[project @ 1996-01-08 20:28:12 by partain]

[ghc-hetmet.git] / ghc / lib / hbc / Algebra.hs

diff --git a/ghc/lib/hbc/Algebra.hs b/ghc/lib/hbc/Algebra.hs
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+module Algebra where
+infixl 6 +. , -.
+infixl 7 *. , /.
+
+--
+-- (x::A)->B is dependant functions
+-- (x = y) A is equality in type A
+--
+
+-- For simplicity we may require decidable equality on the elements.
+class {-(Eq a) =>-} SemiGroup a where
+    (+.) :: a->a->a
+--  assocAdd :: (x::a)->(y::a)->(z::a)->
+--              ((a+.b)+.c = a+.(b+.c)) a
+
+class (SemiGroup a) => Monoid a where
+    zero :: a
+--  leftZero :: (x::a) -> (zero +. x = x) a
+
+class (Monoid a) => Group a where
+    neg :: a->a
+    (-.) :: a->a->a
+    x -. y = x +. neg y
+--  leftNeg :: (x::a) -> (neg x +. x = zero) a
+
+class (Group a) => AbelianGroup a
+--  commAdd :: (x::a)->(y::a)-> (x+.y = y+.x) a
+
+class (AbelianGroup a) => Ring a where
+    (*.) :: a->a->a
+--  assocMul  :: (x::a)->(y::a)->(z::a)->
+--               ((a*.b)*.c = a*.(b*.c)) a
+--  distrRingL :: (x::a)->(y::a)->(z::a)->
+--                (x*.(y+.z) = x*.y +. x*.z)
+--  distrRingR :: (x::a)->(y::a)->(z::a)->
+--                ((y+.z)*.x = y*.x +. z*.x)
+
+class (Ring a) => UnityRing a where
+    one :: a
+--  leftOne :: (x::a)->(one *. x = x) a
+--  rightOne :: (x::a)->(x *. one = x) a
+
+class (Ring a) => CommutativeRing a
+--  commMul :: (x::a)->(y::a)-> (x*.y = y*.x) a
+
+class (CommutativeRing a, UnityRing a) => IntegralDomain a
+--  noZeroDiv :: (x::a)->(y::a)-> (  (x*.y = zero) a  ->  Either ((x=zero) a) ((y=zero) a)  )
+
+class (UnityRing a) => DivisionRing a where
+    inv :: a->a
+    (/.) :: a->a->a
+    x /. y = x *. inv y
+--  leftinv :: (x::a) -> (inv x *. x = one) a
+
+class (DivisionRing a, CommutativeRing a) => Field a
+
+-- Every finite integral domain is a field.
+
+-- Unique Factorization Domain
+class (IntegralDomain a) => UFD a
+--  every non-zero element has a unique factorization
+
+-- Principal Ideal Domain
+class (IntegralDomain a) => PID a
+--  every ideal is a principal ideal
+
+---------------------------------------------------
+
+-- [a] --
+instance SemiGroup [a] where
+    (+.) = (++)
+instance Monoid [a] where
+    zero = []
+
+-- Bool --
+instance SemiGroup Bool where
+    (+.) = (||)
+instance Monoid Bool where
+    zero = False
+instance Group Bool where
+    neg = not
+instance AbelianGroup Bool
+instance Ring Bool where
+    (*.) = (&&)
+instance CommutativeRing Bool 
+instance UnityRing Bool where
+    one = True
+instance DivisionRing Bool where
+    inv x = x
+
+-- Int --
+instance SemiGroup Int where
+    (+.) = (+)
+instance Monoid Int where
+    zero = 0
+instance Group Int where
+    neg = negate
+instance AbelianGroup Int
+instance Ring Int where
+    (*.) = (*)
+instance CommutativeRing Int
+instance UnityRing Int where
+    one = 1
+
+-- Integer --
+instance SemiGroup Integer where
+    (+.) = (+)
+instance Monoid Integer where
+    zero = 0
+instance Group Integer where
+    neg = negate
+instance AbelianGroup Integer
+instance Ring Integer where
+    (*.) = (*)
+instance CommutativeRing Integer
+instance UnityRing Integer where
+    one = 1
+instance IntegralDomain Integer
+
+-- Q --
+-- A new data tupe is needed to do the instance declarations
+data Q = Q Rational {-#STRICT#-} deriving (Eq, Ord)
+instance Text Q where
+#if defined(__HBC__)
+    -- not standard
+    showsType _ = showString "Q"
+#endif
+    showsPrec n (Q p) = showsPrec n p
+instance SemiGroup Q where
+    Q a +. Q b = Q (a+b)
+instance Monoid Q where
+    zero = Q 0
+instance Group Q where
+    neg (Q a) = Q (-a)
+instance AbelianGroup Q
+instance Ring Q where
+    Q a *. Q b = Q (a*b)
+instance CommutativeRing Q
+instance UnityRing Q where
+    one = Q 1
+instance IntegralDomain Q
+instance DivisionRing Q where
+    inv (Q x) = Q (recip x)
+instance Field Q
+