CS 476 Programming Language Design William Mansky From

CS 476 – Programming Language Design William Mansky

From Typed Lambda Calculus to OCaml • User-friendly syntax • Basic types, tuples, records • Inductive datatypes and pattern-matching • Local declarations • References ØType inference • Generics/polymorphism 1

Type Inference • 2

Type Inference • Our typing rules have the form: • We’ve been implementing type checkers that take the bottom type as input and return yes/no • We could also read that type as output • First-pass inference algorithm: label literals with their types, then pass types up the AST 3

Direct Type Inference 4

Direct Type Inference 5

Direct Type Inference 6

Direct Type Inference 7

Direct Type Inference 8

Direct Type Inference 9

Direct Type Inference let type_of (e : exp) : typ = … 10

Direct Type Inference 11

Direct Type Inference 12

Direct Type Inference 13

Direct Type Inference 14

Direct Type Inference 15

Direct Type Inference 16

Direct Type Inference 17

Direct Type Inference 18

Direct Type Inference 19

Type Inference • 20

Constraint-Based Type Inference • Not every lambda-term is well typed 21

Constraint-Based Type Inference • Not every lambda-term is well typed 22

Constraint-Based Type Inference • Not every lambda-term is well typed 23

Constraint-Based Type Inference • 24

Type Inference int f(int x, int y){ return x + y; } let f x y = x + y; ; 25

Constraint-Based Type Inference • 26

Constraint-Based Type Inference • 27

Constraint-Based Type Inference: Rules 28

Constraint-Based Type Inference: Rules 29

Constraint-Based Type Inference • 30