Support Infix functions and user defined operators

doc/features.md

@@ -1,5 +1,6 @@
 # Features overview
 
+* [Infix functions](#infix-functions) 
 * [Option type](#option-type)
 * [Either type](#either-type)
 * [Foldable](#foldable)
@@ -14,6 +15,12 @@
 <!-- * [Type safe cast](#type-safe-cast) -->
 <!-- * [Topological](#topological) -->
 
+## Infix functions
+
+In Erlang, we apply functions using prefix notation - name is followed by its arguments in brackets `plus(1, 2)`. Humans are more used to infix operators than prefix or postfix. If a function takes two arguments, we have the option of using it in infix form, where we place it between its first and second arguments `1 /plus/ 2`. To apply a function using infix notation, we enclose its name in slash characters (/). This allows us to use functions as infix operators.
+
+See details about [infix functions](infix.md). 
+
 
 ## Option type
 

doc/infix.md

@@ -0,0 +1,122 @@
+# Infix functions
+
+In Erlang, we apply functions using prefix notation - name is followed by its arguments in brackets `plus(1, 2)`. Humans are more used to infix operators than prefix or postfix. If a function takes two arguments, we have the option of using it in infix form, where we place it between its first and second arguments `1 /plus/ 2`.
+
+The `parse_transform` feature implements a syntax sugar for *infix*, which is compiled into valid Erlang code using corresponding function at compile-time. To apply a function using infix notation, we enclose its name in slash characters (/). This allows us to use any arity 2 functions as infix operators.
+
+```erlang
+-compile({parse_transform, infix}).
+
+1 /plus/ 1.
+
+F /lists:map/ [1, 2, 3].
+```
+Infix notation does not change a function's behavior, it is purely a syntactic convenience that help readability in a specific situation.
+
+## Operators
+
+The parse transform allows to define custom operator -- a function of arity 2. Just put remote (mod:fun) or local functions enclosed in slashes. The usage of variables as operators is not supported due to confusion with legitimate Erlang expression.
+
+```erlang
+%% infix notation 
+1 /plus/ 1
+F /lists:map/ [1, 2, 3].
+
+%% transformed to function calls
+plus(1, 1).
+lists:map(F, [1, 2, 3])/
+```
+
+Example of math operator for tuples
+
+```erlang
+example() ->
+   {1,2,3} /add/ {4,5,6}, %% {5,7,9}
+   1 /add/ {4,5,6},       %% {5,6,7}
+   {1,2,3} /add/ 1.       %% {2,3,4}
+
+add(X, Y)
+ when is_tuple(X), is_tuple(Y) -> 
+   list_to_tuple([
+      A + B || {A, B} <- lists:zip(tuple_to_list(X), tuple_to_list(Y))
+   ]);
+
+add(X, Y)
+ when is_integer(X), is_tuple(Y) ->
+   list_to_tuple([
+      A + X || A <- tuple_to_list(Y)
+   ]);
+
+add(X, Y)
+ when is_tuple(X), is_integer(Y) ->
+   list_to_tuple([
+      A + Y || A <- tuple_to_list(X)
+   ]).
+```
+
+User defined operators do not/cloud not/will not introduce any kind of polymorphism or overloading that Erlang does not already implement.
+
+## Partial application
+
+The infix notation supports a partial application, just replace left/right operand with unbound variable _
+
+```erlang
+%% partial application
+_ /plus/ 1
+1 /plus/ _
+
+%% transformed to
+fun(X) -> plus(X, 1) end.
+fun(X) -> plus(1, X) end.
+
+%% e.g. infix notation to increment elements in array
+1 /erlang:'+'/ _ /lists:map/ [1,2,3,4].
+```
+
+## Monoid
+
+The infix parse transform allows to define monoid -- an algebraic structure with a single associative binary operation and an identity element. Erlang module with following "behavior" defines a monoid class. 
+
+```erlang
+%% an identity element
+-spec empty() -> _.
+
+%% associative binary operation
+-spec append(_, _) -> _.
+```
+
+Use module name enclosed in stars to refer it.
+
+```erlang
+%% infix notation
+1 *plus* 1.
+
+%% translated to function call.
+plus:append(1, 1).
+```
+
+One of the practical application of monoids -- folding over various data structures. So far, everyone is familiar with folds over lists, but lists aren't the only foldable data structure. We can abstract and define fold over almost any data structure with help of monoids.
+
+```erlang
+plus /fold/ [1, 2, 3].
+
+fold(Monoid, []) ->
+   Monoid:empty();
+fold(Monoid, [H | T]) ->
+   Monoid:append(H, fold(Monoid, T)).
+```
+
+## Known limitations
+
+1. **Import** is not supported yet.
+
+```
+-import(erlang, ['+'/2,]).
+
+two() ->
+   1 /'+'/ 1.
+```
+
+## References
+
+[1] http://erlang.org/pipermail/erlang-questions/2004-March/011929.html

rebar.config

@@ -23,6 +23,7 @@
   ,"src/topological.erl"
   ,"src/traversable.erl"
 
+  ,"src/infix.erl"
 ]}.
 
 %%