Docase notation for Haskell

Docase notation for Haskell

• 1.
  Monadic pattern matchingwith ‘docase’Tomáš Petříček(tomas.petricek@cl.cam.ac.uk)University of Cambridge, UKAdvisors: Alan Mycroft, Don Syme
• 2.
  IntroductionWarm Fuzzy Things(aka Monads)Sequencing of effectful computationsUsed for parallel & concurrent programming Extend monad interface with additional operationsspawn :: Par a -> Par (IVar a) get :: Ivar a -> Par aWhat are common additional operations?Is there nice notation for using them?
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  Multiplying future valuesFuturevaluesCompute resultin backgroundPattern matching“a” waits for a valueSuspended computationRun bothmultiply f1 f2 =docase(f1, f2) of(a, b) -> return (a * b)
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  Multiplying future valuesFuturevaluesCompute resultin backgroundPattern matching“a”waits for a value“?” does not needa value to match“0” waits for aspecific valueRun bothmultiply f1 f2 =docase(f1, f2) of (0, ?) -> return 0 (?, 0) -> return 0(a, b) -> return (a * b)Choice
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  Multiplying future valuesFuturevaluesCompute resultin backgroundPattern matching“a” waits for a value“?” does not needa value to match“0” waits for aspecific valueRun bothmultiply f1 f2 =docase(f1, f2) of (0, ?) -> return 0 (?, 0) -> return 0(a, b) -> return (a * b)ChoiceFail
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  IntroductionMonad with threeadditional operationsParallel composition m a -> m b -> m (a, b)Monadic choice m a -> m a -> m aAliasing of computationsm a -> m (m a)Some of them supported by many monadsParallel programming (Par monad)Parsers for textual input (Parser monad)Reactive & concurrent (Orcmonad?, Chpmonad?)
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  Parsing using JoinadsValidatingCambridge phone numbersContain only digitsConsists of 10 charactersStart with a prefix “1223”Represents intersection of languagesReturns results of all three parsersvalid = docase( many (satisfies isDigit), multiple 10 character,startsWith(string "1223") )of (str, _, _) -> return str
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  Printing buffer usingjoinsJoin calculusChannels store valuesJoins specifyreactionsPattern matchingUse clauses to encode joinslet buffer() =docase (get, putInt, putString) of(r, n, ?) -> reply r (intToString n)(r, ?, s) -> reply r sFirst clauseSecond clauseSecond clauseputIntputStringget
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  Joinads as analgebraic structureSet 𝓙 representing “joinadic” computationsConstant 0 and associative operators ⊗, ⊕:a ⊗ 0 = 0a ⊕ 0 = aa ⊗ b = b ⊗aa ⊗ (b ⊕ c) = (a ⊗ b) ⊕ (a ⊗ c)(𝓙, ⊕, ⊗, 0) is a commutative near-semiring
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  SummaryRelated to newmonad comprehensionsAllows expressing parallel composition Reuse the MonadZiptype class Free for commutative monadsFuture plansImplementing GHC language extensionLooking for more Monad examplesFor more informationhttp://tomasp.net/blog/docase-haskell.aspxhttp://tomasp.net/blog/comprefun.aspx