Add flake checks

flake/checks.nix

@@ -0,0 +1,26 @@
+{ self, inputs, ... }:
+{
+  perSystem =
+    { pkgs, ... }:
+    {
+      checks = {
+        treefmt = (import ./treefmt.nix { inherit inputs pkgs; }).check self;
+
+        statix =
+          let
+            statix-config = pkgs.writeText "statix.toml" ''
+              disabled = ["repeated_keys"]
+            '';
+          in
+          pkgs.runCommand "statix" { buildInputs = [ pkgs.statix ]; } ''
+            statix check ${self} --config ${statix-config}
+            mkdir $out
+          '';
+
+        deadnix = pkgs.runCommand "deadnix" { buildInputs = [ pkgs.deadnix ]; } ''
+          deadnix ${self} --fail --exclude ${self}/flake/formatter.nix
+          mkdir $out
+        '';
+      };
+    };
+}