Write more

resources/page.latex

@@ -2,18 +2,18 @@
 \usepackage{geometry}
 \usepackage{resources/dtrt}
 \geometry{
-	a4paper,
-	total={21.59cm,27.94cm},
-	top=2.8cm,
-	bottom=2.1cm,
-	inner=1.91cm,
-	outer=6.68cm,
-        % For pdf
-        left=1.5cm, 
-        right=1.5cm,
-        % For print
-	%marginparwidth=4cm,
-	%marginparsep=0.8cm
+  a4paper,
+  total={21.59cm,27.94cm},
+  top=2.8cm,
+  bottom=2.1cm,
+  inner=1.91cm,
+  outer=6.68cm,
+  % For pdf
+  left=1.5cm, 
+  right=1.5cm,
+  % For print
+  %marginparwidth=4cm,
+  %marginparsep=0.8cm
 }
 \usepackage{lmodern}
 \usepackage{xcolor}

src/04-extensions/application.hs

@@ -0,0 +1,9 @@
+{-# LANGUAGE TypeApplications #-}
+
+import Data.Proxy
+
+a :: Proxy Int
+a = Proxy @Int
+
+b :: String
+b = show (read @Int "42")

src/32-cryptography/AES.hs

@@ -0,0 +1,38 @@
+{-# LANGUAGE OverloadedStrings #-}
+
+module AES where
+
+import Crypto.Cipher.AES
+import Crypto.Cipher.Types
+import Crypto.Error
+import Crypto.Random.Types
+import Data.ByteString
+
+type AesKey = ByteString
+
+genKey :: IO AesKey
+genKey = getRandomBytes 32 -- AES256 key size
+
+aesEncrypt :: ByteString -> AesKey -> Either CryptoError ByteString
+aesEncrypt input sk =
+  ctrCombine
+    <$> init
+    <*> pure nullIV
+    <*> pure input
+  where
+    init :: Either CryptoError AES256
+    init = eitherCryptoError $ cipherInit sk
+
+aesDecrypt :: ByteString -> AesKey -> Either CryptoError ByteString
+aesDecrypt = aesEncrypt
+
+main :: IO ()
+main = do
+  key <- genKey
+  let message = "The quick brown fox jumped over the lazy dog."
+      mcipherText = aesEncrypt message key
+  case mcipherText of
+    Right cipherText -> do
+      print cipherText
+      print (aesDecrypt cipherText key)
+    Left err -> print err

src/32-cryptography/Galois.hs

@@ -0,0 +1,39 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE OverloadedLists #-}
+
+module Galois where
+
+import Data.Field.Galois
+import Prelude hiding ((/))
+
+-- Prime field
+type Fq = Prime 2147483647
+
+exampleFq :: IO ()
+exampleFq = do
+  print ((1 + 0x7FFFFFFF16) :: Fq)
+  print ((10000 * 10000) :: Fq)
+  print ((1 / 524287) :: Fq)
+
+-- Polynomial term
+data P2
+
+-- Extension field
+type Fq2 = Extension P2 Fq
+
+-- Irreducublie monic polynomial extension
+instance IrreducibleMonic P2 Fq where
+  poly _ = X2 + 1
+
+-- Polynomial 2*x^2 + 1 over Fq2
+p1 :: Fq2
+p1 = [1, 2]
+
+p2 :: Fq2
+p2 = (p1 + p1) * 2
+
+p3 :: Bool
+p3 = p2 / p1 == 4

src/32-cryptography/example.cabal

@@ -15,6 +15,7 @@ library
     cryptonite      >= 0.20 && < 0.30,
     pairing         >= 1.0  && < 2.0,
     elliptic-curve  >= 0.3  && < 0.4,
+    galois-field    >= 1.0  && < 1.1,
     memory          -any,
     bytestring      -any
   default-language:    Haskell2010

tutorial.md

@@ -3889,8 +3889,7 @@ DeriveFunctor
 
 Many instances of functor over datatypes with simple single parameters and
 trivial constructors are simply the result of trivially applying a functions
-over the single constructor's argument. GHC can derive this boilerplace
-automatically in deriving clauses if DeriveFunctor is enabled.
+over the single constructor's argument. GHC can derive this boilerplace automatically in deriving clauses if DeriveFunctor is enabled.
 
 ~~~~ {.haskell include="src/04-extensions/derive_functor.hs"}
 ~~~~
@@ -4044,6 +4043,9 @@ main = do
   print (#foo (MkT True False))
 ```
 
+This is also used in more advanced libraries like [Selda] which do object
+relational mapping between Haskell datatype fields and database columns.
+
 See:
 
 * [OverloadedRecordFields revived](http://www.well-typed.com/blog/2015/03/overloadedrecordfields-revived/)
@@ -4094,13 +4096,16 @@ Or on the version of the base library used.
 #endif
 ```
 
-It can also be abused to do terrible things like metaprogramming with strings,
-but please don't do this.
+One can also use the CPP to emit Haskell source at compile-time. This is used in
+some libraries which have massive boiler plate obligations. This can be abused
+quite easily and doing this kind of compile-time string-munging is a last
+resort.
 
 TypeApplications
 ----------------
 
-TODO
+~~~~ {.haskell include="src/04-extensions/application.hs"}
+~~~~
 
 DerivingVia
 -----------
@@ -10324,12 +10329,18 @@ convertFromBase :: (ByteArrayAccess bin, ByteArray bout) => Base -> bin -> Eithe
 AES Ciphers
 -----------
 
-TODO
+~~~~ {.haskell include="src/32-cryptography/AES.hs"}
+~~~~
 
 Galois Fields
 -------------
 
-TODO
+Many modern cryptographic protocols require the use of finite field arithmetic.
+Finite fields are algebraic structures that have algebraic field structure
+(addition, multiplication, division) and closure 
+
+~~~~ {.haskell include="src/32-cryptography/Galois.hs"}
+~~~~
 
 Elliptic Curves
 ---------------