Ionuț G. Stan - Let’s write a type checker at I T.A.K.E. Unconference 2015
•
1 gostou•1,029 visualizações
Ionuț G. Stan - Let’s write a type checker at I T.A.K.E. Unconference 2015
Recomendados
Mais conteúdo relacionado
Mais procurados
Mais procurados (20)
Destaque
Semelhante a Ionuț G. Stan - Let’s write a type checker at I T.A.K.E. Unconference 2015
Semelhante a Ionuț G. Stan - Let’s write a type checker at I T.A.K.E. Unconference 2015 (20)
Mais de Mozaic Works
Mais de Mozaic Works (20)
Último
Último (20)
Ionuț G. Stan - Let’s write a type checker at I T.A.K.E. Unconference 2015
- 1. Let's Write a Type Checker Ionuț G. Stan — I T.A.K.E. — May 2015
- 2. • Part 1 • Compilers Overview • Type Checking vs Type Inference • Vehicle Language • Wand's Type Inference Algorithm • Part 2 • Live Demonstration The Plan
- 6. Source Code Compiler (fn a => a) 2 Compilers Overview
- 7. Source Code Target Language Compiler (fn a => a) 2 Compilers Overview
- 8. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Compilers Overview
- 9. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Interpreter Compilers Overview
- 10. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Source Code Interpreter Compilers Overview
- 11. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Source Code Interpreter (fn a => a) 2 Compilers Overview
- 12. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Source Code Evaluation Result Interpreter (fn a => a) 2 Compilers Overview
- 13. Source Code Target Language Compiler (fn a => a) 2 (function(a){return a;})(2); Source Code Evaluation Result Interpreter (fn a => a) 2 2 Compilers Overview
- 14. Compilers Overview de T Compiler ) 2 (functi
- 15. Parsing de T Compiler ) 2 (functi Parser
- 16. Abstract Syntax Tree de T Compiler ) 2 (functi Parser Abstract Syntax Tree (AST)
- 17. Abstract Syntax Tree de T Compiler ) 2 (functi Parser APP FUN a VAR a INT 2 Abstract Syntax Tree (AST)
- 18. Code Generation de T Compiler ) 2 (functi Parser CodeGen APP FUN a VAR a INT 2 Abstract Syntax Tree (AST)
- 19. Many Intermediate Phases de T Compiler ) 2 (functi Parser CodeGen ... AST
- 20. Type Checking de T Compiler ) 2 (functi Parser CodeGen Type Checker AST Typed AST ...
- 21. Today's Talk de T Compiler ) 2 (functi Parser CodeGen Type Checker AST Typed AST Today
- 23. • 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
- 24. Vehicle Language
- 25. • Surface Syntax • What's the concrete syntax of the language • Type System • What types are supported by the language Vehicle Language
- 26. 1. Numbers: 1, 2, 3, ... 2. Booleans: true and false 3. Function expressions: fn a => a 4. Function application: inc 42 or 2 + 3 5. If expressions: if cond then t else f Surface Syntax1 1 — a subset of Standard ML
- 27. 1. Numbers: 1, 2, 3, ... 2. Booleans: true and false 3. Function expressions: fn a => a 4. Function application: inc 42 or 2 + 3 5. If expressions: if cond then t else f Surface Syntax1 1 — a subset of Standard ML
- 28. 1. Numbers: 1, 2, 3, ... 2. Booleans: true and false 3. Anonymous functions (lambdas): fn a => a 4. Function application: inc 42 or 2 + 3 5. If expressions: if cond then t else f Surface Syntax1 1 — a subset of Standard ML
- 29. 1. Numbers: 1, 2, 3, ... 2. Booleans: true and false 3. Anonymous functions (lambdas): fn a => a 4. Function application: inc 42 5. If expressions: if cond then t else f Surface Syntax1 1 — a subset of Standard ML
- 30. 1. Numbers: 1, 2, 3, ... 2. Booleans: true and false 3. Anonymous functions (lambdas): fn a => a 4. Function application: inc 42 5. If expressions: if cond then t else f Surface Syntax1 1 — a subset of Standard ML
- 31. 6. Let blocks/expressions: let val name = ... in name end Surface Syntax1 1 — a subset of Standard ML
- 32. Small Example let val inc = fn a => a + 1 in inc 42 end
- 33. 1. Integer type: int 2. Boolean type: bool 3. Function type: int -> bool 4. Generic type variables: 'a, 'b, 'c, etc. Language Types
- 34. 1. Integer type: int 2. Boolean type: bool 3. Function type: int -> bool 4. Generic type variables: 'a, 'b, 'c, etc. Language Types
- 35. 1. Integer type: int 2. Boolean type: bool 3. Function type: int -> bool 4. Generic type variables: 'a, 'b, 'c, etc. Language Types
- 36. 1. Integer type: int 2. Boolean type: bool 3. Function type: int -> bool 4. Generic type variables: 'a, 'b, 'c, etc. Language Types
- 40. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing AST fn isZero => if isZero 1 then 2 else 3
- 41. 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
- 42. 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
- 43. 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
- 44. 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
- 45. 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
- 46. 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
- 47. 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
- 48. 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
- 49. 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
- 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
- 54. 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 → t4t1 Constraint Set
- 55. 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
- 56. 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
- 57. 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
- 58. 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
- 59. 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
- 60. 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
- 61. 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
- 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 ≡ t5 → t4 ≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t1 t5 t4 t6 t7 t6 t7 t2 Constraint Set
- 63. 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
- 64. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing AST : t5 → t4t1≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ t1 → t3 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map
- 65. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing AST : t5 → t4t1≡ int ≡ bool ≡ int ≡ int ≡ t3 ≡ t3 ≡ (t5 → t4) → t3 t5 t4 t6 t7 t6 t7 t2 Constraint Set Solution Map
- 66. 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
- 67. 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
- 68. 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
- 69. 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
- 70. 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
- 71. 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
- 72. 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
- 73. 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
- 74. 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
- 75. 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
- 76. 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
- 77. 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) → intt2 Constraint Set Solution Map
- 78. 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
- 79. 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
- 80. Wand's Algorithm Overview Type Annotation Constraint Generation Constraint Solving Parsing AST fn isZero => if isZero 1 then 2 else 3 (int -> bool) -> int
- 81. • As I said, there are two main classes • Constraint-based ones. We've just seen one example — Wand's algorithm • Substitution-based ones, where constraint generation and solving are not two separate processes, they are interleaved. Example: the classic Hindley-Milner Algorithm W. Type Checking Algorithms
- 84. Thank You!
- 85. • 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