feat(nix/stateMonad): simple Nix state monad implementation

In the absence of do syntactic sugar relatively tedious to write, but
useful to express certain types of algorithms. I found it useful to
memoize intermediate results as they are calculated in order to avoid
recomputing them later in a drv dependency analyzer I've written.

Change-Id: I47cf3c644a96952c70276c9fa4cb3190b1c1e027
Reviewed-on: https://cl.tvl.fyi/c/depot/+/6828
Autosubmit: sterni <sternenseemann@systemli.org>
Tested-by: BuildkiteCI
Reviewed-by: grfn <grfn@gws.fyi>

nix/stateMonad/default.nix

@@ -0,0 +1,76 @@
+# Simple state monad represented as
+#
+#     stateMonad s a = s -> { state : s; value : a }
+#
+{ ... }:
+
+rec {
+  #
+  # Monad
+  #
+
+  # Type: stateMonad s a -> (a -> stateMonad s b) -> stateMonad s b
+  bind = action: f: state:
+    let
+      afterAction = action state;
+    in
+    (f afterAction.value) afterAction.state;
+
+  # Type: stateMonad s a -> stateMonad s b -> stateMonad s b
+  after = action1: action2: bind action1 (_: action2);
+
+  # Type: stateMonad s (stateMonad s a) -> stateMonad s a
+  join = action: bind action (action': action');
+
+  # Type: [a] -> (a -> stateMonad s b) -> stateMonad s null
+  for_ = xs: f:
+    builtins.foldl'
+      (laterAction: x:
+        after (f x) laterAction
+      )
+      (pure null)
+      xs;
+
+  #
+  # Applicative
+  #
+
+  # Type: a -> stateMonad s a
+  pure = value: state: { inherit state value; };
+
+  # TODO(sterni): <*>, lift2, …
+
+  #
+  # Functor
+  #
+
+  # Type: (a -> b) -> stateMonad s a -> stateMonad s b
+  fmap = f: action: bind action (result: pure (f result));
+
+  #
+  # State Monad
+  #
+
+  # Type: (s -> s) -> stateMonad s null
+  modify = f: state: { value = null; state = f state; };
+
+  # Type: stateMonad s s
+  get = state: { value = state; inherit state; };
+
+  # Type: s -> stateMonad s null
+  set = new: modify (_: new);
+
+  # Type: str -> stateMonad set set.${str}
+  getAttr = attr: fmap (state: state.${attr}) get;
+
+  # Type: str -> (any -> any) -> stateMonad s null
+  modifyAttr = attr: f: modify (state: state // {
+    ${attr} = f state.${attr};
+  });
+
+  # Type: str -> any -> stateMonad s null
+  setAttr = attr: value: modifyAttr attr (_: value);
+
+  # Type: s -> stateMonad s a -> a
+  run = state: action: (action state).value;
+}