sop-core-0.5.0.2: True Sums of Products

Safe Haskell | None
Language | Haskell2010

Data.SOP.Dict

Description

Explicit dictionaries.

When working with compound constraints such as constructed using `All` or `All2`, GHC cannot always prove automatically what one would expect to hold.

This module provides a way of explicitly proving conversions between such constraints to GHC. Such conversions still have to be manually applied.

This module remains somewhat experimental. It is therefore not exported via the main module and has to be imported explicitly.

Synopsis

- data Dict (c :: k -> Constraint) (a :: k) where
  - Dict :: forall {k} (c :: k -> Constraint) (a :: k). c a => Dict c a
- pureAll :: forall {k} (xs :: [k]). SListI xs => Dict (All (Top :: k -> Constraint)) xs
- pureAll2 :: forall {k} (xss :: [[k]]). All (SListI :: [k] -> Constraint) xss => Dict (All2 (Top :: k -> Constraint)) xss
- mapAll :: forall {k} (c :: k -> Constraint) (d :: k -> Constraint) (xs :: [k]). (forall (a :: k). Dict c a -> Dict d a) -> Dict (All c) xs -> Dict (All d) xs
- mapAll2 :: forall {k} (c :: k -> Constraint) (d :: k -> Constraint) (xss :: [[k]]). (forall (a :: k). Dict c a -> Dict d a) -> Dict (All2 c) xss -> Dict (All2 d) xss
- zipAll :: forall {k} (c :: k -> Constraint) (xs :: [k]) (d :: k -> Constraint). Dict (All c) xs -> Dict (All d) xs -> Dict (All (And c d)) xs
- zipAll2 :: forall {k} (xss :: [[k]]) (c :: k -> Constraint) (d :: k -> Constraint). All (SListI :: [k] -> Constraint) xss => Dict (All2 c) xss -> Dict (All2 d) xss -> Dict (All2 (And c d)) xss
- unAll_NP :: forall {k} (c :: k -> Constraint) (xs :: [k]). Dict (All c) xs -> NP (Dict c) xs
- unAll_POP :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All2 c) xss -> POP (Dict c) xss
- all_NP :: forall {k} (c :: k -> Constraint) (xs :: [k]). NP (Dict c) xs -> Dict (All c) xs
- all_POP :: forall {k} (xss :: [[k]]) (c :: k -> Constraint). SListI xss => POP (Dict c) xss -> Dict (All2 c) xss
- unAll2 :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All2 c) xss -> Dict (All (All c)) xss
- all2 :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All (All c)) xss -> Dict (All2 c) xss
- withDict :: forall {k} c (a :: k) r. Dict c a -> (c a => r) -> r
- hdicts :: forall {k} {l} h (c :: k -> Constraint) (xs :: l). (AllN h c xs, HPure h) => h (Dict c) xs

# Documentation

data Dict (c :: k -> Constraint) (a :: k) where Source #

An explicit dictionary carrying evidence of a class constraint.

The constraint parameter is separated into a second argument so that ``Dict` c` is of the correct kind to be used directly as a parameter to e.g. `NP`.

Since: 0.2

Constructors

Dict :: forall {k} (c :: k -> Constraint) (a :: k). c a => Dict c a |

#### Instances

Instances details

Show (Dict c a) Source # |
Instance details Defined in Data.SOP.Dict Methods showsPrec :: Int -> Dict c a -> ShowS Source # show :: Dict c a -> String Source # showList :: [Dict c a] -> ShowS Source #

pureAll :: forall {k} (xs :: [k]). SListI xs => Dict (All (Top :: k -> Constraint)) xs Source #

A proof that the trivial constraint holds over all type-level lists.

Since: 0.2

pureAll2 :: forall {k} (xss :: [[k]]). All (SListI :: [k] -> Constraint) xss => Dict (All2 (Top :: k -> Constraint)) xss Source #

A proof that the trivial constraint holds over all type-level lists of lists.

Since: 0.2

mapAll :: forall {k} (c :: k -> Constraint) (d :: k -> Constraint) (xs :: [k]). (forall (a :: k). Dict c a -> Dict d a) -> Dict (All c) xs -> Dict (All d) xs Source #

Lifts a dictionary conversion over a type-level list.

Since: 0.2

mapAll2 :: forall {k} (c :: k -> Constraint) (d :: k -> Constraint) (xss :: [[k]]). (forall (a :: k). Dict c a -> Dict d a) -> Dict (All2 c) xss -> Dict (All2 d) xss Source #

Lifts a dictionary conversion over a type-level list of lists.

Since: 0.2

zipAll :: forall {k} (c :: k -> Constraint) (xs :: [k]) (d :: k -> Constraint). Dict (All c) xs -> Dict (All d) xs -> Dict (All (And c d)) xs Source #

If two constraints `c` and `d` hold over a type-level list `xs`, then the combination of both constraints holds over that list.

Since: 0.2

zipAll2 :: forall {k} (xss :: [[k]]) (c :: k -> Constraint) (d :: k -> Constraint). All (SListI :: [k] -> Constraint) xss => Dict (All2 c) xss -> Dict (All2 d) xss -> Dict (All2 (And c d)) xss Source #

If two constraints `c` and `d` hold over a type-level list of lists `xss`, then the combination of both constraints holds over that list of lists.

Since: 0.2

unAll_NP :: forall {k} (c :: k -> Constraint) (xs :: [k]). Dict (All c) xs -> NP (Dict c) xs Source #

If we have a constraint `c` that holds over a type-level list `xs`, we can create a product containing proofs that each individual list element satisfies `c`.

Since: 0.2

unAll_POP :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All2 c) xss -> POP (Dict c) xss Source #

If we have a constraint `c` that holds over a type-level list of lists `xss`, we can create a product of products containing proofs that all the inner elements satisfy `c`.

Since: 0.2

all_NP :: forall {k} (c :: k -> Constraint) (xs :: [k]). NP (Dict c) xs -> Dict (All c) xs Source #

If we have a product containing proofs that each element of `xs` satisfies `c`, then ``All` c` holds for `xs`.

Since: 0.2

all_POP :: forall {k} (xss :: [[k]]) (c :: k -> Constraint). SListI xss => POP (Dict c) xss -> Dict (All2 c) xss Source #

If we have a product of products containing proofs that each inner element of `xss` satisfies `c`, then ``All2` c` holds for `xss`.

Since: 0.2

unAll2 :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All2 c) xss -> Dict (All (All c)) xss Source #

Deprecated: 'All2 c' is now a synonym of 'All (All c)'

The constraint ``All2` c` is convertible to ``All` (`All` c)`.

Since: 0.2

all2 :: forall {k} (c :: k -> Constraint) (xss :: [[k]]). Dict (All (All c)) xss -> Dict (All2 c) xss Source #

Deprecated: 'All2 c' is now a synonym of 'All (All c)'

The constraint ``All` (`All` c)` is convertible to ``All2` c`.

Since: 0.2

withDict :: forall {k} c (a :: k) r. Dict c a -> (c a => r) -> r Source #

If we have an explicit dictionary, we can unwrap it and pass a function that makes use of it.

Since: 0.2

hdicts :: forall {k} {l} h (c :: k -> Constraint) (xs :: l). (AllN h c xs, HPure h) => h (Dict c) xs Source #

A structure of dictionaries.

Since: 0.2.3.0