(value: unknown) {
if (typeof value === "string") {
return value.trim();
}
}

69. TYPE OF GUARD
function withTypeGuards(value: unknown) {
if (typeof value === "string") {
return value.trim();
}
}

70. TYPE OF GUARD
function withTypeGuards(value: unknown) {
if (typeof value === "string") {
return value.trim(); // string
}
}

71. PA R A M E T R I Z E D P O LY M O R P H I S M

72. E X . A R R AY S
let message: Array<string> = []
message.push("test");
message.push(2);

73. E X . A R R AY S
let message: Array<string> = []
message.push("test");
message.push(2);

74. E X . A R R AY S
let message: Array<string> = []
message.push("test");
message.push(2);

75. E X . A R R AY S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[0]
console.log(el.toLowerCase())

76. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

77. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

78. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

79. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

80. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
const el: string = message[1]
console.log(el.toLowerCase())

81. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

82. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[1]
console.log(el.toLowerCase())

83. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[0]
console.log(el.toLowerCase())

84. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[0]
console.log(el.toLowerCase())

85. U N S O U N D T Y P E S
function unsafeAdd(arr: Array<string | number>): void {
arr.push(3)
}
let message: Array<string> = []
unsafeAdd(message)
const el: string = message[0]
console.log(el.toLowerCase()) / int

86. VA L I D J S C O D E
function unsafeAdd(arr) {
arr.push(3)
}
var message = []
unsafeAdd(message)
var el = message[0]
console.log(el.toLowerCase())

87. S O U N D ?

88. H O W T O M A K E I T S O U N D
function checkIfTypeOk(el, type) {
if(!el instanceof type) throw new ClassCastException()
}
var message: Array<string> = []
unsafeAdd(message)
var el = message[0]
checkIfTypeOk(el, string)
console.log(el.toLowerCase())

89. H O W T O M A K E I T S O U N D
function checkIfTypeOk(el, type) {
if(!el instanceof type) throw new ClassCastException()
}
var message: Array<string> = []
unsafeAdd(message)
var el = message[0]
checkIfTypeOk(el, string)
console.log(el.toLowerCase())

90. H O W T O M A K E I T S O U N D
function checkIfTypeOk(el, type) {
if(!el instanceof type) throw new ClassCastException()
}
var message: Array<string> = []
unsafeAdd(message)
var el = message[0]
checkIfTypeOk(el, string)
console.log(el.toLowerCase())

91. H O W T O M A K E I T S O U N D
function checkIfTypeOk(el, type) {
if(!el instanceof type) throw new ClassCastException()
}
var message: Array<string> = []
unsafeAdd(message)
var el = message[0]
checkIfTypeOk(el, string)
console.log(el.toLowerCase())

92. T R A D E O F F : E A S Y T O U S E / C O R R E C T
C O M PAT I B L E W I T H J S

93. GRADUAL (STATIC WITH TYPE ERASURE)
STRUCTURALLY TYPED IMPLICITELY TYPED UNSOUND

94. S O U R C E S
https://www2.ccs.neu.edu/racket/pubs/ecoop2015-takikawa-et-al.pdf
https://users.soe.ucsc.edu/~abadi/Papers/FTS-submitted.pdf
UNDERSTANDING TYPESCRIPT
https://blog.steveklabnik.com/posts/2010-07-17-what-to-know-before-debating-type-systems
WHAT TO KNOW BEFORE DEBATING TYPE SYSTEMS
TOWARDS PRACTICAL GRADUAL TYPING
https://papl.cs.brown.edu/2014/safety-soundness.html
SAFETY AND SOUNDNESS

95. S O U R C E S
https://www2.ccs.neu.edu/racket/pubs/ecoop2015-takikawa-et-al.pdf
https://users.soe.ucsc.edu/~abadi/Papers/FTS-submitted.pdf
UNDERSTANDING TYPESCRIPT
https://blog.steveklabnik.com/posts/2010-07-17-what-to-know-before-debating-type-systems
WHAT TO KNOW BEFORE DEBATING TYPE SYSTEMS
TOWARDS PRACTICAL GRADUAL TYPING
https://papl.cs.brown.edu/2014/safety-soundness.html
SAFETY AND SOUNDNESS
Q U E S T I O N S ?
T H A N K Y O U !