Copyright | (C) Koz Ross 2022 |
---|---|
License | BSD-3-Clause (see the LICENSE file) |
Maintainer | koz.ross@retro-freedom.nz |
Stability | Experimental |
Portability | GHC only |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
- Computation type:
- Backtracking search, with
r
as a 'ranking' or 'evaluation' type. - Binding strategy:
- Binding a function to a monadic value 'chains together' strategies; having seen the result of one search, decide which policy to use to continue.
- Useful for:
- Search problems.
- Zero and plus:
- None.
- Example type:
Select
r a
A note on commutativity
Some effects are commutative: it doesn't matter which you resolve first, as
all possible orderings of commutative effects are isomorphic. Consider, for
example, the reader and state effects, as exemplified by ReaderT
and
StateT
respectively. If we have
, this is
effectively ReaderT
r (State
s) ar ->
; if we instead have
State
s a ~ r -> s -> (a, s)
, this is effectively
StateT
s (Reader
r) as ->
. Since we
can always reorder function arguments (for example, using Reader
r (a, s) ~ s -> r -> (a, s)flip
, as in
this case) without changing the result, these are
isomorphic, showing that reader and state are commutative, or, more
precisely, commute with each other.
However, this isn't generally the case. Consider instead the error and state
effects, as exemplified by MaybeT
and StateT
respectively.
If we have
, this
is effectively MaybeT
(State
s) a
: put simply,
the error can occur only in the result, but
not the state, which always 'survives'. On the other hand, if we have
State
s (Maybe
a) ~ s -> (Maybe
a, s)
, this is instead StateT
s Maybe
as ->
: here,
if we error, we lose both the state and the result! Thus, error and state effects
do not commute with each other.Maybe
(a, s)
As the MTL is capability-based, we support any ordering of non-commutative
effects on an equal footing. Indeed, if you wish to use
MonadState
, for
example, whether your final monadic stack ends up being
, MaybeT
(State
s)
a
, or anything else, you will be able to write your
desired code without having to consider such differences. However, the way we
implement these capabilities for any given transformer (or rather, any
given transformed stack) is affected by this ordering unless the effects in
question are commutative.StateT
s Maybe
a
We note in this module which effects the accumulation effect does and doesn't commute with; we also note on implementations with non-commutative transformers what the outcome will be. Note that, depending on how the 'inner monad' is structured, this may be more complex than we note: we describe only what impact the 'outer effect' has, not what else might be in the stack.
Commutativity of selection
The selection effect commutes with the identity effect (IdentityT
), but
nothing else.
Synopsis
- class Monad m => MonadSelect r (m :: Type -> Type) | m -> r where
- select :: ((a -> r) -> a) -> m a
- newtype LiftingSelect (t :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a = LiftingSelect (t m a)
Type class
class Monad m => MonadSelect r (m :: Type -> Type) | m -> r where Source #
The capability to search with backtracking. Essentially describes a 'policy function': given the state of the search (and a 'ranking' or 'evaluation' of each possible result so far), pick the result that's currently best.
Laws
Any instance of MonadSelect
must follow these laws:
Since: mtl-2.3
Instances
MonadSelect r m => MonadSelect r (MaybeT m) Source # | 'Extends' the possibilities considered by Since: mtl-2.3 |
Defined in Control.Monad.Select | |
(MonadTrans t, MonadSelect r m, Monad (t m)) => MonadSelect r (LiftingSelect t m) Source # | Since: mtl-2.3 |
Defined in Control.Monad.Select select :: ((a -> r) -> a) -> LiftingSelect t m a Source # | |
(MonadSelect r m, Monoid w) => MonadSelect r (AccumT w m) Source # | 'Readerizes' the accumulator: the 'ranking' function can see the value
that has been accumulated (of type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect r m => MonadSelect r (ExceptT e m) Source # | 'Extends' the possibilities considered by Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect r m => MonadSelect r (IdentityT m) Source # | Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect r (SelectT r Identity) Source # | Since: mtl-2.3 |
MonadSelect r' m => MonadSelect r' (ReaderT r m) Source # | Provides a read-only environment of type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect w m => MonadSelect w (StateT s m) Source # | 'Readerizes' the state: the 'ranking' function can see a value of
type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect w m => MonadSelect w (StateT s m) Source # | 'Readerizes' the state: the 'ranking' function can see a value of
type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect w' m => MonadSelect w' (WriterT w m) Source # | 'Readerizes' the writer: the 'ranking' function can see the value
that's been accumulated (of type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
(MonadSelect w' m, Monoid w) => MonadSelect w' (WriterT w m) Source # | 'Readerizes' the writer: the 'ranking' function can see the value
that's been accumulated (of type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
(MonadSelect w' m, Monoid w) => MonadSelect w' (WriterT w m) Source # | 'Readerizes' the writer: the 'ranking' function can see the value
that's been accumulated (of type Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect r' m => MonadSelect r' (ContT r m) Source # | The continuation describes a way of choosing a 'search' or 'ranking'
strategy for Since: mtl-2.3 |
Defined in Control.Monad.Select | |
MonadSelect w' m => MonadSelect w' (RWST r w s m) Source # | A combination of an 'outer' Since: mtl-2.3 |
Defined in Control.Monad.Select | |
(MonadSelect w' m, Monoid w) => MonadSelect w' (RWST r w s m) Source # | A combination of an 'outer' Since: mtl-2.3 |
Defined in Control.Monad.Select | |
(MonadSelect w' m, Monoid w) => MonadSelect w' (RWST r w s m) Source # | A combination of an 'outer' Since: mtl-2.3 |
Defined in Control.Monad.Select |
Lifting helper type
newtype LiftingSelect (t :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a Source #
A helper type to decrease boilerplate when defining new transformer
instances of MonadSelect
.
Most of the instances in this module are derived using this method; for
example, our instance of ExceptT
is derived as follows:
deriving via (LiftingSelect (ExceptT e) m) instance (MonadSelect r m) => MonadSelect r (ExceptT e m)
Since: mtl-2.3
LiftingSelect (t m a) |