Agda-2.2.5: A dependently typed functional programming language and proof assistantContentsIndex
Agda.Termination.Termination
Description

Termination checker, based on "A Predicative Analysis of Structural Recursion" by Andreas Abel and Thorsten Altenkirch (JFP'01). and "The Size-Change Principle for Program Termination" by Chin Soon Lee, Neil Jones, and Amir Ben-Amram (POPL'01).

TODO: Note that we should also check that data type definitions are strictly positive. Furthermore, for inductive-recursive families we may need to do something more clever.

Synopsis
terminates :: (Ord meta, Monoid meta) => CallGraph meta -> Either meta ()
tests :: IO Bool
Documentation
terminates :: (Ord meta, Monoid meta) => CallGraph meta -> Either meta ()

TODO: This comment seems to be partly out of date.

terminates cs checks if the functions represented by cs terminate. The call graph cs should have one entry (Call) per recursive function application.

Right perms is returned if the functions are size-change terminating.

If termination can not be established, then Left problems is returned instead. Here problems contains an indication of why termination cannot be established. See lexOrder for further details.

Note that this function assumes that all data types are strictly positive.

The termination criterion is taken from Jones et al. In the completed call graph, each idempotent call-matrix from a function to itself must have a decreasing argument. Idempotency is wrt. matrix multiplication.

This criterion is strictly more liberal than searching for a lexicographic order (and easier to implement, but harder to justify).

tests :: IO Bool
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