option monad, and some design changes

lib/exposed.ml

@@ -10,4 +10,11 @@ type 'a stack =
 
 type 'a tree =
     | Leaf
-    | Branch of 'a * 'a tree list
+    | Branch of 'a * 'a tree list
+
+
+let id (x : 'a) = x
+
+let ( >> ) f g x = g (f x)
+
+let ( << ) g f x = g (f x)

lib/exposed.mli

@@ -13,4 +13,13 @@ type 'a stack =
 (* A purely functional tree with arbitrarily many branches at each node. *)
 type 'a tree =
     | Leaf
-    | Branch of 'a * 'a tree list
+    | Branch of 'a * 'a tree list
+
+(** Identity function. *)
+val id : 'a -> 'a
+
+(** Function composition. (f >> g) x represents g (f x). *)
+val ( >> ) : ('a -> 'b) -> ('b -> 'c) -> 'a -> 'c
+
+(** Function composition. (f << g) x represents f (g x). *)
+val ( << ) : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b

lib/functions.ml

@@ -1,5 +0,0 @@
-let id (x : 'a) = x
-
-let ( >> ) f g x = g (f x)
-
-let ( << ) g f x = g (f x)

lib/functions.mli

@@ -1,8 +0,0 @@
-(** Identity function. *)
-val id : 'a -> 'a
-
-(** Function composition. (f >> g) x represents g (f x). *)
-val ( >> ) : ('a -> 'b) -> ('b -> 'c) -> 'a -> 'c
-
-(** Function composition. (f << g) x represents f (g x). *)
-val ( << ) : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b

lib/list.ml

@@ -1,5 +1,5 @@
 open FromStdlib
-open Types
+open Exposed
 
 let empty : 'a list = []
 

lib/list.mli

@@ -1,4 +1,4 @@
-open Types
+open Exposed
 
 (** The empty list *)
 val empty : 'a list

lib/main.ml

@@ -1,3 +1,3 @@
-open FromStdlib open Types
+open FromStdlib open Exposed
 
 let _ = printf "Hello, World\n"

lib/makefile

@@ -4,14 +4,13 @@ build:
 	ocamlopt -i fromStdlib.ml > fromStdlib.mli
 	ocamlopt -S -O3 -c fromStdlib.mli fromStdlib.ml
 
-	# types for other modules separated to easily expose without module reference in projects	
-	ocamlopt -S -O3 -nopervasives -c types.mli types.ml
+	# exposed types and functions, that can be opened module wide
+	ocamlopt -S -O3 -nopervasives -c exposed.mli exposed.ml
 
 	# the following files make up the core custom standard library code
 	ocamlopt -S -O3 -nopervasives -c int.mli int.ml
 	ocamlopt -S -O3 -nopervasives -c float.mli float.ml
-	ocamlopt -S -O3 -nopervasives -c float.mli float.ml
-	ocamlopt -S -O3 -nopervasives -c functions.mli functions.ml
+	ocamlopt -S -O3 -nopervasives -c option.mli option.ml
 	ocamlopt -S -O3 -nopervasives -c stack.mli stack.ml
 	ocamlopt -S -O3 -nopervasives -c list.mli list.ml
 	ocamlopt -S -O3 -nopervasives -c map.mli map.ml
@@ -24,7 +23,7 @@ build:
 	ocamlopt -S -O3 -nopervasives -c main.mli main.ml
 
 	# after all files are individually compiled with -nopervasives, this is compiled with it so that fromStdlib has the necessary linking
-	ocamlopt -S -O3 fromStdlib.cmx types.cmx int.cmx float.cmx functions.cmx stack.cmx list.cmx map.cmx queue.cmx set.cmx tree.cmx main.cmx -o program
+	ocamlopt -S -O3 fromStdlib.cmx exposed.cmx int.cmx float.cmx option.cmx stack.cmx list.cmx map.cmx queue.cmx set.cmx tree.cmx main.cmx -o program
 
 # clean removes all except source files. autogenerated mli files are also removed.
 clean:

lib/option.ml

@@ -0,0 +1,23 @@
+open Exposed
+
+let return (x : 'a) : 'a option = Some x
+
+let ( ~= ) = return
+
+let bind (x : 'a option) (f : 'a -> 'b option) : 'b option =
+    match x with
+    | None -> None
+    | Some a -> f a
+
+let ( >>= ) = bind
+
+let binary_operator (x : 'a option) (y : 'b option) (f : 'a -> 'b -> 'c) : 'c option =
+    x >>= (fun a -> y >>= (fun b -> ~= (f a b)))
+
+let map (x : 'a option) (f : 'a -> 'b) : 'b option =
+    x >>= (fun a -> ~= (f a))
+
+let compose (f : 'a -> 'b option) (g : 'b -> 'c option) : 'a -> 'c option =
+    (fun x -> f x >>= g)
+    
+let ( >=> ) = compose

lib/option.mli

@@ -0,0 +1,23 @@
+(* Monadic return for option type. Trivially boxes the variable of type 'a into a 'a option by applying the Some constructor. *)
+val return : 'a -> 'a option
+
+(* Monadic return for option type. Trivially boxes the variable of type 'a into a 'a option by applying the Some constructor. *)
+val ( ~= ) : 'a -> 'a option
+
+(* Monadic bind for option type. Passes the 'a stored within the 'a option through the supplied function. If the first argument is None, the result is None. *)
+val bind : 'a option -> ('a -> 'b option) -> 'b option
+
+(* Monadic bind for option type. Passes the 'a stored within the 'a option through the supplied function. If the first argument is None, the result is None. *)
+val ( >>= ) : 'a option -> ('a -> 'b option) -> 'b option
+
+(* Binary operator, applied to the variables of type 'a and 'b respectively in the first two arguments. *)
+val binary_operator : 'a option -> 'b option -> ('a -> 'b -> 'c) -> 'c option
+
+(* Maps the supplied function to the 'a within the first argument. *)
+val map : 'a option -> ('a -> 'b) -> 'b option
+
+(* Monadic function composition. *)
+val compose : ('a -> 'b option) -> ('b -> 'c option) -> 'a -> 'c option
+
+(* Monadic function composition. *)
+val ( >=> ) : ('a -> 'b option) -> ('b -> 'c option) -> 'a -> 'c option

lib/queue.ml

@@ -1,5 +1,5 @@
 open List
-open Types
+open Exposed
 
 let enqueue (a : 'a) (qu : 'a queue) : 'a queue =
     { qu with front = a :: qu.back }

lib/queue.mli

@@ -1,4 +1,4 @@
-open Types
+open Exposed
 
 (** Adds an element to the back of the queue, returning the new queue. Runs in O(1). *)
 val enqueue : 'a -> 'a queue -> 'a queue

lib/stack.ml

@@ -1,5 +1,5 @@
 open FromStdlib
-open Types
+open Exposed
 
 let pop (st : 'a stack) : 'a option * 'a stack =
     match st with

lib/stack.mli

@@ -1,4 +1,4 @@
-open Types
+open Exposed
 
 (** Removes the top element from the stack, returning a tuple of the new stack, and None if the stack was empty, or Some [x] if [x] was on top of the stack. Popping an empty stack will result in the returned stack also being empty. Runs in O(1). *)
 val pop : 'a stack -> 'a option * 'a stack

lib/tree.ml

@@ -1,5 +1,5 @@
 open FromStdlib
-open Types
+open Exposed
 
 let combine (tr1 : 'a tree) (tr2 : 'a tree) (topBranch : 'a) : 'a tree =
     Branch (topBranch, tr1 :: tr2 :: [])

lib/tree.mli

@@ -1,4 +1,4 @@
-open Types
+open Exposed
 
 (* Combines two trees of the same type, with the specified value at the new top node. Runs in O(1). *)
 val combine : 'a tree -> 'a tree -> 'a -> 'a tree