DEPENDENTLY TYPED STATE MACHINES COMPOSE CONF 2018 

WHO AM I? ▸ Tim McGilchrist @lambda_foo ▸ Haskell / OCaml programmer at Ansarada ▸ Curious about Distributed Systems ▸ Convinced about Types 

BACKGROUND HOW DID I GET HERE? 

TCP/IP STATE MACHINE 

RAFT LEADER ELECTION 

IDRIS IS A PACMAN COMPLETE LANGUAGE Edwin Brady 

IDRIS ▸ general purpose language ▸ full dependent types with dependent pattern matching ▸ eager evaluation ▸ interfaces (ala Haskell's type classes) ▸ What if Haskell had full dependent types? 

PROBLEMS 

VECT : NAT -> TYPE -> TYPE 

PAPER STATES ALL THE WAY DOWN ▸ "A useful pattern in dependently typed programming is to define a state transition system” ▸ “an architecture for dependently typed applications” ▸ “How to implement a state transition system as a dependent type “ ▸ "How to combine state transition systems into a larger system" 

GENERALISING STATEFUL PROGRAMS ▸ Types should capture the states of resources ▸ Stateful APIs should compose ▸ Types should be readable ▸ Error messages should be readable 

THE RECIPE IMPLEMENTING DEPENDENT STATE MACHINES 1. Draw State Diagram for the problem 2. Define State Machine as a Type 3. Implement State functions 4. Running State functions 

INTERFACE DATASTORE (M : TYPE -> TYPE) WHERE ACCOUNT LOGIN AND ACCESS Login (success) Logout Logged In Logged Out Login (failure) Read Secret 

ACCOUNT LOGIN AS TYPE 

ACCOUNT LOGIN AS TYPE ▸ Type level functions everywhere 

USING DATASTORE 

IMPLEMENTING DATASTORE 

(.) : (B -> C) -> (A -> B) -> A -> C TYPES OF COMPOSITION ▸ Horizontally - multiple state machines within a function ▸ Vertically - implement state machine in terms of another Examples: Application on top of a Communication Protocol Multiple resources, File IO plus State 

HORIZONTALLY - STATE PLUS DATASTORE 

VERTICALLY - STATE PLUS DATASTORE ▸ A composite resource is built up from a list of other resources. ▸ Use functions split and combine. 

LIFT : MONAD M => M T -> STRANS M T RES (CONST RES) CLEANING UP THE TYPES ▸ Type level function ST ▸ List of actions on resources 

DATASTORE - CLEAN 

REMOVE : VAR -> TYPE -> ACTION TY PRETTY ERRORS 

ST : (TYPE -> TYPE) -> (TY : TYPE) -> LIST (ACTION TY) -> TYPE RELATED WORK ▸ Algebraic Effects in Idris, Haskell, and Purescript ▸ Encoding State Machines ▸ Session Types ▸ Linear Types 

MKRES : LABEL -> TYPE -> RESOURCE RESOURCES ▸ States All the Way Down, E Brady ▸ Programming and Reasoning with Algebraic Effects and Dependent Types, E Brady ▸ Idris website http://docs.idris-lang.org/ ▸ Type Driven Design with Idris (book) 

ST : (TYPE -> TYPE) -> (TY : TYPE) -> LIST (ACTION TY) -> TYPE THANK YOU ▸ What questions do you have? ▸ Do you want to see more code? 

MORE TYPES 

TYPE INDEXED MONADS