[access trie] make max depth configurable

Reviewed By: jberdine

Differential Revision: D5689923

fbshipit-source-id: 471363d

infer/src/checkers/Trace.ml

@@ -34,7 +34,9 @@ module type S = sig
   module Sources : sig
     module Known : module type of AbstractDomain.FiniteSet (Source)
 
-    module Footprint = AccessTree.PathSet
+    module FootprintConfig : AccessTree.Config
+
+    module Footprint : module type of AccessTree.PathSet (FootprintConfig)
 
     type astate = {known: Known.astate; footprint: Footprint.astate}
 
@@ -162,7 +164,8 @@ module Make (Spec : Spec) = struct
 
   module Sources = struct
     module Known = AbstractDomain.FiniteSet (Source)
-    module Footprint = AccessTree.PathSet
+    module FootprintConfig = AccessTree.DefaultConfig
+    module Footprint = AccessTree.PathSet (FootprintConfig)
 
     type astate = {known: Known.astate; footprint: Footprint.astate}
 

infer/src/checkers/Trace.mli

@@ -37,8 +37,10 @@ module type S = sig
     (** Set of sources returned by callees of the current function *)
     module Known : module type of AbstractDomain.FiniteSet (Source)
 
+    module FootprintConfig : AccessTree.Config
+
     (** Set of access paths representing the sources that may flow in from the caller *)
-    module Footprint = AccessTree.PathSet
+    module Footprint : module type of AccessTree.PathSet (FootprintConfig)
 
     type astate = {known: Known.astate; footprint: Footprint.astate}
 

infer/src/checkers/accessTree.ml

@@ -54,7 +54,16 @@ module type S = sig
   val pp_node : F.formatter -> node -> unit
 end
 
-module Make (TraceDomain : AbstractDomain.WithBottom) = struct
+module type Config = sig
+  val max_depth : int
+end
+
+module DefaultConfig = struct
+  (* arbitrarily chosen large value *)
+  let max_depth = Int.max_value / 2
+end
+
+module Make (TraceDomain : AbstractDomain.WithBottom) (Config : Config) = struct
   module TraceDomain = TraceDomain
 
   module AccessMap = PrettyPrintable.MakePPMap (struct
@@ -94,6 +103,10 @@ module Make (TraceDomain : AbstractDomain.WithBottom) = struct
 
   let make_starred_leaf trace = (trace, Star)
 
+  let empty_normal_leaf = make_normal_leaf TraceDomain.empty
+
+  let empty_starred_leaf = make_starred_leaf TraceDomain.empty
+
   (* no need to make it tail-recursive, trees shouldn't be big enough to blow up the call stack *)
   let rec node_depth (_, tree) = 1 + tree_depth tree
 
@@ -213,18 +226,39 @@ module Make (TraceDomain : AbstractDomain.WithBottom) = struct
     | None, node_opt | node_opt, None
      -> node_opt
 
+  (* truncate [node] to a tree of depth <= [depth]. [depth] must be positive *)
+  let node_depth_truncate (_, tree as node) depth =
+    let rec node_depth_truncate_ depth (trace, tree as node) =
+      match tree with
+      | Star
+       -> node
+      | Subtree subtree
+       -> if Int.( <= ) depth 0 then
+            let trace' = join_all_traces trace tree in
+            make_starred_leaf trace'
+          else
+            let subtree' = AccessMap.map (node_depth_truncate_ (depth - 1)) subtree in
+            (trace, Subtree subtree')
+    in
+    if tree_depth tree > depth then node_depth_truncate_ depth node
+    else (* already short enough; don't bother truncating *)
+      node
+
   (* helper for [add_access]. [last_trace] is the trace associated with [tree] in the parent. *)
   let access_tree_add_trace ~node_to_add ~seen_array_access ~is_exact accesses node =
-    let rec access_tree_add_trace_ ~seen_array_access accesses node =
+    let rec access_tree_add_trace_ ~seen_array_access accesses node depth =
       match (accesses, node) with
       | [], (trace, tree) -> (
         match (is_exact, seen_array_access) with
         | true, false
          -> (* adding x.f, do strong update on both subtree and its traces *)
-            node_to_add
+            node_depth_truncate node_to_add (Config.max_depth - depth)
         | true, true
-         -> (* adding x[_], do weak update on subtree and on its immediate trace *)
-            node_join node_to_add node
+         -> (* adding x[_], do weak update on subtree and on its immediate trace. note : [node]
+               already satisfies the depth invariant because it's already in the tree; no need to
+               truncate it. *)
+            let truncated_node = node_depth_truncate node_to_add (Config.max_depth - depth) in
+            node_join truncated_node node
         | _
          -> (* adding x.f* or x[_]*, join with traces of subtree and replace it with * *)
             let node_trace, node_tree = node_to_add in
@@ -233,34 +267,42 @@ module Make (TraceDomain : AbstractDomain.WithBottom) = struct
       | _, (_, Star)
        -> node_join node_to_add node
       | access :: accesses, (trace, Subtree subtree)
-       -> let access_node =
-            try AccessMap.find access subtree
-            with Not_found -> make_normal_leaf TraceDomain.empty
-          in
-          (* once we encounter a subtree rooted in an array access, we have to do weak updates in
-             the entire subtree. the reason: if I do x[i].f.g = <interesting trace>, then
-             x[j].f.g = <empty trace>, I don't want to overwrite <interesting trace>. instead, I
-             should get <interesting trace> |_| <empty trace> *)
-          let seen_array_access =
-            seen_array_access
-            ||
-            match access with
-            | AccessPath.ArrayAccess _
-             -> true
-            | AccessPath.FieldAccess _
-             -> false
+       -> let depth' = depth + 1 in
+          let access_node' =
+            if depth' >= Config.max_depth then
+              access_tree_add_trace_ ~seen_array_access accesses empty_starred_leaf depth'
+            else
+              let access_node =
+                try AccessMap.find access subtree
+                with Not_found -> empty_normal_leaf
+              in
+              (* once we encounter a subtree rooted in an array access, we have to do weak updates in
+               the entire subtree. the reason: if I do x[i].f.g = <interesting trace>, then
+               x[j].f.g = <empty trace>, I don't want to overwrite <interesting trace>. instead, I
+               should get <interesting trace> |_| <empty trace> *)
+              let seen_array_access =
+                seen_array_access
+                ||
+                match access with
+                | AccessPath.ArrayAccess _
+                 -> true
+                | AccessPath.FieldAccess _
+                 -> false
+              in
+              access_tree_add_trace_ ~seen_array_access accesses access_node depth'
           in
-          let access_node' = access_tree_add_trace_ ~seen_array_access accesses access_node in
           (trace, Subtree (AccessMap.add access access_node' subtree))
     in
-    access_tree_add_trace_ ~seen_array_access accesses node
+    access_tree_add_trace_ ~seen_array_access accesses node 1
 
   let add_node ap node_to_add tree =
     let base, accesses = AccessPath.Abs.extract ap in
     let is_exact = AccessPath.Abs.is_exact ap in
     let base_node =
       try BaseMap.find base tree
-      with Not_found -> make_normal_leaf TraceDomain.empty
+      with Not_found ->
+        (* note: we interpret max_depth <= 0 as max_depth = 1 *)
+        if Config.max_depth > 1 then empty_normal_leaf else empty_starred_leaf
     in
     let base_node' =
       access_tree_add_trace ~node_to_add ~seen_array_access:false ~is_exact accesses base_node
@@ -344,8 +386,8 @@ module Make (TraceDomain : AbstractDomain.WithBottom) = struct
   let pp fmt base_tree = BaseMap.pp ~pp_value:pp_node fmt base_tree
 end
 
-module PathSet = struct
-  include Make (AbstractDomain.BooleanOr)
+module PathSet (Config : Config) = struct
+  include Make (AbstractDomain.BooleanOr) (Config)
 
   (* print as a set of paths rather than a map of paths to bools *)
   let pp fmt tree =

infer/src/checkers/accessTree.mli

@@ -81,7 +81,14 @@ module type S = sig
   val pp_node : Format.formatter -> node -> unit
 end
 
-module Make (TraceDomain : AbstractDomain.WithBottom) : S with module TraceDomain = TraceDomain
+module type Config = sig
+  val max_depth : int
+end
+
+module DefaultConfig : Config
+
+module Make (TraceDomain : AbstractDomain.WithBottom) (Config : Config) :
+  S with module TraceDomain = TraceDomain
 
 (** Concise representation of a set of access paths *)
 module PathSet : module type of Make (AbstractDomain.BooleanOr)

infer/src/quandary/ClangTaintAnalysis.ml

@@ -13,7 +13,7 @@ module L = Logging
 
 include TaintAnalysis.Make (struct
   module Trace = ClangTrace
-  module AccessTree = AccessTree.Make (Trace)
+  module AccessTree = AccessTree.Make (Trace) (AccessTree.DefaultConfig)
 
   let to_summary_access_tree tree = QuandarySummary.AccessTree.Clang tree
 

infer/src/quandary/JavaTaintAnalysis.ml

@@ -13,7 +13,7 @@ module L = Logging
 
 include TaintAnalysis.Make (struct
   module Trace = JavaTrace
-  module AccessTree = AccessTree.Make (Trace)
+  module AccessTree = AccessTree.Make (Trace) (AccessTree.DefaultConfig)
 
   let to_summary_access_tree access_tree = QuandarySummary.AccessTree.Java access_tree
 

infer/src/quandary/QuandarySummary.ml

@@ -12,8 +12,8 @@
 open! IStd
 module F = Format
 module L = Logging
-module Java = AccessTree.Make (JavaTrace)
-module Clang = AccessTree.Make (ClangTrace)
+module Java = AccessTree.Make (JavaTrace) (AccessTree.DefaultConfig)
+module Clang = AccessTree.Make (ClangTrace) (AccessTree.DefaultConfig)
 
 module AccessTree = struct
   type t = Java of Java.t | Clang of Clang.t

infer/src/quandary/QuandarySummary.mli

@@ -13,9 +13,9 @@ open! IStd
 
 module F = Format
 
-module Java : module type of AccessTree.Make (JavaTrace)
+module Java : module type of AccessTree.Make (JavaTrace) (AccessTree.DefaultConfig)
 
-module Clang : module type of AccessTree.Make (ClangTrace)
+module Clang : module type of AccessTree.Make (ClangTrace) (AccessTree.DefaultConfig)
 
 module AccessTree : sig
   type t = Java of Java.t | Clang of Clang.t

infer/src/quandary/TaintSpec.ml

@@ -24,7 +24,7 @@ type sanitizer = Return  (** a sanitizer that removes taint from its return valu
 module type S = sig
   module Trace : Trace.S
 
-  module AccessTree : module type of AccessTree.Make (Trace)
+  module AccessTree : module type of AccessTree.Make (Trace) (AccessTree.DefaultConfig)
 
   val handle_unknown_call :
     Typ.Procname.t -> Typ.t option -> HilExp.t list -> Tenv.t -> action list

infer/src/unit/TaintTests.ml

@@ -40,7 +40,7 @@ end)
 
 module MockTaintAnalysis = TaintAnalysis.Make (struct
   module Trace = MockTrace
-  module AccessTree = AccessTree.Make (Trace)
+  module AccessTree = AccessTree.Make (Trace) (AccessTree.DefaultConfig)
 
   let of_summary_access_tree _ = assert false
 

infer/src/unit/accessTreeTests.ml

@@ -36,25 +36,29 @@ module MockTraceDomain = struct
   let pp fmt s = if phys_equal s top then F.fprintf fmt "T" else pp fmt s
 end
 
-module Domain = AccessTree.Make (MockTraceDomain)
+module MakeTree (Config : AccessTree.Config) = struct
+  include AccessTree.Make (MockTraceDomain) (Config)
 
-let assert_trees_equal tree1 tree2 =
-  let rec access_tree_equal (trace1, subtree1) (trace2, subtree2) =
-    MockTraceDomain.equal trace1 trace2
-    &&
-    match (subtree1, subtree2) with
-    | Domain.Star, Domain.Star
-     -> true
-    | Domain.Subtree t1, Domain.Subtree t2
-     -> Domain.AccessMap.equal access_tree_equal t1 t2
-    | _
-     -> false
-  in
-  let base_tree_equal tree1 tree2 = Domain.BaseMap.equal access_tree_equal tree1 tree2 in
-  let pp_diff fmt (actual, expected) =
-    F.fprintf fmt "Expected to get tree %a but got %a" Domain.pp expected Domain.pp actual
-  in
-  OUnit2.assert_equal ~cmp:base_tree_equal ~pp_diff tree1 tree2
+  let assert_trees_equal tree1 tree2 =
+    let rec access_tree_equal (trace1, subtree1) (trace2, subtree2) =
+      MockTraceDomain.equal trace1 trace2
+      &&
+      match (subtree1, subtree2) with
+      | Star, Star
+       -> true
+      | Subtree t1, Subtree t2
+       -> AccessMap.equal access_tree_equal t1 t2
+      | _
+       -> false
+    in
+    let base_tree_equal tree1 tree2 = BaseMap.equal access_tree_equal tree1 tree2 in
+    let pp_diff fmt (actual, expected) =
+      F.fprintf fmt "Expected to get tree %a but got %a" pp expected pp actual
+    in
+    OUnit2.assert_equal ~cmp:base_tree_equal ~pp_diff tree1 tree2
+end
+
+module Domain = MakeTree (AccessTree.DefaultConfig)
 
 let tests =
   let open AccessPathTestUtils in
@@ -200,49 +204,52 @@ let tests =
       (* normal tests *)
       (* add base when absent *)
       let x_y_base_tree_with_added_trace = mk_x_y_base_tree added_trace in
-      assert_trees_equal (Domain.add_trace x added_trace y_base_tree)
+      Domain.assert_trees_equal (Domain.add_trace x added_trace y_base_tree)
         x_y_base_tree_with_added_trace ;
       (* add base when present *)
-      assert_trees_equal (Domain.add_trace x added_trace x_y_base_tree)
+      Domain.assert_trees_equal (Domain.add_trace x added_trace x_y_base_tree)
         x_y_base_tree_with_added_trace ;
       let x_y_base_tree_with_y_trace = mk_x_y_base_tree y_trace in
-      assert_trees_equal (Domain.add_trace x added_trace x_y_base_tree_with_y_trace)
+      Domain.assert_trees_equal (Domain.add_trace x added_trace x_y_base_tree_with_y_trace)
         x_y_base_tree_with_added_trace ;
       (* add path when absent *)
       let xFG_tree_added_trace = mk_xFG_tree added_trace in
-      assert_trees_equal (Domain.add_trace xFG added_trace x_base_tree) xFG_tree_added_trace ;
+      Domain.assert_trees_equal (Domain.add_trace xFG added_trace x_base_tree) xFG_tree_added_trace ;
       (* add path when present *)
       let xFG_tree_y_trace = mk_xFG_tree y_trace in
-      assert_trees_equal (Domain.add_trace xFG added_trace xFG_tree_y_trace) xFG_tree_added_trace ;
+      Domain.assert_trees_equal (Domain.add_trace xFG added_trace xFG_tree_y_trace)
+        xFG_tree_added_trace ;
       (* add starred path when base absent *)
       let xF_star_tree_added_trace =
         Domain.make_starred_leaf added_trace |> Domain.AccessMap.singleton f
         |> Domain.make_node MockTraceDomain.empty |> Domain.BaseMap.singleton x_base
       in
-      assert_trees_equal (Domain.add_trace xF_star added_trace Domain.empty)
+      Domain.assert_trees_equal (Domain.add_trace xF_star added_trace Domain.empty)
         xF_star_tree_added_trace ;
       (* add starred path when base present *)
-      assert_trees_equal (Domain.add_trace xF_star added_trace x_base_tree)
+      Domain.assert_trees_equal (Domain.add_trace xF_star added_trace x_base_tree)
         xF_star_tree_added_trace ;
       (* adding array path should do weak updates *)
       let aArrF_tree = mk_xArrF_tree array_f_trace in
       let aArrF_tree_joined_trace =
         mk_xArrF_tree (MockTraceDomain.join added_trace array_f_trace)
       in
-      assert_trees_equal (Domain.add_trace xArrF added_trace aArrF_tree) aArrF_tree_joined_trace ;
+      Domain.assert_trees_equal (Domain.add_trace xArrF added_trace aArrF_tree)
+        aArrF_tree_joined_trace ;
       (* starred tests *)
       (* we should do a strong update when updating x.f* with x.f *)
       let yF_tree_added_trace =
         Domain.make_normal_leaf added_trace |> Domain.AccessMap.singleton f
         |> Domain.make_node y_trace |> Domain.BaseMap.singleton y_base
       in
-      assert_trees_equal (Domain.add_trace yF added_trace yF_star_tree) yF_tree_added_trace ;
+      Domain.assert_trees_equal (Domain.add_trace yF added_trace yF_star_tree) yF_tree_added_trace ;
       (* but not when updating x* with x.f *)
       let x_star_tree_added_trace =
         let joined_trace = MockTraceDomain.join x_trace added_trace in
         Domain.BaseMap.singleton x_base (Domain.make_starred_leaf joined_trace)
       in
-      assert_trees_equal (Domain.add_trace xF added_trace x_star_tree) x_star_tree_added_trace ;
+      Domain.assert_trees_equal (Domain.add_trace xF added_trace x_star_tree)
+        x_star_tree_added_trace ;
       (* when updating x.f.g with x.f*, we should remember traces associated with f and g even as
          we replace that subtree with a * *)
       let xF_star_tree_joined_traces =
@@ -252,13 +259,14 @@ let tests =
         Domain.make_starred_leaf joined_trace |> Domain.AccessMap.singleton f
         |> Domain.make_node x_trace |> Domain.BaseMap.singleton x_base
       in
-      assert_trees_equal (Domain.add_trace xF_star added_trace xFG_tree) xF_star_tree_joined_traces ;
+      Domain.assert_trees_equal (Domain.add_trace xF_star added_trace xFG_tree)
+        xF_star_tree_joined_traces ;
       (* [add_node] tests are sparse, since [add_trace] is just [add_node] <empty node>. main things
          to test are (1) adding a non-empty node works, (2) adding a non-empty node does the proper
          joins in the weak update case *)
       (* case (1): adding XFG to y base tree works *)
       let y_xFG_tree = Domain.BaseMap.add y_base Domain.empty_node (mk_xFG_tree xFG_trace) in
-      assert_trees_equal (Domain.add_node x (mk_xFG_node xFG_trace) y_base_tree) y_xFG_tree ;
+      Domain.assert_trees_equal (Domain.add_node x (mk_xFG_node xFG_trace) y_base_tree) y_xFG_tree ;
       (* case (2): adding a non-empty node does weak updates when required *)
       let arr_tree =
         let arr_subtree =
@@ -268,7 +276,7 @@ let tests =
         Domain.AccessMap.singleton array (Domain.make_node xF_trace arr_subtree)
         |> Domain.make_node MockTraceDomain.empty |> Domain.BaseMap.singleton x_base
       in
-      assert_trees_equal (Domain.add_node xArr g_subtree aArrF_tree) arr_tree
+      Domain.assert_trees_equal (Domain.add_node xArr g_subtree aArrF_tree) arr_tree
     in
     "add_trace" >:: add_trace_test_
   in
@@ -317,18 +325,18 @@ let tests =
   let join_test =
     let join_test_ _ =
       (* normal |_| normal *)
-      assert_trees_equal (Domain.join x_base_tree y_base_tree) x_y_base_tree ;
-      assert_trees_equal (Domain.join y_base_tree x_base_tree) x_y_base_tree ;
-      assert_trees_equal (Domain.join x_y_base_tree x_base_tree) x_y_base_tree ;
-      assert_trees_equal (Domain.join x_base_tree xFG_tree) xFG_tree ;
+      Domain.assert_trees_equal (Domain.join x_base_tree y_base_tree) x_y_base_tree ;
+      Domain.assert_trees_equal (Domain.join y_base_tree x_base_tree) x_y_base_tree ;
+      Domain.assert_trees_equal (Domain.join x_y_base_tree x_base_tree) x_y_base_tree ;
+      Domain.assert_trees_equal (Domain.join x_base_tree xFG_tree) xFG_tree ;
       (* starred |_| starred *)
-      assert_trees_equal (Domain.join x_star_tree yF_star_tree) x_yF_star_tree ;
+      Domain.assert_trees_equal (Domain.join x_star_tree yF_star_tree) x_yF_star_tree ;
       (* normal |_| starred *)
-      assert_trees_equal (Domain.join tree xFG_tree) tree ;
+      Domain.assert_trees_equal (Domain.join tree xFG_tree) tree ;
       (* [x_star_tree] and [x_base_tree] both have trace "{ x }" associated with x... *)
-      assert_trees_equal (Domain.join x_star_tree x_base_tree) x_star_tree ;
+      Domain.assert_trees_equal (Domain.join x_star_tree x_base_tree) x_star_tree ;
       (* ...but [xFG_tree] has some nested traces that should get joined with "{ x }" *)
-      assert_trees_equal (Domain.join x_star_tree xFG_tree) x_star_tree_xFG_trace
+      Domain.assert_trees_equal (Domain.join x_star_tree xFG_tree) x_star_tree_xFG_trace
     in
     "join" >:: join_test_
   in
@@ -346,7 +354,7 @@ let tests =
       let x_tree_x_trace = make_x_base_tree x_trace in
       let x_tree_y_trace = make_x_base_tree y_trace in
       let x_tree_top_trace = make_x_base_tree MockTraceDomain.top in
-      assert_trees_equal (widen x_tree_x_trace x_tree_y_trace) x_tree_top_trace ;
+      Domain.assert_trees_equal (widen x_tree_x_trace x_tree_y_trace) x_tree_top_trace ;
       (* adding stars to a base works:
          x |-> ({}, empty) \/ y |-> ({}, empty) =
          (x |-> ({}, empty), y |-> ({}, Star) )
@@ -354,7 +362,7 @@ let tests =
       let x_y_star_base_tree =
         Domain.BaseMap.add y_base (Domain.make_starred_leaf MockTraceDomain.empty) x_base_tree
       in
-      assert_trees_equal (widen x_base_tree y_base_tree) x_y_star_base_tree ;
+      Domain.assert_trees_equal (widen x_base_tree y_base_tree) x_y_star_base_tree ;
       (* adding stars to a subtree works:
          x |-> ("y", empty) \/
          x |-> ("x" , f |-> ("f", g |-> ("g", empty))) =
@@ -364,7 +372,7 @@ let tests =
         Domain.AccessMap.singleton f (Domain.make_starred_leaf MockTraceDomain.top)
         |> Domain.make_node MockTraceDomain.top |> Domain.BaseMap.singleton x_base
       in
-      assert_trees_equal (widen x_tree_y_trace xFG_tree) xF_star_tree ;
+      Domain.assert_trees_equal (widen x_tree_y_trace xFG_tree) xF_star_tree ;
       (* widening is not commutative, and is it not join:
          x |-> ("x" , f |-> ("f", g |-> ("g", empty))) \/
          x |-> ("y", empty) =
@@ -374,7 +382,7 @@ let tests =
         let _, xFG_node = x_subtree in
         Domain.BaseMap.singleton x_base (MockTraceDomain.top, xFG_node)
       in
-      assert_trees_equal (widen xFG_tree x_tree_y_trace) xFG_tree_widened_trace
+      Domain.assert_trees_equal (widen xFG_tree x_tree_y_trace) xFG_tree_widened_trace
     in
     "widen" >:: widen_test_
   in
@@ -406,10 +414,62 @@ let tests =
       assert_equal (Domain.depth xFG_tree) 3 ;
       assert_equal (Domain.depth x_star_tree) 1 ;
       assert_equal (Domain.depth yF_star_tree) 2 ;
-      assert_equal (Domain.depth x_yF_star_tree) 2 ;
-      ()
+      assert_equal (Domain.depth x_yF_star_tree) 2
     in
     "depth" >:: depth_test_
   in
+  let max_depth_test =
+    let max_depth_test_ _ =
+      let module Max1 = MakeTree (struct
+        let max_depth = 1
+      end) in
+      let f_node =
+        Max1.AccessMap.singleton f (Max1.make_normal_leaf x_trace)
+        |> Max1.make_node MockTraceDomain.empty
+      in
+      let x_tree = Max1.BaseMap.singleton x_base (Max1.make_normal_leaf x_trace) in
+      let x_star_tree = Max1.BaseMap.singleton x_base (Max1.make_starred_leaf x_trace) in
+      (* adding (x.f, "x") to a tree with max height 1 should yield  x |-> ("x", * ) *)
+      Max1.assert_trees_equal (Max1.add_trace xF x_trace Max1.empty) x_star_tree ;
+      (* same, but with (x.f.g, "x") *)
+      Max1.assert_trees_equal (Max1.add_trace xFG x_trace Max1.empty) x_star_tree ;
+      (* adding node (f, "x") via access path x should also yield the same tree *)
+      Max1.assert_trees_equal (Max1.add_node x f_node Max1.empty) x_star_tree ;
+      (* adding (x, "x") shouldn't add stars *)
+      Max1.assert_trees_equal (Max1.add_trace x x_trace Max1.empty) x_tree ;
+      let module Max2 = MakeTree (struct
+        let max_depth = 2
+      end) in
+      let f_node =
+        Max2.AccessMap.singleton f (Max2.make_normal_leaf x_trace)
+        |> Max2.make_node MockTraceDomain.empty
+      in
+      let fG_node =
+        Max2.make_access_node MockTraceDomain.empty g x_trace |> Max2.AccessMap.singleton f
+        |> Max2.make_node MockTraceDomain.empty
+      in
+      let f_star_node =
+        Max2.AccessMap.singleton f (Max2.make_starred_leaf x_trace)
+        |> Max2.make_node MockTraceDomain.empty
+      in
+      let x_tree = Max2.BaseMap.singleton x_base Max2.empty_node in
+      let xF_tree = Max2.BaseMap.singleton x_base f_node in
+      let xF_star_tree = Max2.BaseMap.singleton x_base f_star_node in
+      (* adding x.f to an empty tree should't add stars... *)
+      Max2.assert_trees_equal (Max2.add_trace xF x_trace Max2.empty) xF_tree ;
+      (* ... but adding x.f.g should *)
+      Max2.assert_trees_equal (Max2.add_trace xFG x_trace Max2.empty) xF_star_tree ;
+      (* adding the node (f.g, "x") to a tree with x should produce the same result *)
+      Max2.assert_trees_equal (Max2.add_node x fG_node x_tree) xF_star_tree
+    in
+    "max_depth" >:: max_depth_test_
+  in
   "access_tree_suite"
-  >::: [get_trace_test; add_trace_test; lteq_test; join_test; widen_test; fold_test; depth_test]
+  >::: [ get_trace_test
+       ; add_trace_test
+       ; lteq_test
+       ; join_test
+       ; widen_test
+       ; fold_test
+       ; depth_test
+       ; max_depth_test ]