An effect for nondeterministic computations

An effect for culling nondeterministic computations.

An effect to delimit backtracking within nondeterministic contexts.

An effect for spliting a nondeterministic computation into its head and tail.

Split is typically used as a primitive effect. If you define a Carrier that relies on a novel non-trivial monad transformer, then you need to make a ThreadsEff instance for that monad transformer to lift Split (if possible).

The following threading constraints accept Split:

• ReaderThreads
• StateThreads
• StateLazyThreads
• WriterThreads
• WriterLazyThreads

A pseudo-effect for connected NonDet, Cull, Cut, and Split effects.

Logic should only ever be used inside of Eff and Effs constraints. It is not a real effect! See Bundle.

Introduce two new branches stemming from the current one.

Fail the current branch and proceed to the next branch, backtracking to the nearest use of 'choose'/'fromList' that still has unprocessed branches.

Introduce new branches stemming from the current one using a list of values.

Cull nondeterminism in the argument, limiting the number of branches it may introduce to be at most 1.

cull (return True `choose' return False) == return True

cull (lose `choose' return False) == return False

Fail the current branch, and prevent backtracking up until the nearest enclosing use of call (if any).

cutfail `choose' m == cutfail

Commit to the current branch: prevent all backtracking that would move execution to before cut was invoked, up until the nearest enclosing use of call (if any).

call (fromList [1,2] >>= \a -> cut >> fromList [a,a+3]) == fromList [1,4]

 call ((cut >> return True) choose return False) == return True

Delimit the prevention of backtracking from uses of cut and cutfail.

call cutfail `choose' m = m

Split a nondeterministic computation into its first result and the rest of the computation, if possible.

Note that split cutfail == cutfail. If you don't want that behavior, use split (call m) instead of split m.

Runs a NonDet effect.

Unlike runLogic and runCullCut, this doesn't provide any means of interacting with created branches through Split, Cull or Cut.

However, it also doesn't impose any primitive effects, meaning runNonDet doesn't restrict what interpreters are run before it.

Derivs (NonDetC m) = NonDet ': Derivs m

Prims  (NonDetC m) = Prims m

Runs a NonDet effect, but stop once the first valid result is found.

This is like runNonDet with the Alternative specialized to Maybe, but once a valid result is found, it won't run all other branches.

This is the equivalent of runCullCut @Maybe . cull or runLogic @Maybe . cull, but doesn't impose any primitive effects, meaning runNonDet1 doesn't restrict what interpreters are run before it.

Derivs (NonDetC m) = NonDet ': Derivs m

Prims  (NonDetC m) = Prims m

Runs connected NonDet, Cull, and Cut effects.

Unlike runLogic, this doesn't provide the full power of Split. This allows for a larger variety of interpreters to be run before runCullCut compared to runLogic, since Split is significantly harder to thread compared to Cull and Cut.

Derivs (CullCutC m) = Cull ': Cut ': NonDet ': Derivs m

Prims  (CullCutC m) = Regional CullOrCall ': Prims m

Runs connected NonDet, Cull, Cut, and Split effects -- i.e. Logic.

Derivs (LogicC m) = Split ': Cull ': Cut ': NonDet ': Derivs m

Prims  (LogicC m) = Split ': Regional CullOrCall ': Prims m

Split is a very restrictive primitive effect. Most notably, interpreters for effects with failure -- such as runError -- can't be used before runLogic. If you want to use such interpreters before runLogic, consider using runCullCut or runNonDet instead.

NonDetThreads accepts the following primitive effects:

• Regional s
• Optional s (when s is a functor)
• Unravel p
• ListenPrim s (when s is a Monoid)
• ListenPrim s (when s is a Monoid)
• ReaderPrim i