| Copyright | (c) Yusuke Matsushita 2015 |
|---|---|
| License | BSD3 |
| Maintainer | Yusuke Matsushita |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Type.Compare
Description
Compare two types of any (possibly different) kinds.
- type family Compare a b :: Ordering
- data LargestK = Largest
- data SmallestK = Smallest
- type family CompareUser a b :: Ordering
- type family OrdCase o x y z :: l
- type family CompareCase a b x y z :: l
- type family a <! b :: Bool
- type family a >=! b :: Bool
- type family a >! b :: Bool
- type family a <=! b :: Bool
- type family Max a b :: k
- type family Min a b :: k
Base
type family Compare a b :: Ordering Source
Compare two types of any (possibly different) kinds.
Since Compare itself is a closed type family, add instances to CompareUser if you want to compare other types.
Equations
| Compare (Down a) (Down b) = Compare b a | |
| Compare Largest Largest = EQ | |
| Compare _' Largest = LT | |
| Compare Largest _' = GT | |
| Compare Smallest Smallest = EQ | |
| Compare _' Smallest = GT | |
| Compare Smallest _' = LT | |
| Compare False False = EQ | |
| Compare False True = LT | |
| Compare True False = GT | |
| Compare True True = EQ | |
| Compare LT LT = EQ | |
| Compare LT EQ = LT | |
| Compare LT GT = LT | |
| Compare EQ LT = GT | |
| Compare EQ EQ = EQ | |
| Compare EQ GT = LT | |
| Compare GT LT = GT | |
| Compare GT EQ = GT | |
| Compare GT GT = EQ | |
| Compare m n = CmpNat m n | |
| Compare s t = CmpSymbol s t | |
| Compare Nothing Nothing = EQ | |
| Compare Nothing (Just b) = LT | |
| Compare (Just a) Nothing = GT | |
| Compare (Just a) (Just b) = Compare a b | |
| Compare (Left _') (Right _'') = LT | |
| Compare (Right _') (Left _'') = GT | |
| Compare (Left a) (Left b) = Compare a b | |
| Compare (Right a) (Right b) = Compare a b | |
| Compare [] [] = EQ | |
| Compare [] (b : bs) = LT | |
| Compare (a : as) [] = GT | |
| Compare (a : as) (b : bs) = Compare a b $$ Compare as bs | |
| Compare () () = EQ | |
| Compare `(a1, a2)` `(b1, b2)` = Compare a1 b1 $$ Compare a2 b2 | |
| Compare `(a1, a2, a3)` `(b1, b2, b3)` = (Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3 | |
| Compare `(a1, a2, a3, a4)` `(b1, b2, b3, b4)` = ((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4 | |
| Compare `(a1, a2, a3, a4, a5)` `(b1, b2, b3, b4, b5)` = (((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5 | |
| Compare `(a1, a2, a3, a4, a5, a6)` `(b1, b2, b3, b4, b5, b6)` = ((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6 | |
| Compare `(a1, a2, a3, a4, a5, a6, a7)` `(b1, b2, b3, b4, b5, b6, b7)` = (((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7 | |
| Compare `(a1, a2, a3, a4, a5, a6, a7, a8)` `(b1, b2, b3, b4, b5, b6, b7, b8)` = ((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8 | |
| Compare `(a1, a2, a3, a4, a5, a6, a7, a8, a9)` `(b1, b2, b3, b4, b5, b6, b7, b8, b9)` = (((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8) $$ Compare a9 b9 | |
| Compare `(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10)` `(b1, b2, b3, b4, b5, b6, b7, b8, b9, b10)` = ((((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8) $$ Compare a9 b9) $$ Compare a10 b10 | |
| Compare () () = EQ | |
| Compare (a1, a2) (b1, b2) = Compare a1 b1 $$ Compare a2 b2 | |
| Compare (a1, a2, a3) (b1, b2, b3) = (Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3 | |
| Compare (a1, a2, a3, a4) (b1, b2, b3, b4) = ((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4 | |
| Compare (a1, a2, a3, a4, a5) (b1, b2, b3, b4, b5) = (((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5 | |
| Compare (a1, a2, a3, a4, a5, a6) (b1, b2, b3, b4, b5, b6) = ((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6 | |
| Compare (a1, a2, a3, a4, a5, a6, a7) (b1, b2, b3, b4, b5, b6, b7) = (((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7 | |
| Compare (a1, a2, a3, a4, a5, a6, a7, a8) (b1, b2, b3, b4, b5, b6, b7, b8) = ((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8 | |
| Compare (a1, a2, a3, a4, a5, a6, a7, a8, a9) (b1, b2, b3, b4, b5, b6, b7, b8, b9) = (((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8) $$ Compare a9 b9 | |
| Compare (a1, a2, a3, a4, a5, a6, a7, a8, a9, a10) (b1, b2, b3, b4, b5, b6, b7, b8, b9, b10) = ((((((((Compare a1 b1 $$ Compare a2 b2) $$ Compare a3 b3) $$ Compare a4 b4) $$ Compare a5 b5) $$ Compare a6 b6) $$ Compare a7 b7) $$ Compare a8 b8) $$ Compare a9 b9) $$ Compare a10 b10 | |
| Compare a b = CompareUser a b |
type family CompareUser a b :: Ordering Source
Compare two types, of any kinds, which are not compared within Compare. Users can add instances.
Utility
type family CompareCase a b x y z :: l Source
Equations
| CompareCase a b x y z = OrdCase (Compare a b) x y z |
type family Max a b :: k Source
Equations
| Max a b = CompareCase a b b b a |
type family Min a b :: k Source
Equations
| Min a b = CompareCase a b a a b |