Totally Typed Domain When dependent types meets DDD

Why? Type driven development and Dependent types look cool! Model the domain closely ! Make impossible states impossible ! Some guarantees

Type ... Define ... Refine

Dependent types

?Holes

Nice compiler Interactive Strict but helpful

Proof search

%default total

Unit tests It compiles so it's obviously correct right? NO

Unit tests It compiles so it's obviously correct right? YES Unit tests implemented in the type system

Small types Big types ~= inheritance Small types ~= composition Compose well

Ok fancy types, but all inputs are string Validate user input => Strong typing Strong typing => enforces validation A type can be a permission to do something

Tic Tac Toe placeMark : (freePos: List Pos) -> Pos-> List Pos vs
 
 placeMark : (freePos: Vect (S n) Pos) // available positions, (S n) means n+1 
 -> (p: Pos) // position to be marked
 -> (Elem p freePos) // proof that position p is in freePos
 -> Vect n Pos // remaining positions, 1 less than input

TypeDD ~ TestDD

Fast feedback? Dynamic No compilation Can hack Static All branches Type mistakes Autocomplete

Recursive types

Sometimes the types are clean But not the code

Conclusions ! Types are proofs ! Compilers ~ tests ! Small types ! Qualified types <=> encoded knowledge ! Feedback ! Compilers will evolve