Idris States: Dependent types, not just for vectors?

Building state machines in our software is a common practice. They are used to model
all kinds of interesting and not so interesting problems like communication protocols,
user accounts and general business processes.

When we build these in a functional language like Haskell we get certain guarantees from
using ADTs, functions and the type system. What is harder is encoding checks and guarantees
around when state transitions are valid. In this talk we will look at how a depdendently typed
language (Idris) can build state machines with further guarantees and correctness.

This talk was inspired by reading Edwin Brady's paper \"State Machines all the way down\"
and much of the code is available at http://docs.idris-lang.org/en/latest/st/index.html

Transcript

1. DEPENDENT TYPES, NOT JUST
   FOR VECTORS?
   FP-SYD 2017
   

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2. WHO AM I?
   ▸ Tim McGilchrist @lambda_foo
   ▸ Haskell programmer at Ambiata
   ▸ Curious about Distributed Systems
   ▸ Curious about Types
   

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3. BACKGROUND
   HOW DID I GET HERE?
   

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4. ACTORS AND ERLANG
   Mailbox
   Process
   

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5. SESSION TYPES
   ▸ Describe communication protocols
   ▸ Session types codify the structure of communication
   ▸ Data types codify the structures communicated
   

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6. PROBLEMS
   

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7. (X : TYPE) -> TYPE -> (X -> TYPE) -> TYPE
   EFFECT SYSTEMS
   ▸ Available in Idris and Purescript
   ▸ Use effects to model state machines.
   

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8. EFFECT PROBLEMS
   ▸ "it was not possible to implement one effectful API in
   terms of others" E Brady
   ▸ "difficult to describe the relationship between separate
   resources" E Brady
   ▸ Composing problems?
   

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9. IDRIS IS A
   PACMAN
   COMPLETE
   LANGUAGE
   Edwin Brady
   

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10. VECTOR LENGTH PROGRAMMING
    λΠ>:doc Vect
    Data type Data.Vect.Vect : (len : Nat) -> (elem : Type) -> Type
    Vectors: Generic lists with explicit length in the type
    Arguments:
    len : Nat -- the length of the list
    elem : Type -- the type of elements
    Constructors:
    Nil : Vect 0 elem
    Empty vector
    (::) : (x : elem) -> (xs : Vect len elem) -> Vect (S len) elem
    A non-empty vector of length S len, consisting of a head element and the rest of
    the list, of length len.
    

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11. 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"
    

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

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13. ENTER STRANS
    ▸ m - underlying monad
    ▸ ty - result type of the program
    ▸ in_ctxt - input context
    ▸ out_ctxt
    

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14. DATASTORE
    

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15. USING DATASTORE
    

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16. TEXT
    

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17. (.) : (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 a Communication Protocol
    Multiple resources, File IO plus State
    

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18. STATE PLUS DATASTORE
    

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19. TEXT
    CLEANING UP THE TYPES
    ▸ Type level function ST
    ▸ List of actions on resources
    

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20. DATASTORE - CLEAN
    

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21. TEXT
    PRETTY ERRORS
    

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22. TEXT
    CONCLUSION
    ▸ Need to tie this back to Actors.
    ▸ Encoding State Machines.
    ▸ Session Types
    ▸ Effect Systems
    

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23. TEXT
    RESOURCES
    ▸ States All the Way Down, Edwin Brady
    ▸ Programming and Reasoning with Algebraic Effects and
    Dependent Types, Edwin Brady
    ▸ Session Types http://simonjf.com/2016/05/28/session-
    type-implementations.html
    ▸ Idris website http://docs.idris-lang.org/
    

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