A Type Inferencer for ML in 200 Lines of Scala

Transcript

1. A Type Inferencer for ML In 200 Lines of Scala

   Ionuț G. Stan — CODΞCΔMP Iași — October 2016

2. About Me

3. • Software Developer at Eloquentix About Me

4. • Software Developer at Eloquentix • I work mostly with

   Scala About Me

5. • Software Developer at Eloquentix • I work mostly with

   Scala • I like FP, programming languages, compilers About Me

6. • Software Developer at Eloquentix • I work mostly with

   Scala • I like FP, programming languages, compilers • I started the Bucharest FP meetup group About Me

7. • Software Developer at Eloquentix • I work mostly with

   Scala • I like FP, programming languages, compilers • I started the Bucharest FP meetup group • I occasionally blog at igstan.ro About Me

8. • Software Developer at Eloquentix • I work mostly with

   Scala • I like FP, programming languages, compilers • I started the Bucharest FP meetup group • I occasionally blog at igstan.ro • Happy to discuss tech stuff at ionut.g.stan@gmail.com About Me

9. Plan

10. Plan • Compilers Overview

11. Plan • Compilers Overview • Vehicle Language: µML

12. Plan • Compilers Overview • Vehicle Language: µML • Wand's

    Type Inference Algorithm

13. Plan • Compilers Overview • Vehicle Language: µML • Wand's

    Type Inference Algorithm • Intuition

14. Plan • Compilers Overview • Vehicle Language: µML • Wand's

    Type Inference Algorithm • Intuition • Code

15. Compilers Overview

16. Compiler Compilers Overview

17. Compiler Compilers Overview Source Language

18. Target Language Compiler Compilers Overview Source Language

19. Target Language Compiler (fn a => a) 2 Compilers Overview

    Source Language

20. Target Language Compiler (fn a => a) 2 (function(a){return a})(2)

    Compilers Overview Source Language

21. Compilers Overview uage T Compiler ) 2 (funct

22. Parsing T Compiler ) 2 Parser uage (funct

23. Abstract Syntax Tree T Compiler ) 2 Parser APP FUN

    a VAR a INT 2 Abstract Syntax Tree (AST) uage (funct

24. Code Generation T Compiler ) 2 Parser CodeGen APP FUN

    a VAR a INT 2 Abstract Syntax Tree (AST) uage (funct

25. Many Intermediate Phases T Compiler ) 2 Parser CodeGen ...

    AST (funct uage

26. Type Checking T Compiler ) 2 Parser CodeGen Type Checker

    AST ... uage (funct

27. Today's Talk T Compiler ) 2 Parser CodeGen Type Checker

    AST Today's T alk ... uage (funct

28. Type Checking vs Type Inference

29. • Type Checking • Ensures declared types are used consistently

    • All types must be declared • Traverse AST and compare def site with use site • Type Inference • Ensures consistency as well • Types need not be declared, though; are deduced! • Two main classes of algorithms • We'll see one instance today Type Checking vs Inference

30. Vehicle Language: µML

31. • Surface Syntax • What does the language look like

    • Type System • What types the language supports Vehicle Language: µML

32. 1. Integers: 1, 23, 456, etc. µML — Surface Syntax

33. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. µML — Surface Syntax

34. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false µML — Surface Syntax

35. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false 4. Single-argument anonymous functions: fn a => a µML — Surface Syntax

36. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false 4. Single-argument anonymous functions: fn a => a 5. Function application: inc 42 µML — Surface Syntax

37. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false 4. Single-argument anonymous functions: fn a => a 5. Function application: inc 42 6. If expressions: if cond then t else f µML — Surface Syntax

38. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false 4. Single-argument anonymous functions: fn a => a 5. Function application: inc 42 6. If expressions: if cond then t else f 7. Addition and subtraction: a + b, a - b µML — Surface Syntax

39. 1. Integers: 1, 23, 456, etc. 2. Identifiers (only letters):

    inc, cond, a, etc. 3. Booleans: true and false 4. Single-argument anonymous functions: fn a => a 5. Function application: inc 42 6. If expressions: if cond then t else f 7. Addition and subtraction: a + b, a - b 8. Parenthesized expressions: (a + b) µML — Surface Syntax

40. 9. Let blocks/expressions:
 
 let
 val name = ...
 in


    name
 end µML — Surface Syntax

41. Small Example let val inc = fn a => a

    + 1 in inc 42 end

42. µML — Language Types

43. 1. Integer type: int µML — Language Types

44. 1. Integer type: int 2. Boolean type: bool µML —

    Language Types

45. 1. Integer type: int 2. Boolean type: bool 3. Function

    type: int -> bool µML — Language Types

46. Today's Algorithm Overview

47. Wand's Algorithm Overview

48. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST

49. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST fn isZero => if isZero 1 then 2 else 3

50. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

51. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

52. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

53. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

54. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

55. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

56. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

57. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

58. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

59. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN isZero IF APP VAR isZero INT 1 INT 2 INT 3 fn isZero => if isZero 1 then 2 else 3

60. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN IF APP AR ero INT 1 INT 2 INT 3 FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3

61. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUN IF APP AR ero INT 1 INT 2 INT 3 FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3

62. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 Constraint Set

63. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 t1 Constraint Set

64. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int t1 t5 Constraint Set

65. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool t1 t5 t4 Constraint Set

66. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int t1 t5 t4 t6 Constraint Set

67. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int t1 t5 t4 t6 t7 Constraint Set

68. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 t1 t5 t4 t6 t7 t6 Constraint Set

69. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 t1 t5 t4 t6 t7 t6 t7 Constraint Set

70. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t1 t5 t4 t6 t7 t6 t7 t2 Constraint Set

71. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t1 t5 t4 t6 t7 t6 t7 t2 Constraint Set

72. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t1 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

73. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : t5 → t4 t1 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

74. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : t5 → t4 t1 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

75. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : t5 → t4 t1 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ (t5 → t4) → t3 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

76. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : t5 → t4 : int t1 t5 ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ (t5 → t4) → t3 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

77. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : t5 → t4 : int t1 t5 ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ (t5 → t4) → t3 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

78. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → t4 : int t1 t5 ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ (int → t4) → t3 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map

79. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → t4 : int : bool t1 t5 t4 ≡ int ≡ int ≡ t3 ≡ t3 ≡ (int → t4) → t3 t6 t7 t6 t7 t2 Constraint Set Solution Map

80. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → t4 : int : bool t1 t5 t4 ≡ int ≡ int ≡ t3 ≡ t3 ≡ (int → t4) → t3 t6 t7 t6 t7 t2 Constraint Set Solution Map

81. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool t1 t5 t4 ≡ int ≡ int ≡ t3 ≡ t3 ≡ (int → bool) → t3 t6 t7 t6 t7 t2 Constraint Set Solution Map

82. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int t1 t5 t4 t6 ≡ int ≡ t3 ≡ t3 ≡ (int → bool) → t3 t7 t6 t7 t2 Constraint Set Solution Map

83. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int t1 t5 t4 t6 ≡ int ≡ t3 ≡ t3 ≡ (int → bool) → t3 t7 t6 t7 t2 Constraint Set Solution Map

84. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int t1 t5 t4 t6 ≡ int ≡ t3 ≡ t3 ≡ (int → bool) → t3 t7 int t7 t2 Constraint Set Solution Map

85. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int t1 t5 t4 t6 t7 ≡ t3 ≡ t3 ≡ (int → bool) → t3 int t7 t2 Constraint Set Solution Map

86. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int t1 t5 t4 t6 t7 ≡ t3 ≡ t3 ≡ (int → bool) → t3 int t7 t2 Constraint Set Solution Map

87. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int t1 t5 t4 t6 t7 ≡ t3 ≡ t3 ≡ (int → bool) → t3 int int t2 Constraint Set Solution Map

88. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int t1 t5 t4 t6 t7 t3 ≡ t3 ≡ (int → bool) → t3 int t2 Constraint Set Solution Map

89. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int t1 t5 t4 t6 t7 t3 ≡ t3 ≡ (int → bool) → t3 int t2 Constraint Set Solution Map

90. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int t1 t5 t4 t6 t7 t3 ≡ int ≡ (int → bool) → int int t2 Constraint Set Solution Map

91. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int t1 t5 t4 t6 t7 t3 ≡ int ≡ (int → bool) → int int t2 Constraint Set Solution Map

92. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int t1 t5 t4 t6 t7 t3 ≡ (int → bool) → int t2 Constraint Set Solution Map

93. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST : int → bool : int : bool : int : int : int : (int → bool) → int t1 t5 t4 t6 t7 t3 t2 Constraint Set Solution Map

94. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST FUNt2 isZerot1 IFt3 APPt4 VARt1 isZero INTt5 1 INTt6 2 INTt7 3 : int → bool : int : bool : int : int : int : (int → bool) → int t1 t5 t4 t6 t7 t3 t2 Solution Map

95. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing

    AST fn isZero => if isZero 1 then 2 else 3 (int -> bool) -> int

96. • As I said, there are two main classes. •

    Constraint-based: we've just seen one example — Wand's algorithm. • Substitution-based: all phases are interleaved, e.g., Algorithm W. Type Inference Algorithms

97. • Sunil Kothari and James L. Caldwell. Type Reconstruction Algorithms

    - A Survey • Mitchell Wand. A simple algorithm and proof for type inference • Bastiaan Heeren, Jurriaan Hage and Doaitse Swierstra. Generalizing Hindley-Milner Type Inference Algorithms • Oleg Kiselyov and Chung-chieh Shan. Interpreting Types as Abstract Values • Shriram Krishnamurthi. Programming Languages: Application and Interpretation, chapter 15 • Shriram Krishnamurthi. Programming Languages: Application and Interpretation, lecture 24 • Shriram Krishnamurthi. Programming Languages: Application and Interpretation, lecture 25 • Bastiaan Heeren. Top Quality Type Error Messages • Stephen Diehl. Write You a Haskell, chapter 6 • Andrew Appel. Modern Compiler Implementation in ML, chapter 16 • Benjamin Pierce. Types and Programming Languages, chapter 22 • Martin Odersky. Scala by Example, chapter 16 • Danny Gratzer. https://github.com/jozefg/hm • Arlen Cox. ML Type Inference and Unification! • Radu Rugină. CS 312, Type Inference Resources

98. github.com / igstan / codecamp-2016

99. Thank You!