-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Sum and Product types and such
--   
--   This library provides first-class multi-arity product- and sum-types
--   and neat type-level utilities for their composition. The solution is
--   quite simple and doesn’t require the advanced proficiency in the
--   language to be applied in practice.
--   
--   For a comprehensive introduction please see <a>this blog post</a>.
@package compound-types
@version 0.1.3


-- | Implementations of the lazy data-structures.
module CompoundTypes.Lazy
data Sum2 _1 _2
Sum2_1 :: _1 -> Sum2 _1 _2
Sum2_2 :: _2 -> Sum2 _1 _2
data Sum3 _1 _2 _3
Sum3_1 :: _1 -> Sum3 _1 _2 _3
Sum3_2 :: _2 -> Sum3 _1 _2 _3
Sum3_3 :: _3 -> Sum3 _1 _2 _3
data Sum4 _1 _2 _3 _4
Sum4_1 :: _1 -> Sum4 _1 _2 _3 _4
Sum4_2 :: _2 -> Sum4 _1 _2 _3 _4
Sum4_3 :: _3 -> Sum4 _1 _2 _3 _4
Sum4_4 :: _4 -> Sum4 _1 _2 _3 _4
data Sum5 _1 _2 _3 _4 _5
Sum5_1 :: _1 -> Sum5 _1 _2 _3 _4 _5
Sum5_2 :: _2 -> Sum5 _1 _2 _3 _4 _5
Sum5_3 :: _3 -> Sum5 _1 _2 _3 _4 _5
Sum5_4 :: _4 -> Sum5 _1 _2 _3 _4 _5
Sum5_5 :: _5 -> Sum5 _1 _2 _3 _4 _5
data Sum6 _1 _2 _3 _4 _5 _6
Sum6_1 :: _1 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_2 :: _2 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_3 :: _3 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_4 :: _4 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_5 :: _5 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_6 :: _6 -> Sum6 _1 _2 _3 _4 _5 _6
data Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_1 :: _1 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_2 :: _2 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_3 :: _3 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_4 :: _4 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_5 :: _5 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_6 :: _6 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_7 :: _7 -> Sum7 _1 _2 _3 _4 _5 _6 _7

-- | Automatically derives the sum-type of the according arity from
--   expressions such as:
--   
--   <pre>
--   Int + Char + Bool
--   </pre>
--   
--   In that case it will resolve to:
--   
--   <pre>
--   Sum3 Int Char Bool
--   </pre>

-- | An operator for removing elements from the sum-types. E.g.,
--   
--   <pre>
--   Int + Char + Bool - Char
--   </pre>
--   
--   is the same type as
--   
--   <pre>
--   Int + Bool
--   </pre>

-- | What you get, when the subtraction cannot yet be performed.
--   
--   Happens when the minuend doesn't contain the subtrahend. E.g.,
--   
--   <pre>
--   Char - Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Unsubtracted Char Bool
--   </pre>
--   
--   However it's possible to get back to the normal type, when you perform
--   the required addition afterwards. E.g.,
--   
--   <pre>
--   Char - Bool + Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Char
--   </pre>
--   
--   This construct actually exists primarily for that purpose.
data Unsubtracted minuend subtrahend
data Product2 _1 _2
Product2 :: _1 -> _2 -> Product2 _1 _2
data Product3 _1 _2 _3
Product3 :: _1 -> _2 -> _3 -> Product3 _1 _2 _3
data Product4 _1 _2 _3 _4
Product4 :: _1 -> _2 -> _3 -> _4 -> Product4 _1 _2 _3 _4
data Product5 _1 _2 _3 _4 _5
Product5 :: _1 -> _2 -> _3 -> _4 -> _5 -> Product5 _1 _2 _3 _4 _5
data Product6 _1 _2 _3 _4 _5 _6
Product6 :: _1 -> _2 -> _3 -> _4 -> _5 -> _6 -> Product6 _1 _2 _3 _4 _5 _6
data Product7 _1 _2 _3 _4 _5 _6 _7
Product7 :: _1 -> _2 -> _3 -> _4 -> _5 -> _6 -> _7 -> Product7 _1 _2 _3 _4 _5 _6 _7

-- | Automatically derives the product-type of the according arity from
--   expressions such as:
--   
--   <pre>
--   Int * Char * Bool
--   </pre>
--   
--   In that case it will resolve to:
--   
--   <pre>
--   Product3 Int Char Bool
--   </pre>

-- | An operator for removing elements from the product-types. E.g.,
--   
--   <pre>
--   Int * Char * Bool / Char
--   </pre>
--   
--   is the same type as
--   
--   <pre>
--   Int * Bool
--   </pre>

-- | What you get, when the division cannot yet be performed.
--   
--   Happens when the dividend doesn't contain the divisor. E.g.,
--   
--   <pre>
--   Char / Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Undivided Char Bool
--   </pre>
--   
--   However it's possible to get back to the normal type, when you perform
--   the required multiplication afterwards. E.g.,
--   
--   <pre>
--   Char / Bool * Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Char
--   </pre>
--   
--   This construct actually exists primarily for that purpose.
data Undivided dividend divisor


-- | Implementations of the strict data-structures.
module CompoundTypes.Strict
data Sum2 _1 _2
Sum2_1 :: !_1 -> Sum2 _1 _2
Sum2_2 :: !_2 -> Sum2 _1 _2
data Sum3 _1 _2 _3
Sum3_1 :: !_1 -> Sum3 _1 _2 _3
Sum3_2 :: !_2 -> Sum3 _1 _2 _3
Sum3_3 :: !_3 -> Sum3 _1 _2 _3
data Sum4 _1 _2 _3 _4
Sum4_1 :: !_1 -> Sum4 _1 _2 _3 _4
Sum4_2 :: !_2 -> Sum4 _1 _2 _3 _4
Sum4_3 :: !_3 -> Sum4 _1 _2 _3 _4
Sum4_4 :: !_4 -> Sum4 _1 _2 _3 _4
data Sum5 _1 _2 _3 _4 _5
Sum5_1 :: !_1 -> Sum5 _1 _2 _3 _4 _5
Sum5_2 :: !_2 -> Sum5 _1 _2 _3 _4 _5
Sum5_3 :: !_3 -> Sum5 _1 _2 _3 _4 _5
Sum5_4 :: !_4 -> Sum5 _1 _2 _3 _4 _5
Sum5_5 :: !_5 -> Sum5 _1 _2 _3 _4 _5
data Sum6 _1 _2 _3 _4 _5 _6
Sum6_1 :: !_1 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_2 :: !_2 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_3 :: !_3 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_4 :: !_4 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_5 :: !_5 -> Sum6 _1 _2 _3 _4 _5 _6
Sum6_6 :: !_6 -> Sum6 _1 _2 _3 _4 _5 _6
data Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_1 :: !_1 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_2 :: !_2 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_3 :: !_3 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_4 :: !_4 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_5 :: !_5 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_6 :: !_6 -> Sum7 _1 _2 _3 _4 _5 _6 _7
Sum7_7 :: !_7 -> Sum7 _1 _2 _3 _4 _5 _6 _7

-- | Automatically derives the sum-type of the according arity from
--   expressions such as:
--   
--   <pre>
--   Int + Char + Bool
--   </pre>
--   
--   In that case it will resolve to:
--   
--   <pre>
--   Sum3 Int Char Bool
--   </pre>

-- | An operator for removing elements from the sum-types. E.g.,
--   
--   <pre>
--   Int + Char + Bool - Char
--   </pre>
--   
--   is the same type as
--   
--   <pre>
--   Int + Bool
--   </pre>

-- | What you get, when the subtraction cannot yet be performed.
--   
--   Happens when the minuend doesn't contain the subtrahend. E.g.,
--   
--   <pre>
--   Char - Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Unsubtracted Char Bool
--   </pre>
--   
--   However it's possible to get back to the normal type, when you perform
--   the required addition afterwards. E.g.,
--   
--   <pre>
--   Char - Bool + Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Char
--   </pre>
--   
--   This construct actually exists primarily for that purpose.
data Unsubtracted minuend subtrahend
data Product2 _1 _2
Product2 :: !_1 -> !_2 -> Product2 _1 _2
data Product3 _1 _2 _3
Product3 :: !_1 -> !_2 -> !_3 -> Product3 _1 _2 _3
data Product4 _1 _2 _3 _4
Product4 :: !_1 -> !_2 -> !_3 -> !_4 -> Product4 _1 _2 _3 _4
data Product5 _1 _2 _3 _4 _5
Product5 :: !_1 -> !_2 -> !_3 -> !_4 -> !_5 -> Product5 _1 _2 _3 _4 _5
data Product6 _1 _2 _3 _4 _5 _6
Product6 :: !_1 -> !_2 -> !_3 -> !_4 -> !_5 -> !_6 -> Product6 _1 _2 _3 _4 _5 _6
data Product7 _1 _2 _3 _4 _5 _6 _7
Product7 :: !_1 -> !_2 -> !_3 -> !_4 -> !_5 -> !_6 -> !_7 -> Product7 _1 _2 _3 _4 _5 _6 _7

-- | Automatically derives the product-type of the according arity from
--   expressions such as:
--   
--   <pre>
--   Int * Char * Bool
--   </pre>
--   
--   In that case it will resolve to:
--   
--   <pre>
--   Product3 Int Char Bool
--   </pre>

-- | An operator for removing elements from the product-types. E.g.,
--   
--   <pre>
--   Int * Char * Bool / Char
--   </pre>
--   
--   is the same type as
--   
--   <pre>
--   Int * Bool
--   </pre>

-- | What you get, when the division cannot yet be performed.
--   
--   Happens when the dividend doesn't contain the divisor. E.g.,
--   
--   <pre>
--   Char / Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Undivided Char Bool
--   </pre>
--   
--   However it's possible to get back to the normal type, when you perform
--   the required multiplication afterwards. E.g.,
--   
--   <pre>
--   Char / Bool * Bool
--   </pre>
--   
--   produces
--   
--   <pre>
--   Char
--   </pre>
--   
--   This construct actually exists primarily for that purpose.
data Undivided dividend divisor