src/RealFunction.hs: ignore orphan instance warnings.

[spline3.git] / src / RealFunction.hs

diff --git a/src/RealFunction.hs b/src/RealFunction.hs
index 5e0832d24d515ea750c7452ee0f2e336d07d4f5b..37babf6b7fc351c1ac6621b2eaa4ce0e8962b056 100644 (file)
--- a/src/RealFunction.hs
+++ b/src/RealFunction.hs
@@ -1,34 +1,77 @@
-{-# LANGUAGE TypeSynonymInstances #-}
+{-# OPTIONS_GHC -Wno-orphans #-}
+{-# LANGUAGE FlexibleInstances #-}
 
-module RealFunction
+module RealFunction (
+  RealFunction,
+  cmult,
+  fexp )
 where
 
-
+-- Presumably this is faster without a newtype wrapper, and that's why
+-- we're about to define a bunch of orphan instances below. Note the
+-- GHC pragma thingy at the top of this file to ignore those warnings.
 type RealFunction a = (a -> Double)
 
+
+-- | A 'Show' instance is required to be a 'Num' instance.
 instance Show (RealFunction a) where
-    show _ = "Real Function"
+    -- | There is nothing of value that we can display about a
+    --   function, so simply print its type.
+    show _ = "<RealFunction>"
+
 
+-- | An 'Eq' instance is required to be a 'Num' instance.
 instance Eq (RealFunction a) where
-    _ == _ = False
+    -- | Nothing else makes sense here; always return 'False'.
+    _ == _ = error "You can't compare functions for equality."
 
+
+-- | The 'Num' instance for RealFunction allows us to perform
+--   arithmetic on functions in the usual way.
 instance Num (RealFunction a) where
-    f1 + f2  = \x -> (f1 x) + (f2 x)
-    f1 - f2  = \x -> (f1 x) - (f2 x)
-    f1 * f2  = \x -> (f1 x) * (f2 x)
-    negate f = \x -> -1 * (f x)
-    abs    f = \x -> abs (f x)
-    signum f = \x -> signum (f x)
-    fromInteger i = \_ -> (fromInteger i)    
+    (f1 + f2)  x = (f1 x) + (f2 x)
+    (f1 - f2)  x = (f1 x) - (f2 x)
+    (f1 * f2)  x = (f1 x) * (f2 x)
+    (negate f) x = -1 * (f x)
+    (abs    f) x = abs (f x)
+    (signum f) x = signum (f x)
+    fromInteger i _ = fromInteger i
 
 
--- Takes a constant, and a function as arguments. Returns a new
--- function representing the original function times the constant.
+-- | Takes a constant, and a function as arguments. Returns a new
+--   function representing the original function times the constant.
+--
+--   ==== __Examples__
+--
+--   >>> let square x = x**2
+--   >>> square 1
+--   1.0
+--   >>> square 2
+--   4.0
+--   >>> let f = cmult 2 square
+--   >>> f 1
+--   2.0
+--   >>> f 2
+--   8.0
+--
 cmult :: Double -> (RealFunction a) -> (RealFunction a)
 cmult coeff f = (*coeff) . f
 
--- Takes a function f and an exponent n. Returns a new function, f^n.
+
+-- | Takes a function @f@ and an exponent @n@. Returns a new function,
+--   @g@, defined by g(x) = (f(x))^n. This is /not/ @f@ composed
+--   with itself @n@ times.
+--
+--   ==== __Examples__
+--
+--   >>> let square x = x**2
+--   >>> square 2
+--   4.0
+--   >>> let f = fexp square 3
+--   >>> f 2
+--   64.0
+--
 fexp :: (RealFunction a) -> Int -> (RealFunction a)
 fexp f n
-     | n == 0 = (\_ -> 1)
+     | n == 0 = const 1
      | otherwise = \x -> (f x)^n