ocaml-tsort

This module provides topological sort based on Kahn's algorithm. It's not very fast, but it's easy to use and provides friendly error reporting.

It works on assoc lists (('a * 'a list) list). The keys are "tasks" and the values are lists of their dependencies.

Sorting DAGs

Most of the time cyclic dependencies are bad. The main function, Tsort.sort returns value of this type:

type 'a sort_result =
  Sorted of 'a list 
| ErrorCycle of 'a list

The function is:

val sort : ('a * 'a list) list -> 'a sort_result

Examples:

# Tsort.sort [("foundation", []); ("walls", ["foundation"]); ("roof", ["walls"])] ;;
- : string Tsort.sort_result = Tsort.Sorted ["foundation"; "walls"; "roof"]

# Tsort.sort [("foundation", ["building permit"]); ("walls", ["foundation"]); ("roof", ["walls"])] ;;
- : string Tsort.sort_result =
Tsort.Sorted ["building permit"; "foundation"; "walls"; "roof"]

# Tsort.sort [("foundation", ["roof"]); ("walls", ["foundation"]); ("roof", ["walls"])] ;;
- : string Tsort.sort_result = Tsort.ErrorCycle ["roof"; "foundation"; "walls"]

As you can see from the second example, if there's a dependency on a node that doesn't exist in the assoc list keys, it's automatically inserted, and assumed to have no dependencies.

Detecting non-existent dependencies

If your graph comes directly from user input, there's a good chance that dependency on a non-existent node is a user error.

To prevent it, use Tsort.find_nonexistent_nodes. Example:

# Tsort.find_nonexistent_nodes [("foundation", ["building permit"]); ("walls", ["foundation"]); ("roof", ["walls"])] ;;
- : (string * string list) list = [("foundation", ["building permit"])]

Sorting graphs with cycles

Sometimes cycles are fine. In this case you can use Tsort.sort_strongly_connected_components to split your graph into strongly connected components and sort its condensation.

Contrived example: you want to line up the Addams family so that children come after parents, but spouse and sibling pairs are not separated.

# Tsort.sort_strongly_connected_components
  ["Morticia", ["Gomez"]; "Gomez", ["Morticia"];
   "Wednesday", ["Morticia"; "Gomez"; "Pugsley"]; "Pugsley", ["Morticia"; "Gomez"; "Wednesday"];
   "Grandmama", []; "Fester", []] ;;

- : string list list =
[["Fester"]; ["Morticia"; "Gomez"]; ["Grandmama"]; ["Wednesday"; "Pugsley"]]

There's also Tsort.find_strongly_connected_components if you just want to find what they are. For the data above, it would return [["Morticia"; "Gomez"]; ["Wednesday"; "Pugsley"]; ["Grandmama"]; ["Fester"]].