Agda.Termination.CallGraph

Contents

Description

Call graphs and related concepts, more or less as defined in "A Predicative Analysis of Structural Recursion" by Andreas Abel and Thorsten Altenkirch.

Synopsis

Structural orderings

data Order Source

The order called R in the paper referred to above. Note that Unknown <= Le <= Lt.

See Call for more information.

TODO: document orders which are call-matrices themselves.

Constructors

Lt
Le
Unknown
Mat (Matrix Integer Order)

Instances

Eq Order
Ord Order
Show Order
Arbitrary Order
CoArbitrary Order

(.*.) :: Order -> Order -> Order Source

Multiplication of Orders. (Corresponds to sequential composition.)

supremum :: [Order] -> Order Source

The supremum of a (possibly empty) list of Orders.

Call matrices

type Index = Integer Source

Call matrix indices.

newtype CallMatrix Source

Call matrices. Note the call matrix invariant (callMatrixInvariant).

Constructors

CallMatrix
Fields mat :: Matrix Index Order

Instances

Eq CallMatrix
Ord CallMatrix
Show CallMatrix
Arbitrary CallMatrix
CoArbitrary CallMatrix

(>*<) :: Call -> Call -> Call Source

Call combination.

Precondition: see <*>; furthermore the source of the first argument should be equal to the target of the second one.

callMatrixInvariant :: CallMatrix -> Bool Source

In a call matrix at most one element per row may be different from Unknown.

Calls

data Call Source

This datatype encodes information about a single recursive function application. The columns of the call matrix stand for source function arguments (patterns); the first argument has index 0, the second 1, and so on. The rows of the matrix stand for target function arguments. Element (i, j) in the matrix should be computed as follows:

Lt (less than) if the j-th argument to the target function is structurally strictly smaller than the i-th pattern.
Le (less than or equal) if the j-th argument to the target function is structurally smaller than the i-th pattern.
Unknown otherwise.

The structural ordering used is defined in the paper referred to above.

Constructors

Call
Fields source :: Index The function making the call. target :: Index The function being called. cm :: CallMatrix The call matrix describing the call.

Instances

Eq Call
Ord Call
Show Call
Arbitrary Call
CoArbitrary Call

callInvariant :: Call -> Bool Source

Call invariant.

Call graphs

data CallGraph meta Source

A call graph is a set of calls. Every call also has some associated meta information, which should be Monoidal so that the meta information for different calls can be combined when the calls are combined.

Instances

Eq meta => Eq (CallGraph meta)
Show meta => Show (CallGraph meta)

callGraphInvariant :: CallGraph meta -> Bool Source

CallGraph invariant.

fromList :: Monoid meta => [(Call, meta)] -> CallGraph metaSource

Converts a list of calls with associated meta information to a call graph.

toList :: CallGraph meta -> [(Call, meta)]Source

Converts a call graph to a list of calls with associated meta information.

empty :: CallGraph metaSource

Creates an empty call graph.

union :: Monoid meta => CallGraph meta -> CallGraph meta -> CallGraph metaSource

Takes the union of two call graphs.

insert :: Monoid meta => Call -> meta -> CallGraph meta -> CallGraph metaSource

Inserts a call into a call graph.

complete :: Monoid meta => CallGraph meta -> CallGraph metaSource

complete cs completes the call graph cs. A call graph is complete if it contains all indirect calls; if f -> g and g -> h are present in the graph, then f -> h should also be present.

showBehaviour :: Show meta => CallGraph meta -> String Source

Displays the recursion behaviour corresponding to a call graph.

Tests

tests :: IO Bool Source