Types in ML-Influenced Languages Exploring modern type inference 

What is ML? No, not machine learning ● “Meta Language” ● Originally designed as a language to build a theorem prover by Robin Milner ● Strong, static typing ● Enables powerful type inference via the Hindley-Milner algorithm ● We’ll focus on those last two pieces in modern implementations ● Code samples will be in OCaml 

Type Inference ● Type inference refers to the methods that allow a machine to understand and enforce a type used in a function without the programmer actually declaring a type signature ● Allows the compiler to enforce types by checking all usages of functions and their type signatures before runtime 

Type Inference: Example 1 What type is the argument? What is the return type? 

What type is the argument? What is the return type? Type Inference: Example 2 

What types are the arguments? What is the return type? Type Inference: Example 3 

Parametric Polymorphism ● Similar to generics in other languages ● Given all the information at hand, the computer cannot tell exactly what type is required, therefore it must work for any type a’ and return any type b’ 

Currying and Partial Application ● A curried function is a function that takes multiple arguments before executing, but accepts one argument at a time. 

Currying and Partial Application Typically, you get both for free and safely in typed, functional languages. All functions are curried by default. 

Safe partial application 

Advanced Types: Type Aliases A type alias, or type synonym, is a new name for an existing type. This opens the door for more expressive domain modeling 

Type Aliases - records Records are a data structure in many languages designed to hold multiple pieces of data (like tuples!) but with named fields and accessors 

Algebraic Data Types - Sum Types (aka Union Types) ● A type that represents a limited variety of arbitrary, user defined types 

Algebraic Data Types - Constructors with Data ● Our types can hold onto data ● Note the * in definition - refers to a “product type” 

How are types not classes? ● Classes encapsulate behavior and state, types focus on data 

Pattern Matching This enables exhaustive type checking from the compiler when using a type! 

Pattern Matching 

Representing null - the option type ● Also called optionals (Swift), Maybe (Haskell, Elm) 

Live Code 

Other languages 

If you want to learn more Effective ML by Yaron Minsky ● https://blog.janestreet.com/effective-ml-revisited/ ● https://blog.janestreet.com/effective-ml-video/ Domain Modeling Made Functional ● https://fsharpforfunandprofit.com/ddd/ Why Type-First Development Matters ● http://tomasp.net/blog/type-first-development.aspx/