Datafix.Denotational

Provides an alternative method (to MonadDependency/Datafix.Explicit) of formulating data-flow problems as a Denotation built in the context of MonadDatafix. This offers better usability for defining static analyses, as the problem of allocating nodes in the data-flow graph is abstracted from the user.

Documentation

class (Monad m, MonadDomain (DepM m)) => MonadDatafix m where

Builds on an associated DepM that is a MonadDomain (like any MonadDependency) by providing a way to track dependencies without explicit Node management. Essentially, this allows to specify a build plan for a DataFlowProblem through calls to datafix in analogy to fix or mfix.

Minimal complete definition

datafix

Associated Types

type DepM m :: * -> *

The monad in which data dependencies are expressed. Can and will be instantiated to some MonadDependency, if you choose to go through ProblemBuilder.

Methods

datafix :: dom ~ Domain (DepM m) => ChangeDetector dom -> (LiftedFunc dom (DepM m) -> m (a, LiftedFunc dom (DepM m))) -> m a

This is the closest we can get to an actual fixed-point combinator.

We need to provide a ChangeDetector for detecting the fixed-point as well as a function to be iterated. In addition to returning a better approximation of itself in terms of itself, it can return an arbitrary value of type a. Because the iterated function might want to datafix additional times (think of nested let bindings), the return values are wrapped in m.

Finally, the arbitrary a value is returned, in analogy to a in mfix :: MonadFix m => (a -> m a) -> m a.

Instances

MonadDependency m => MonadDatafix (ProblemBuilder m)

Associated Types

type DepM (ProblemBuilder m :: * -> *) :: * -> *

Methods

datafix :: (* ~ dom) (Domain (DepM (ProblemBuilder m))) => ChangeDetector dom -> (LiftedFunc dom (DepM (ProblemBuilder m)) -> ProblemBuilder m (a, LiftedFunc dom (DepM (ProblemBuilder m)))) -> ProblemBuilder m a

datafixEq :: forall m dom a. MonadDatafix m => dom ~ Domain (DepM m) => Eq (ReturnType dom) => (LiftedFunc dom (DepM m) -> m (a, LiftedFunc dom (DepM m))) -> m a

Shorthand that partially applies datafix to an eqChangeDetector.

type Denotation dom = forall m. (MonadDatafix m, dom ~ Domain (DepM m)) => m (LiftedFunc dom (DepM m))

A denotation of some syntactic entity in a semantic domain, built in a some MonadDatafix context.