The basic Logic monad, for performing backtracking computations returning values (e.g. Logic a will return values of type a).

A smart constructor for Logic computations.

Runs a Logic computation with the specified initial success and failure continuations.

>>> runLogic empty (+) 0
0

>>> runLogic (pure 5 <|> pure 3 <|> empty) (+) 0
8

Extracts the first result from a Logic computation, failing if there are no results.

>>> observe (pure 5 <|> pure 3 <|> empty)
5

>>> observe empty
*** Exception: No answer.

Extracts up to a given number of results from a Logic computation.

>>> let nats = pure 0 <|> fmap (+ 1) nats
>>> observeMany 5 nats
[0,1,2,3,4]

Extracts all results from a Logic computation.

>>> observe (pure 5 <|> empty <|> empty <|> pure 3 <|> empty)
[5,3]

A monad transformer for performing backtracking computations layered over another monad m.

Runs a LogicT computation with the specified initial success and failure continuations.

The second argument ("success continuation") takes one result of the LogicT computation and the monad to run for any subsequent matches.

The third argument ("failure continuation") is called when the LogicT cannot produce any more results.

For example:

>>> yieldWords = foldr ((<|>) . pure) empty
>>> showEach wrd nxt = putStrLn wrd >> nxt
>>> runLogicT (yieldWords ["foo", "bar"]) showEach (putStrLn "none!")
foo
bar
none!
>>> runLogicT (yieldWords []) showEach (putStrLn "none!")
none!
>>> showFirst wrd _ = putStrLn wrd
>>> runLogicT (yieldWords ["foo", "bar"]) showFirst (putStrLn "none!")
foo

Extracts the first result from a LogicT computation, failing if there are no results at all.

Extracts up to a given number of results from a LogicT computation.

Extracts all results from a LogicT computation, unless blocked by the underlying monad.

For example, given

>>> let nats = pure 0 <|> fmap (+ 1) nats

some monads (like Identity, Reader, Writer, and State) will be productive:

>>> take 5 $ runIdentity (observeAllT nats)
[0,1,2,3,4]

but others (like ExceptT, and ContT) will not:

>>> take 20 <$> runExcept (observeAllT nats)

In general, if the underlying monad manages control flow then observeAllT may be unproductive under infinite branching, and observeManyT should be used instead.