refactor: redo signatures and fix documentation

src/Reader.ml

@@ -1,10 +1,9 @@
 module type S =
 sig
-  module Env : Sigs.Type
-
-  val read : unit -> Env.t
-  val scope : (Env.t -> Env.t) -> (unit -> 'a) -> 'a
-  val run : env:Env.t -> (unit -> 'a) -> 'a
+  type env
+  val read : unit -> env
+  val scope : (env -> env) -> (unit -> 'a) -> 'a
+  val run : env:env -> (unit -> 'a) -> 'a
   val register_printer : ([`Read] -> string option) -> unit
 end
 

src/Reader.mli

@@ -16,24 +16,21 @@
    ]}
 *)
 
-(** This should be equivalent to {!Unmonad} applying to the standard reader monad. *)
-
 module type S =
 sig
   (** Signatures of read effects. *)
 
-  (** Type of environments. *)
-  module Env : Sigs.Type
-  (** @open *)
+  type env
+  (** The type of environments. *)
 
-  val read : unit -> Env.t
+  val read : unit -> env
   (** Read the environment. *)
 
-  val scope : (Env.t -> Env.t) -> (unit -> 'a) -> 'a
+  val scope : (env -> env) -> (unit -> 'a) -> 'a
   (** [scope f t] runs the thunk [t] under the new environment that is the result of applying [f] to the current environment. *)
 
-  val run : env:Env.t -> (unit -> 'a) -> 'a
-  (** [run t] runs the thunk [t] which may perform reading effects. *)
+  val run : env:env -> (unit -> 'a) -> 'a
+  (** [run ~env t] runs the thunk [t] which may perform reading effects on the value [env]. *)
 
   val register_printer : ([`Read] -> string option) -> unit
   (** [register_printer p] registers a printer [p] via {!val:Printexc.register_printer} to convert the unhandled internal effect into a string for the OCaml runtime system to display. Ideally, the internal effect should have been handled by {!val:run} and there is no need to use this function, but when it is not the case, this function can be helpful for debugging. The functor {!module:Reader.Make} always registers a simple printer to suggest using {!val:run}, but you can register new ones to override it. The return type of the printer [p] should return [Some s] where [s] is the resulting string, or [None] if it chooses not to convert a particular effect. The registered printers are tried in reverse order until one of them returns [Some s] for some [s]; that is, the last registered printer is tried first. Note that this function is a wrapper of {!val:Printexc.register_printer} and all the registered printers (via this function or {!val:Printexc.register_printer}) are put into the same list.
@@ -44,5 +41,5 @@ sig
   *)
 end
 
-module Make (Env : Sigs.Type) : S with module Env := Env
+module Make (Env : Sigs.Type) : S with type env := Env.t
 (** The implementation of read effects. *)

src/Sequencer.ml

@@ -1,10 +1,9 @@
 module type S =
 sig
-  module Elt : Sigs.Type
-
-  val yield : Elt.t -> unit
-  val run : (unit -> unit) -> Elt.t Seq.t
-  val register_printer : ([`Yield of Elt.t] -> string option) -> unit
+  type elt
+  val yield : elt -> unit
+  val run : (unit -> unit) -> elt Seq.t
+  val register_printer : ([`Yield of elt] -> string option) -> unit
 end
 
 module Make (Elt : Sigs.Type) =

src/Sequencer.mli

@@ -19,16 +19,16 @@ module type S =
 sig
   (** Signatures of sequencing effects. *)
 
-  module Elt : Sigs.Type
-  (** @open *)
+  type elt
+  (** The type of elements. *)
 
-  val yield : Elt.t -> unit
+  val yield : elt -> unit
   (** Yield the element. *)
 
-  val run : (unit -> unit) -> Elt.t Seq.t
+  val run : (unit -> unit) -> elt Seq.t
   (** [run t] runs the thunk [t] which may perform sequencing effects. *)
 
-  val register_printer : ([`Yield of Elt.t] -> string option) -> unit
+  val register_printer : ([`Yield of elt] -> string option) -> unit
   (** [register_printer p] registers a printer [p] via {!val:Printexc.register_printer} to convert unhandled internal effects into strings for the OCaml runtime system to display. Ideally, all internal effects should have been handled by {!val:run} and there is no need to use this function, but when it is not the case, this function can be helpful for debugging. The functor {!module:Sequencer.Make} always registers a simple printer to suggest using {!val:run}, but you can register new ones to override it. The return type of the printer [p] should return [Some s] where [s] is the resulting string, or [None] if it chooses not to convert a particular effect. The registered printers are tried in reverse order until one of them returns [Some s] for some [s]; that is, the last registered printer is tried first. Note that this function is a wrapper of {!val:Printexc.register_printer} and all the registered printers (via this function or {!val:Printexc.register_printer}) are put into the same list.
 
       The input type of the printer [p] is a variant representation of the internal effects used in this module. They correspond to the effects trigger by {!val:yield}. More precisely, [`Yield elt] corresponds to the effect triggered by [yield elt].
@@ -37,5 +37,5 @@ sig
   *)
 end
 
-module Make (Elt : Sigs.Type) : S with module Elt := Elt
+module Make (Elt : Sigs.Type) : S with type elt := Elt.t
 (** The implementation of sequencing effects. *)

src/State.ml

@@ -1,12 +1,11 @@
 module type S =
 sig
-  module State : Sigs.Type
-
-  val get : unit -> State.t
-  val set : State.t -> unit
-  val modify : (State.t -> State.t) -> unit
-  val run : init:State.t -> (unit -> 'a) -> 'a
-  val register_printer : ([`Get | `Set of State.t] -> string option) -> unit
+  type state
+  val get : unit -> state
+  val set : state -> unit
+  val modify : (state -> state) -> unit
+  val run : init:state -> (unit -> 'a) -> 'a
+  val register_printer : ([`Get | `Set of state] -> string option) -> unit
 end
 
 module Make (State : Sigs.Type) =

src/State.mli

@@ -11,30 +11,27 @@
    ]}
 *)
 
-(** This should be equivalent to {!module:Unmonad} applying to the standard state monad when continuations are one-shot.
-    (The current implementation uses mutable references and this statement has not been formally proved.) *)
-
 module type S =
 sig
   (** Signatures of read effects. *)
 
-  module State : Sigs.Type
-  (** @open *)
+  type state
+  (** The type of states. *)
 
-  val get : unit -> State.t
+  val get : unit -> state
   (** [get ()] reads the current state. *)
 
-  val set : State.t -> unit
+  val set : state -> unit
   (** [set x] makes [x] the new state. *)
 
-  val modify : (State.t -> State.t) -> unit
+  val modify : (state -> state) -> unit
   (** [modify f] applies [f] to the current state and then set the result as the new state. *)
 
-  val run : init:State.t -> (unit -> 'a) -> 'a
-  (** [run t] runs the thunk [t] which may perform state effects. *)
+  val run : init:state -> (unit -> 'a) -> 'a
+  (** [run ~init t] runs the thunk [t] which may perform state effects. The initial state is [init]. *)
 
-  val register_printer : ([`Get | `Set of State.t] -> string option) -> unit
-  (** [register_printer p] registers a printer [p] via {!val:Printexc.register_printer} to convert unhandled internal effects into strings for the OCaml runtime system to display. Ideally, all internal effects should have been handled by {!val:run} and there is no need to use this function, but when it is not the case, this function can be helpful for debugging. The functor {!module:State.Make} always registers a simple printer to suggest using {!val:run}, but you can register new ones to override it. The return type of the printer [p] should return [Some s] where [s] is the resulting string, or [None] if it chooses not to convert a particular effect. The registered printers are tried in reverse order until one of them returns [Some s] for some [s]; that is, the last registered printer is tried first. Note that this function is a wrapper of {!val:Printexc.register_printer} and all the registered printers (via this function or {!val:Printexc.register_printer}) are put into the same list.
+  val register_printer : ([`Get | `Set of state] -> string option) -> unit
+  (** [register_printer p] registers a printer [p] via {!val:Printexc.register_printer} to convert unhandled internal effects into strings for the OCaml runtime system to display. Ideally, all internal effects should have been handled by {!val:run} and there is no need to use this function, but when it is not the case, this function can be helpful for debugging. The functor {!module:Make} always registers a simple printer to suggest using {!val:run}, but you can register new ones to override it. The return type of the printer [p] should return [Some s] where [s] is the resulting string, or [None] if it chooses not to convert a particular effect. The registered printers are tried in reverse order until one of them returns [Some s] for some [s]; that is, the last registered printer is tried first. Note that this function is a wrapper of {!val:Printexc.register_printer} and all the registered printers (via this function or {!val:Printexc.register_printer}) are put into the same list.
 
       The input type of the printer [p] is a variant representation of the internal effects used in this module. They correspond to the effects trigger by {!val:get} and {!val:set}. More precisely,
       - [`Get] corresponds to the effect triggered by [get ()].
@@ -44,5 +41,5 @@ sig
   *)
 end
 
-module Make (State : Sigs.Type) : S with module State := State
+module Make (State : Sigs.Type) : S with type state := State.t
 (** The implementation of state effects. *)

src/UniqueID.ml

@@ -1,6 +1,6 @@
 module type S =
 sig
-  module Elt : Sigs.Type
+  type elt
 
   module ID :
   sig
@@ -12,11 +12,11 @@ sig
   end
   type id = ID.t
 
-  val register : Elt.t -> id
-  val retrieve : id -> Elt.t
-  val export : unit -> Elt.t Seq.t
-  val run : ?init:Elt.t Seq.t -> (unit -> 'a) -> 'a
-  val register_printer : ([`Register of Elt.t | `Retrieve of id | `Export] -> string option) -> unit
+  val register : elt -> id
+  val retrieve : id -> elt
+  val export : unit -> elt Seq.t
+  val run : ?init:elt Seq.t -> (unit -> 'a) -> 'a
+  val register_printer : ([`Register of elt | `Retrieve of id | `Export] -> string option) -> unit
 end
 
 module Make (Elt : Sigs.Type) =

src/UniqueID.mli

@@ -7,8 +7,8 @@ module type S =
 sig
   (** Signatures of the effects. *)
 
-  module Elt : Sigs.Type
-  (** @open *)
+  type elt
+  (** The type of elements *)
 
   (** The type of IDs and its friends. *)
   module ID :
@@ -32,22 +32,22 @@ sig
   type id = ID.t
   (** The type of unique IDs. The client should not assume a particular indexing scheme. *)
 
-  val register : Elt.t -> id
+  val register : elt -> id
   (** Register a new item and get an ID. Note that registering the same item twice will get two different IDs. *)
 
-  val retrieve : id -> Elt.t
+  val retrieve : id -> elt
   (** Retrieve the item associated with the ID. *)
 
-  val export : unit -> Elt.t Seq.t
+  val export : unit -> elt Seq.t
   (** Export the internal storage for serialization. Once exported, the representation is persistent and can be traversed without the effect handler. *)
 
-  val run : ?init:Elt.t Seq.t -> (unit -> 'a) -> 'a
+  val run : ?init:elt Seq.t -> (unit -> 'a) -> 'a
   (** [run t] runs the thunk [t] and handles the effects for generating unique IDs.
 
       @param init The initial storage, which should be the output of some previous {!val:export}.
   *)
 
-  val register_printer : ([`Register of Elt.t | `Retrieve of id | `Export] -> string option) -> unit
+  val register_printer : ([`Register of elt | `Retrieve of id | `Export] -> string option) -> unit
   (** [register_printer p] registers a printer [p] via {!val:Printexc.register_printer} to convert unhandled internal effects into strings for the OCaml runtime system to display. Ideally, all internal effects should have been handled by {!val:run} and there is no need to use this function, but when it is not the case, this function can be helpful for debugging. The functor {!module:UniqueID.Make} always registers a simple printer to suggest using {!val:run}, but you can register new ones to override it. The return type of the printer [p] should return [Some s] where [s] is the resulting string, or [None] if it chooses not to convert a particular effect. The registered printers are tried in reverse order until one of them returns [Some s] for some [s]; that is, the last registered printer is tried first. Note that this function is a wrapper of {!val:Printexc.register_printer} and all the registered printers (via this function or {!val:Printexc.register_printer}) are put into the same list.
 
       The input type of the printer [p] is a variant representation of the internal effects used in this module. They correspond to the effects trigger by {!val:register}, {!val:retrieve} and {!val:export}. More precisely,
@@ -59,5 +59,5 @@ sig
   *)
 end
 
-module Make (Elt : Sigs.Type) : S with module Elt := Elt
+module Make (Elt : Sigs.Type) : S with type elt := Elt.t
 (** The implementation of the effects. *)

test/TestReader.ml

@@ -38,7 +38,7 @@ let gen_cmd =
 
 let gen_prog = Q.Gen.list gen_cmd
 
-module ReaderTester (S : Algaeff.Reader.S with module Env := Int) =
+module ReaderTester (S : Algaeff.Reader.S with type env := int) =
 struct
   let trace ~env prog =
     let rec go =

test/TestSequencer.ml

@@ -34,7 +34,7 @@ and prog = cmd list
 let gen_cmd = Q.Gen.map (fun i -> Yield i) Q.Gen.int
 let gen_prog = Q.Gen.list gen_cmd
 
-module SequencerTester (S : Algaeff.Sequencer.S with module Elt := Int) =
+module SequencerTester (S : Algaeff.Sequencer.S with type elt := int) =
 struct
   let trace (prog : prog) =
     let go = function (Yield i) -> S.yield i in

test/TestState.ml

@@ -33,7 +33,7 @@ let gen_cmd =
 
 let gen_prog = Q.Gen.list gen_cmd
 
-module StateTester (S : Algaeff.State.S with module State := Int) =
+module StateTester (S : Algaeff.State.S with type state := int) =
 struct
   let trace ~init prog =
     let go =