Docase notation for Haskell

Monadic pattern matching with ‘docase’
Tomáš Petříček(tomas.petricek@cl.cam.ac.uk)University of Cambridge, UK
Advisors: Alan Mycroft, Don Syme

Introduction
Warm Fuzzy Things (aka Monads)
Sequencing of effectful computations
Used for parallel & concurrent programming
Extend monad interface with additional operations
spawn :: Par a -> Par (IVar a) get :: Ivar a -> Par a
What are common additional operations?
Is there nice notation for using them?

Multiplying future values
Future values
Compute resultin background
Pattern matching
“a” waits for a value
Suspended computation
Run both
multiply f1 f2 =
docase(f1, f2) of
(a, b) -> return (a * b)

Future values
Pattern matching
“a”waits for a value
“?” does not needa value to match
“0” waits for aspecific value
Run both
multiply f1 f2 =
docase(f1, f2) of
(0, ?) -> return 0
(?, 0) -> return 0
Choice

Future values
Pattern matching
“a” waits for a value
“?” does not needa value to match
“0” waits for aspecific value
Run both
multiply f1 f2 =
docase(f1, f2) of
(0, ?) -> return 0
(?, 0) -> return 0
Choice
Fail

Introduction
Monad with three additional operations
Parallel composition
m a -> m b -> m (a, b)
Monadic choice
m a -> m a -> m a
Aliasing of computations
m a -> m (m a)
Some of them supported by many monads
Parallel programming (Par monad)
Parsers for textual input (Parser monad)
Reactive & concurrent (Orcmonad?, Chpmonad?)

Parsing using Joinads
Validating Cambridge phone numbers
Contain only digits
Consists of 10 characters
Start with a prefix “1223”
Represents intersection of languages
Returns results of all three parsers
valid = docase( many (satisfies isDigit),
multiple 10 character,
startsWith(string "1223") )
of (str, _, _) -> return str

Printing buffer using joins
Join calculus
Channels store values
Joins specifyreactions
Pattern matching
Use clauses to encode joins
let buffer() =
docase (get, putInt, putString) of
(r, n, ?) ->
reply r (intToString n)
(r, ?, s) ->
reply r s
First clause
Second clause
Second clause
putInt
putString
get

Joinads as an algebraic structure
Set 𝓙 representing “joinadic” computations
Constant 0 and associative operators ⊗, ⊕:
a ⊗ 0 = 0
a ⊕ 0 = a
a ⊗ b = b ⊗a
a ⊗ (b ⊕ c) = (a ⊗ b) ⊕ (a ⊗ c)
(𝓙, ⊕, ⊗, 0) is a commutative near-semiring

Summary
Related to new monad comprehensions
Allows expressing parallel composition
Reuse the MonadZiptype class
Free for commutative monads
Future plans
Implementing GHC language extension
Looking for more Monad examples
For more information
http://tomasp.net/blog/docase-haskell.aspx
http://tomasp.net/blog/comprefun.aspx

Docase notation for Haskell

by Tomas Petricek

Accessibility

Categories

Upload Details

Usage Rights

Statistics

Docase notation for Haskell Presentation Transcript