CLEANUP: switching from "right-to-left" to "left-to-right" function composition operator.

Short story:

    This pull-request:

    (1) removes the definition of the "right-to-left" function composition operator

    (2) adds the definition of the "left-to-right" function composition operator

    (3) rewrites the code relying on "right-to-left" function composition to rely on "left-to-right" function composition operator instead.

Long story:

    In mathematics, function composition is traditionally denoted with ∘ operator.

    Ocaml standard library does not provide analogous operator under any name.

    Batteries Included provides provides two alternatives:

    	_ % _

    and

    	_ %> _

    The first operator one corresponds to the classical ∘ operator routinely used in mathematics.
    I.e.:

    	(f4 % f3 % f2 % f1) x  ≜  (f4 ∘ f3 ∘ f2 ∘ f1) x

    We can call it "right-to-left" composition because:
    - the function we write as first (f4) will be called as last
    - and the function write as last (f1) will be called as first.

    The meaning of the second operator is this:

    	(f1 %> f2 %> f3 %> f4) x  ≜  (f4 ∘ f3 ∘ f2 ∘ f1) x

    We can call it "left-to-right" composition because:
    - the function we write as first (f1) will be called first
    - and the function we write as last (f4) will be called last
    That is, the functions are written in the same order in which we write and read them.

    I think that it makes sense to prefer the "left-to-right" variant because
    it enables us to write functions in the same order in which they will be actually called
    and it thus better fits our culture
    (we read/write from left to right).

1 files changed, 8 insertions, 4 deletions

diff --git a/lib/util.mli b/lib/util.mli
index 6bed7e355..cf8041a0d 100644
--- a/lib/util.mli
+++ b/lib/util.mli
@@ -84,13 +84,17 @@ val matrix_transpose : 'a list list -> 'a list list
 
 val identity : 'a -> 'a
 
-(** Function composition: the mathematical [∘] operator.
+(** Left-to-right function composition:
+    
+    [f1 %> f2] is [fun x -> f2 (f1 x)].
 
-    So [g % f] is a synonym for [fun x -> g (f x)].
+    [f1 %> f2 %> f3] is [fun x -> f3 (f2 (f1 x))].
 
-    Also because [%] is right-associative, [h % g % f] means [fun x -> h (g (f x))].
+    [f1 %> f2 %> f3 %> f4] is [fun x -> f4 (f3 (f2 (f1 x)))]
+
+    etc.
 *)
-val (%) : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b
+val ( %> ) : ('a -> 'b) -> ('b -> 'c) -> 'a -> 'c
 
 val const : 'a -> 'b -> 'a
 val iterate : ('a -> 'a) -> int -> 'a -> 'a