Instance FieldElement into Num typeclass

1 files changed, 15 insertions, 18 deletions

diff --git a/ecc.hs b/ecc.hs
index 200b613..8146711 100644
--- a/ecc.hs
+++ b/ecc.hs
@@ -9,36 +9,33 @@ data FieldElement =
 instance Show FieldElement where
   show a = "FieldElement_" ++ show (prime a) ++ " " ++ show (number a)
 
-add :: FieldElement -> FieldElement -> FieldElement
-add (FieldElement a b) (FieldElement c d)
-  | b /= d = error "Distinct Fields"
-  | otherwise = FieldElement (mod (a + c) b) b
-
-sub :: FieldElement -> FieldElement -> FieldElement
-sub (FieldElement a b) (FieldElement c d)
-  | b /= d = error "Distinct Fields"
-  | otherwise = FieldElement (mod (a - c) b) b
-
-mul :: FieldElement -> FieldElement -> FieldElement
-mul (FieldElement a b) (FieldElement c d)
-  | b /= d = error "Distinct Fields"
-  | otherwise = FieldElement (mod (a * c) b) b
-
 assert :: Bool -> Bool
 assert False = error "WRONG"
 assert x = x
 
+instance Num FieldElement where
+  (FieldElement a b) + (FieldElement c d)
+    | b /= d = error "Distinct Fields"
+    | otherwise = FieldElement (mod (a + c) b) b
+  (FieldElement a b) * (FieldElement c d)
+    | b /= d = error "Distinct Fields"
+    | otherwise = FieldElement (mod (a * c) b) b
+  abs a = a
+  signum _ = 1
+  negate (FieldElement a b) = FieldElement (mod (b - a) b) b
+  fromInteger _ = error "can't transform"
+
 aa =
   let a = FieldElement 2 31
       b = FieldElement 15 31
    in assert
         (and
-           [ add a b == FieldElement 17 31
+           [ a + b == FieldElement 17 31
            , a /= b
-           , sub a b == FieldElement 18 31
+           , a - b == FieldElement 18 31
            ])
 
 bb =
   let a = FieldElement 19 31
       b = FieldElement 24 31
-   in mul a b
+   in a * b