diff --git a/lib/path/tests/default.nix b/lib/path/tests/default.nix
index 784a3af68b6e4..9a31e42828f48 100644
--- a/lib/path/tests/default.nix
+++ b/lib/path/tests/default.nix
@@ -7,10 +7,14 @@
     inherit system;
   },
   libpath ? ../..,
+  # Random seed
+  seed ? null,
 }:
 pkgs.runCommand "lib-path-tests" {
   nativeBuildInputs = with pkgs; [
     nix
+    jq
+    bc
   ];
 } ''
   # Needed to make Nix evaluation work
@@ -23,5 +27,8 @@ pkgs.runCommand "lib-path-tests" {
   nix-instantiate --eval lib/path/tests/unit.nix \
     --argstr libpath "$TEST_LIB"
 
+  echo "Running property tests lib/path/tests/prop.sh"
+  bash lib/path/tests/prop.sh ${toString seed}
+
   touch $out
 ''
diff --git a/lib/path/tests/generate.awk b/lib/path/tests/generate.awk
new file mode 100644
index 0000000000000..811dd0c46d332
--- /dev/null
+++ b/lib/path/tests/generate.awk
@@ -0,0 +1,64 @@
+# Generate random path-like strings, separated by null characters.
+#
+# Invocation:
+#
+#     awk -f ./generate.awk -v <variable>=<value> | tr '\0' '\n'
+#
+# Customizable variables (all default to 0):
+# - seed: Deterministic random seed to use for generation
+# - count: Number of paths to generate
+# - extradotweight: Give extra weight to dots being generated
+# - extraslashweight: Give extra weight to slashes being generated
+# - extranullweight: Give extra weight to null being generated, making paths shorter
+BEGIN {
+  # Random seed, passed explicitly for reproducibility
+  srand(seed)
+
+  # Don't include special characters below 32
+  minascii = 32
+  # Don't include DEL at 128
+  maxascii = 127
+  upperascii = maxascii - minascii
+
+  # add extra weight for ., in addition to the one weight from the ascii range
+  upperdot = upperascii + extradotweight
+
+  # add extra weight for /, in addition to the one weight from the ascii range
+  upperslash = upperdot + extraslashweight
+
+  # add extra weight for null, indicating the end of the string
+  # Must be at least 1 to have strings end at all
+  total = upperslash + 1 + extranullweight
+
+  # new=1 indicates that it's a new string
+  new=1
+  while (count > 0) {
+
+    # Random integer between [0, total)
+    value = int(rand() * total)
+
+    if (value < upperascii) {
+      # Ascii range
+      printf("%c", value + minascii)
+      new=0
+
+    } else if (value < upperdot) {
+      # Dot range
+      printf "."
+      new=0
+
+    } else if (value < upperslash) {
+      # If it's the start of a new path, only generate a / in 10% of cases
+      # This is always an invalid subpath, which is not a very interesting case
+      if (new && rand() > 0.1) continue
+      printf "/"
+
+    } else {
+      # Do not generate empty strings
+      if (new) continue
+      printf "\x00"
+      count--
+      new=1
+    }
+  }
+}
diff --git a/lib/path/tests/prop.nix b/lib/path/tests/prop.nix
new file mode 100644
index 0000000000000..67e5c1e9d61c7
--- /dev/null
+++ b/lib/path/tests/prop.nix
@@ -0,0 +1,60 @@
+# Given a list of path-like strings, check some properties of the path library
+# using those paths and return a list of attribute sets of the following form:
+#
+#     { <string> = <lib.path.subpath.normalise string>; }
+#
+# If `normalise` fails to evaluate, the attribute value is set to `""`.
+# If not, the resulting value is normalised again and an appropriate attribute set added to the output list.
+{
+  # The path to the nixpkgs lib to use
+  libpath,
+  # A flat directory containing files with randomly-generated
+  # path-like values
+  dir,
+}:
+let
+  lib = import libpath;
+
+  # read each file into a string
+  strings = map (name:
+    builtins.readFile (dir + "/${name}")
+  ) (builtins.attrNames (builtins.readDir dir));
+
+  inherit (lib.path.subpath) normalise isValid;
+  inherit (lib.asserts) assertMsg;
+
+  normaliseAndCheck = str:
+    let
+      originalValid = isValid str;
+
+      tryOnce = builtins.tryEval (normalise str);
+      tryTwice = builtins.tryEval (normalise tryOnce.value);
+
+      absConcatOrig = /. + ("/" + str);
+      absConcatNormalised = /. + ("/" + tryOnce.value);
+    in
+      # Check the lib.path.subpath.normalise property to only error on invalid subpaths
+      assert assertMsg
+        (originalValid -> tryOnce.success)
+        "Even though string \"${str}\" is valid as a subpath, the normalisation for it failed";
+      assert assertMsg
+        (! originalValid -> ! tryOnce.success)
+        "Even though string \"${str}\" is invalid as a subpath, the normalisation for it succeeded";
+
+      # Check normalisation idempotency
+      assert assertMsg
+        (originalValid -> tryTwice.success)
+        "For valid subpath \"${str}\", the normalisation \"${tryOnce.value}\" was not a valid subpath";
+      assert assertMsg
+        (originalValid -> tryOnce.value == tryTwice.value)
+        "For valid subpath \"${str}\", normalising it once gives \"${tryOnce.value}\" but normalising it twice gives a different result: \"${tryTwice.value}\"";
+
+      # Check that normalisation doesn't change a string when appended to an absolute Nix path value
+      assert assertMsg
+        (originalValid -> absConcatOrig == absConcatNormalised)
+        "For valid subpath \"${str}\", appending to an absolute Nix path value gives \"${absConcatOrig}\", but appending the normalised result \"${tryOnce.value}\" gives a different value \"${absConcatNormalised}\"";
+
+      # Return an empty string when failed
+      if tryOnce.success then tryOnce.value else "";
+
+in lib.genAttrs strings normaliseAndCheck
diff --git a/lib/path/tests/prop.sh b/lib/path/tests/prop.sh
new file mode 100755
index 0000000000000..c956e55bbfa05
--- /dev/null
+++ b/lib/path/tests/prop.sh
@@ -0,0 +1,179 @@
+#!/usr/bin/env bash
+
+# Property tests for the `lib.path` library
+#
+# It generates random path-like strings and runs the functions on
+# them, checking that the expected laws of the functions hold
+
+set -euo pipefail
+shopt -s inherit_errexit
+
+# https://stackoverflow.com/a/246128
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+
+if test -z "${TEST_LIB:-}"; then
+    TEST_LIB=$SCRIPT_DIR/../..
+fi
+
+tmp="$(mktemp -d)"
+clean_up() {
+    rm -rf "$tmp"
+}
+trap clean_up EXIT
+mkdir -p "$tmp/work"
+cd "$tmp/work"
+
+# Defaulting to a random seed but the first argument can override this
+seed=${1:-$RANDOM}
+echo >&2 "Using seed $seed, use \`lib/path/tests/prop.sh $seed\` to reproduce this result"
+
+# The number of random paths to generate. This specific number was chosen to
+# be fast enough while still generating enough variety to detect bugs.
+count=500
+
+debug=0
+# debug=1 # print some extra info
+# debug=2 # print generated values
+
+# Fine tuning parameters to balance the number of generated invalid paths
+# to the variance in generated paths.
+extradotweight=64   # Larger value: more dots
+extraslashweight=64 # Larger value: more slashes
+extranullweight=16  # Larger value: shorter strings
+
+die() {
+    echo >&2 "test case failed: " "$@"
+    exit 1
+}
+
+if [[ "$debug" -ge 1 ]]; then
+    echo >&2 "Generating $count random path-like strings"
+fi
+
+# Read stream of null-terminated strings entry-by-entry into bash,
+# write it to a file and the `strings` array.
+declare -a strings=()
+mkdir -p "$tmp/strings"
+while IFS= read -r -d $'\0' str; do
+    echo -n "$str" > "$tmp/strings/${#strings[@]}"
+    strings+=("$str")
+done < <(awk \
+    -f "$SCRIPT_DIR"/generate.awk \
+    -v seed="$seed" \
+    -v count="$count" \
+    -v extradotweight="$extradotweight" \
+    -v extraslashweight="$extraslashweight" \
+    -v extranullweight="$extranullweight")
+
+if [[ "$debug" -ge 1 ]]; then
+    echo >&2 "Trying to normalise the generated path-like strings with Nix"
+fi
+
+# Precalculate all normalisations with a single Nix call. Calling Nix for each
+# string individually would take way too long
+nix-instantiate --eval --strict --json \
+    --argstr libpath "$TEST_LIB" \
+    --argstr dir "$tmp/strings" \
+    "$SCRIPT_DIR"/prop.nix \
+    >"$tmp/result.json"
+
+# Uses some jq magic to turn the resulting attribute set into an associative
+# bash array assignment
+declare -A normalised_result="($(jq '
+    to_entries
+    | map("[\(.key | @sh)]=\(.value | @sh)")
+    | join(" \n")' -r < "$tmp/result.json"))"
+
+# Looks up a normalisation result for a string
+# Checks that the normalisation is only failing iff it's an invalid subpath
+# For valid subpaths, returns 0 and prints the normalisation result
+# For invalid subpaths, returns 1
+normalise() {
+    local str=$1
+    # Uses the same check for validity as in the library implementation
+    if [[ "$str" == "" || "$str" == /* || "$str" =~ ^(.*/)?\.\.(/.*)?$ ]]; then
+        valid=
+    else
+        valid=1
+    fi
+
+    normalised=${normalised_result[$str]}
+    # An empty string indicates failure, this is encoded in ./prop.nix
+    if [[ -n "$normalised" ]]; then
+        if [[ -n "$valid" ]]; then
+            echo "$normalised"
+        else
+            die "For invalid subpath \"$str\", lib.path.subpath.normalise returned this result: \"$normalised\""
+        fi
+    else
+        if [[ -n "$valid" ]]; then
+            die "For valid subpath \"$str\", lib.path.subpath.normalise failed"
+        else
+            if [[ "$debug" -ge 2 ]]; then
+                echo >&2 "String \"$str\" is not a valid subpath"
+            fi
+            # Invalid and it correctly failed, we let the caller continue if they catch the exit code
+            return 1
+        fi
+    fi
+}
+
+# Intermediate result populated by test_idempotency_realpath
+# and used in test_normalise_uniqueness
+#
+# Contains a mapping from a normalised subpath to the realpath result it represents
+declare -A norm_to_real
+
+test_idempotency_realpath() {
+    if [[ "$debug" -ge 1 ]]; then
+        echo >&2 "Checking idempotency of each result and making sure the realpath result isn't changed"
+    fi
+
+    # Count invalid subpaths to display stats
+    invalid=0
+    for str in "${strings[@]}"; do
+        if ! result=$(normalise "$str"); then
+            ((invalid++)) || true
+            continue
+        fi
+
+        # Check the law that it doesn't change the result of a realpath
+        mkdir -p -- "$str" "$result"
+        real_orig=$(realpath -- "$str")
+        real_norm=$(realpath -- "$result")
+
+        if [[ "$real_orig" != "$real_norm" ]]; then
+            die "realpath of the original string \"$str\" (\"$real_orig\") is not the same as realpath of the normalisation \"$result\" (\"$real_norm\")"
+        fi
+
+        if [[ "$debug" -ge 2 ]]; then
+            echo >&2 "String \"$str\" gets normalised to \"$result\" and file path \"$real_orig\""
+        fi
+        norm_to_real["$result"]="$real_orig"
+    done
+    if [[ "$debug" -ge 1 ]]; then
+        echo >&2 "$(bc <<< "scale=1; 100 / $count * $invalid")% of the total $count generated strings were invalid subpath strings, and were therefore ignored"
+    fi
+}
+
+test_normalise_uniqueness() {
+    if [[ "$debug" -ge 1 ]]; then
+        echo >&2 "Checking for the uniqueness law"
+    fi
+
+    for norm_p in "${!norm_to_real[@]}"; do
+        real_p=${norm_to_real["$norm_p"]}
+        for norm_q in "${!norm_to_real[@]}"; do
+            real_q=${norm_to_real["$norm_q"]}
+            # Checks normalisation uniqueness law for each pair of values
+            if [[ "$norm_p" != "$norm_q" && "$real_p" == "$real_q" ]]; then
+                die "Normalisations \"$norm_p\" and \"$norm_q\" are different, but the realpath of them is the same: \"$real_p\""
+            fi
+        done
+    done
+}
+
+test_idempotency_realpath
+test_normalise_uniqueness
+
+echo >&2 tests ok