Traverse the callgraph bottom-up with an accumulator function.

 callGraphSCCTraversal cg f seed

This example applies the folding function f over each strongly-connected component in the callgraph bottom-up with a starting seed. Each strongly-connected component is processed as a unit. The final accumulated value (based on seed) is returned.

The function f is responsible for approximating the analysis value for the SCC in whatever way makes sense for the analysis.

Just like callGraphSCCTraversal, except strongly-connected components are analyzed in parallel. Each component is analyzed as soon as possible after its dependencies have been analyzed.

A class for types that can be derived from a Function.

An abstract representation of a composable analysis. Construct these with the smart constructors composableAnalysis, composableDependencyAnalysis, composableAnalysisM, and composableDependencyAnalysisM.

Use callGraphComposeAnalysis to convert a list of these into a summary function for use with the call graph traversals.

Make a call-graph SCC summary function from a pure summary function. The function is applied to each function in the SCC in an arbitrary order. It returns the resulting summary obtained by repeated evaluation until a fixed-point is reached.

Make a call-graph SCC summary function from a basic monadic summary function and a function to evaluate the function in its monad and unwrap the monadic value.

The monadic equivalent of callGraphAnalysis.

Compose a list of analyses into a pure summary function for use in a callGraphSCCTraversal. The advantage of using a composable analysis is that it only traverses the call graph once. At each SCC, all analyses are applied until their fixed-point is reached.

This makes it easier to share intermediate values (like CFGs) between analyses without having to recompute them or store them on the side.

The input analyses are processed *in order* (left-to-right). This means that analyses with dependencies should come *after* the analyses they depend on in the list. This is not currently statically enforced - your dependency summaries will just be missing information you might have expected if you get the order wrong.

Create a pure composable analysis from a summary function and a Lens that accesses the summary for this function (given the composite summary). The lens is used to access the current state of this analysis and to update the state for this analysis after it is run.

Like composableAnalysis, but with an extra lens that is used to extract *dependency* information from the composite summary, which is then fed into this summary function.

The intended use is that some analysis will have a dependency on an earlier analysis summary. The lens is used to extract the relevant part of the composite summary. A dependency on multiple earlier analysis summaries can be expressed by providing a lens that extracts a *tuple* containing all relevant analyses.

A monadic version of composableAnalysis. The first argument here is a function to unwrap a monadic value (something like runIdentity or runReader).

A monadic version of composableDependencyAnalysis.