y      !"#$%&'()*+,-./0123456789:; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [\]^_`abcdefghijklmnopqrstuvwx Trustworthy+:=JKM&A sum data type, for composing effects Parameter r> is phantom: it just tells what could be in the union. Where r is t1 :> t2 ... :> tn,  r v* can be constructed with a value of type ti v4. Ideally, we should be able to add the constraint Member t r.RNOTE: exposing the constructor below allows users to bypass the type system. See  for example.yzyyz Trustworthy '(2468=JK{3This class is used for emulating monad transformersClass Member is defined only for the sake of the interface compatibility with OpenUnion1. Generally, the closed type family Member' below could be used instead.The  t r specifies whether t& is present anywhere in the sum type r, where t is some effectful type, e.g. Lift |, State Int`. }{~y{ }{~ Trustworthy '+2468=JK is similar to V, but it allows types to belong to a "set". For every set, only one member can be in rb at any given time. This allows us to specify exclusivity and uniqueness among arbitrary effects: w-- Terminal effects (effects which must be run last) data Terminal -- Make Lifts part of the Terminal effects set. -- The fundep assures that there can only be one Terminal effect for any r. instance Member (Lift m) r => SetMember Terminal (Lift m) r -- Only allow a single unique Lift effect, by making a "Lift" set. instance Member (Lift m) r => SetMember Lift (Lift m) rfor the sake of gcast1 used below in infix form of  fromMaybe.Construct a Union.7Try extracting the contents of a Union as a given type.jExtract the contents of a Union as a given type. If the Union isn't of that type, a runtime error occurs.Try extracting the contents of a Union as a given type. If we can't, return a reduced Union that excludes the type we just checked. )Juggle types for a Union. Use cautiously.       Trustworthy!"+,:M The traditional view of Free constructions (case embedding impure values nested in f. Traditionally this is the Control.Monad.Free.Free$ constructor, but that's confusing. case embedding pure values 8The abstract Free datatype. Original work available at  Ihttp://okmij.org/ftp/Haskell/AlgorithmsH1.html#reflection-without-remorse.cType used to denote monadic chain of binds. As expected this builds on the Kleisli representation.DSpecific type-aligned sequence used to store chain of monadic binds.Inject a pure value into Free Inject an impure value into FreeCase analysis for the  $ construction. Similar in spirit to  and .A way to get a  U construction from the view by constructing an explicit expression with one element.A way to evaluate the   construction to its view (i.e., head normal form). This includes the logic to perform one level of monadic bind as needed from the  representation.The essence of monadic ', i.e., append/concatenation (of sorts) 'function to be applied if value is Pure&function to be applied on Impure valueFree value to be mapped overresult      Trustworthy 2346:EHJKMEBasic type returned by all computations with extensible effects. The  r' type is a type synonym where the type rC is the type of effects that can be handled, and the missing type aD (from the type application) is the type of value that is returned.Expressed another way: an  can either be a value (i.e.,   case), or an effect of type  r producing another  (i.e.,   case). The result is that an + can produce an arbitrarily long chain of  r' effects, terminated with a pure value.As is made explicit below, the 3 type is simply the Free monad resulting from the  r functor. type  r a =   ( r) aVGiven a method of turning requests into results, we produce an effectful computation.'Get the result from a pure computation..Given a request, either handle it or relay it.Given a request, either handle it or relay it. Both the handler and the relay can produce the same type of request that was handled.RequestRelay the requestHandle the request of type t   Trustworthy+3:JKMNondeterministic choicefchoose lst non-deterministically chooses one value from the lst choose [] thus corresponds to failure3MonadPlus-like operators are expressible via choose3MonadPlus-like operators are expressible via choose4Run a nondeterministic effect, returning all values. Trustworthy+-3JKStatus of a thread: done or reporting the value of the type a (For simplicity, a co-routine reports a value but accepts unit)Type parameter r# is the effect we're yielding from.Type parameter a is the type that is yielded.Type parameter wO is the type of the value returned from the coroutine when it has completed.!The yield request: reporting a value of type e and suspending the coroutine. For readability, a coroutine accepts a unit to produce its value.#2Yield a value of type a and suspend the coroutine.$&Launch a thread and report its status. !"#$ !"#$!"#$  !"#$ Trustworthy +2346:JKM%Lift a Monad m to an effect.'Lift a Monad to an Effect.(_The handler of Lift requests. It is meant to be terminal: we only allow a single Lifted Monad.%&'(%&'(%&'(%&'( Trustworthy+-3JK *DThese are exceptions of the type e. This is akin to the error monad.,/Throw an exception in an effectful computation.-?Makes an effect fail, preventing future effects from happening..2Run a computation that might produce an exception./<Runs a failable effect, such that failed computation return  , and  the return value on success.0mRun a computation that might produce exceptions, and give it a way to deal with the exceptions that come up.1sAdd a default value (i.e. failure handler) to a fallible computation. This hides the fact that a failure happened.2iRun a computation until it produces an exception, and convert and throw that exception in a new context.36Treat Lefts as exceptions and Rights as return values.43 in a lifted Monad5Lift a maybe into the )! effect, causing failure if it's .6Ignores a failure event. Since the event can fail, you cannot inspect its return type, because it has none on failure. To inspect it, use /.)*+,-./01The fallible computation."The computation to run on failure.23456)*+,-./0123456*+),-./0123456 )*+,-./0123456 Trustworthy+3JK:The interpreter -- it is like reify . reflect with a twist Compare this implementation with the huge implementation of call in Hinze 2000 (Figure 9) Each clause corresponds to the axiom of call or cutfalse. All axioms are covered. The code clearly expresses the intuition that call watches the choice points of its argument computation. When it encounteres a cutfalse request, it discards the remaining choicepoints. It completely handles CutFalse effects but not non-determinism.789:789:78:9789:  Trustworthy+36BJK; Create unique Enumerable values.=6Produce a value that has not been previously produced.>&Run an effect requiring unique values.;<=>;<=>;<=>;<=>  Trustworthy+-36JK?xThe request for a value of type e from the current environment. This environment is analogous to a parameter of type e.A$Get the current value from a Reader.BnLocally rebind the value in the dynamic environment. This function both requests and handles Reader requests.C>Request the environment value using a transformation function.DbThe handler of Reader requests. The return type shows that all Reader requests are fully handled.?@ABCD?@ABCD?@ABCD?@ABCD  Trustworthy+-36JKExThe request for a value of type e from the current environment. This environment is analogous to a parameter of type e.G$Get the current value from a Reader.HmLocally rebind the value in the dynamic environment. This function both requests and admins Reader requests.I>Request the environment value using a transformation function.JbThe handler of Reader requests. The return type shows that all Reader requests are fully handled.EFGHIJEFGHIJEFGHIJEFGHIJ  Trustworthy+-36JKKStrict state effectMWrite a new value of the state.N&Return the current value of the state.O$Transform the state with a function.PRun a State effect.Q/Run a State effect, discarding the final state.R.Run a State effect and return the final state.KLMNOP Initial stateEffect incorporating State0Effect containing final state and a return valueQRKLMNOPQRKLNMOPQRKLMNOPQR  Trustworthy+-36JKSStrict state effectUWrite a new value of the state.V&Return the current value of the state.W$Transform the state with a function.XRun a State effect.Y/Run a State effect, discarding the final state.Z.Run a State effect and return the final state.STUVWX Initial stateEffect incorporating State0Effect containing final state and a return valueYZSTUVWXYZSTVUWXYZSTUVWXYZ Trustworthy+-36JK[DThe request to remember a value of type w in the current environment]Write a new value.^#Transform the state being produced._LHandle Writer requests, using a user-provided function to accumulate values.`:Handle Writer requests by taking the first value provided.a6Handle Writer requests by overwriting previous values.bEHandle Writer requests, using a Monoid instance to accumulate values.[\]^_`ab[\]^_`ab[\]^_`ab[\]^_`ab Trustworthy+-36JKcDThe request to remember a value of type w in the current environmenteWrite a new value.f#Transform the state being produced.gLHandle Writer requests, using a user-provided function to accumulate values.h:Handle Writer requests by taking the first value provided.i6Handle Writer requests by overwriting previous values.jEHandle Writer requests, using a Monoid instance to accumulate values.cdefghijcdefghijcdefghijcdefghij Trustworthy+-3JKkTrace effect for debuggingmPrint a string as a trace.n#Run a computation producing Traces.klmnklmnklmnklmn Trustworthy +36:HJKMoELift values to an effect. You can think this is a generalization of Lift.qLift a value to a monad.r2Convert values using given interpreter to effects.opqropqropqropqr Trustworthy!"+3sDefine data using GADTs.w7Then, implements interpreters from the data to effects.stuvwxstuvwxsutvwxsutvwx !"#$%&'()*+,--./0123244567789:;;<=>?@ABCDEFGGHI J J K L M M N O P Q M M N O P Q R R S T U V W X R R S T U V W XYYZ[\]^_YYZ[\]^_``abccdefghijklmnopqrstuvwxyxz{|}~~~"~~extensible-effects-1.9.1.0Data.OpenUnionControl.Monad.Free.Reflection Control.EffControl.Eff.ChooseControl.Eff.CoroutineControl.Eff.LiftControl.Eff.ExceptionControl.Eff.CutControl.Eff.FreshControl.Eff.Reader.LazyControl.Eff.Reader.StrictControl.Eff.State.LazyControl.Eff.State.StrictControl.Eff.Writer.LazyControl.Eff.Writer.StrictControl.Eff.TraceControl.Eff.OperationalControl.Eff.Operational.ExampleData.OpenUnion.Internal.Base unsafeReUnion"Data.OpenUnion.Internal.OpenUnion2:>UnionMember SetMemberinjprjprjForcedecompweakenFreeViewImpurePureFreefreePure freeImpurefreeMapfromViewtoViewEffsendrun handleRelay interposeChoosechoosemzero'mplus' runChoiceYDoneYieldyieldrunCLiftliftrunLiftFailExcthrowExcdierunExcrunFailcatchExconFail rethrowExc liftEither liftEitherM liftMaybe ignoreFailCutFalsecutfalsecallFreshfreshrunFreshReaderasklocalreader runReaderStateputgetmodifyrunState evalState execStateWritertellcensor runWriterrunFirstWriter runLastWriterrunMonoidWriterTracetracerunTraceProgram singleton runProgramJailScanPrintprogadventIO adventPure$fFunctorUnionMemberUghc-prim GHC.TypesIOMemberU'EQUMember'$fMemberU'kFalsetagt:>$fMemberU'kTruetagtag:>$fMemberUktagt1:> $fMembertrIdrunId$fSetMember(->)settrFreeExpTCQbase Data.Eithereither Data.Maybemaybe^>>=GHC.Base>>= $fMonadFree$fApplicativeFree $fFunctorFree$fFunctorChoose$fMonadBasebFree $fMonadIOFree $fFunctorLiftNothingJust$fFunctorProgram