Added documentation (#239)

* Added documentation

* Update readme

* Update readme

* Format fix

* Events

* Stdlib mention

* Frac doc

* Frac doc comparison warning

* Typos

* Format fix, TOC added

* Fixed link

* Update editor message

* Split TOC

* Moved out AEVM ABI

* Minor format

Co-Authored-By: Hans Svensson <hanssv@gmail.com>

* Typo

Co-Authored-By: Hans Svensson <hanssv@gmail.com>

* Grammar

Co-Authored-By: Hans Svensson <hanssv@gmail.com>

* Language

Co-authored-by: Hans Svensson <hanssv@gmail.com>

README.md

@@ -2,13 +2,19 @@
 
 This is the __sophia__ compiler for the æternity system which compiles contracts written in __sophia__ code to the æternity VM code.
 
-For more information about æternity smart contracts and the sophia language see [Smart Contracts](https://github.com/aeternity/protocol/blob/master/contracts/contracts.md) and the [Sophia Language](https://github.com/aeternity/protocol/blob/master/contracts/sophia.md).
-
 It is an OTP application written in Erlang and is by default included in
 [the æternity node](https://github.com/aeternity/epoch). However, it can
 also be included in other systems to compile contracts coded in sophia which
 can then be loaded into the æternity system.
 
+
+## Documentation
+
+* [Smart Contracts on aeternity Blockchain](https://github.com/aeternity/protocol/blob/master/contracts/contracts.md).
+* [Sophia Documentation](docs/sophia.md).
+* [Sophia Standard Library](docs/sophia_stdlib.md).
+
+
 ## Versioning
 
 `aesophia` has a version that is only loosely connected to the version of the
@@ -17,6 +23,7 @@ minor/patch version. The `aesophia` compiler version MUST be bumped whenever
 there is a change in how byte code is generated, but it MAY also be bumped upon
 API changes etc.
 
+
 ## Interface Modules
 
 The basic modules for interfacing the compiler:

priv/stdlib/Frac.aes

@@ -62,17 +62,13 @@ namespace Frac =
     else simplify(Neg(abs_int(n), abs_int(d)))
 
   function eq(a : frac, b : frac) : bool =
-    let na = num(a)
+    let (na, da) = to_pair(a)
-    let nb = num(b)
+    let (nb, db) = to_pair(b)
-    let da = den(a)
-    let db = den(b)
     (na == nb && da == db) || na * db == nb * da // they are more likely to be normalized
 
   function neq(a : frac, b : frac) : bool =
-    let na = num(a)
+    let (na, da) = to_pair(a)
-    let nb = num(b)
+    let (nb, db) = to_pair(b)
-    let da = den(a)
-    let db = den(b)
     (na != nb || da != db) && na * db != nb * da
 
   function geq(a : frac, b : frac) : bool = num(a) * den(b) >= num(b) * den(a)
@@ -131,10 +127,8 @@ namespace Frac =
     else cl
 
   function add(a : frac, b : frac) : frac =
-    let na = num(a)
+    let (na, da) = to_pair(a)
-    let nb = num(b)
+    let (nb, db) = to_pair(b)
-    let da = den(a)
-    let db = den(b)
     if   (da == db) make_frac(na + nb, da)
     else make_frac(na * db + nb * da, da * db)