Add basic directed acyclic graph data structure

Also make use of this instead of Nixpkgs's strings-with-deps library
in activation script generation.

modules/lib/dag.nix

@@ -0,0 +1,124 @@
+# A generalization of Nixpkgs's `strings-with-deps.nix`.
+#
+# The main differences from the Nixpkgs version are
+#
+#  - not specific to strings, i.e., any payload is OK,
+#
+#  - the addition of the function `dagEntryBefore` indicating a
+#    "wanted by" relationship.
+
+with import <nixpkgs/lib/strings.nix>;
+with import <nixpkgs/lib/attrsets.nix>;
+with import <nixpkgs/lib/lists.nix>;
+
+rec {
+
+  emptyDag = {};
+
+  isDag = dag:
+    let
+      isEntry = e: (e ? data) && (e ? after) && (e ? before);
+    in
+      builtins.isAttrs dag && all (x: x) (mapAttrsToList (n: isEntry) dag);
+
+  # Takes an attribute set containing entries built by
+  # dagEntryAnywhere, dagEntryAfter, and dagEntryBefore to a
+  # topologically sorted list of entries.
+  #
+  # Internally this function uses the `toposort` function in
+  # `<nixpkgs/lib/lists.nix>` and its value is accordingly.
+  #
+  # Specifically, the result on success is
+  #
+  #    { result = [{name = ?; data = ?;} …] }
+  #
+  # For example
+  #
+  #    nix-repl> dagTopoSort {
+  #                a = dagEntryAnywhere "1";
+  #                b = dagEntryAfter ["a" "c"] "2";
+  #                c = dagEntryBefore ["d"] "3";
+  #                d = dagEntryBefore ["e"] "4";
+  #                e = dagEntryAnywhere "5";
+  #              } == {
+  #                result = [
+  #                  { data = "1"; name = "a"; }
+  #                  { data = "3"; name = "c"; }
+  #                  { data = "2"; name = "b"; }
+  #                  { data = "4"; name = "d"; }
+  #                  { data = "5"; name = "e"; }
+  #                ];
+  #              }
+  #    true
+  #
+  # And the result on error is
+  #
+  #    {
+  #      cycle = [ {after = ?; name = ?; data = ?} … ];
+  #      loops = [ {after = ?; name = ?; data = ?} … ];
+  #    }
+  #
+  # For example
+  #
+  #    nix-repl> dagTopoSort {
+  #                a = dagEntryAnywhere "1";
+  #                b = dagEntryAfter ["a" "c"] "2";
+  #                c = dagEntryAfter ["d"] "3";
+  #                d = dagEntryAfter ["b"] "4";
+  #                e = dagEntryAnywhere "5";
+  #              } == {
+  #                cycle = [
+  #                  { after = ["a" "c"]; data = "2"; name = "b"; }
+  #                  { after = ["d"]; data = "3"; name = "c"; }
+  #                  { after = ["b"]; data = "4"; name = "d"; }
+  #                ];
+  #                loops = [
+  #                  { after = ["a" "c"]; data = "2"; name = "b"; }
+  #                ];
+  #              } == {}
+  #    true
+  dagTopoSort = dag:
+    let
+      dagBefore = dag: name:
+        mapAttrsToList (n: v: n) (
+          filterAttrs (n: v: any (a: a == name) v.before) dag
+        );
+      normalizedDag =
+        mapAttrs (n: v: {
+          name = n;
+          data = v.data;
+          after = v.after ++ dagBefore dag n;
+        }) dag;
+      before = a: b: any (c: a.name == c) b.after;
+      sorted = toposort before (mapAttrsToList (n: v: v) normalizedDag);
+    in
+      if sorted ? result then
+        { result = map (v: { inherit (v) name data; }) sorted.result; }
+      else
+        sorted;
+
+  # Applies a function to each element of the given DAG.
+  dagMap = f: dag: mapAttrs (n: v: v // { data = f n v.data; }) dag;
+
+  # Create a DAG entry with no particular dependency information.
+  dagEntryAnywhere = data: {
+    inherit data;
+    before = [];
+    after = [];
+  };
+
+  dagEntryBetween = before: after: data: {
+    inherit data before after;
+  };
+
+  dagEntryAfter = after: data: {
+    inherit data after;
+    before = [];
+  };
+
+  dagEntryBefore = before: data: {
+    inherit data before;
+    after = [];
+  };
+
+}