Agda-2.6.2.1.20220320: A dependently typed functional programming language and proof assistant
Safe HaskellSafe-Inferred
LanguageHaskell2010

Agda.Utils.Permutation

Synopsis

Documentation

data Permutation Source #

Partial permutations. Examples:

permute [1,2,0] [x0,x1,x2] = [x1,x2,x0] (proper permutation).

permute [1,0] [x0,x1,x2] = [x1,x0] (partial permuation).

permute [1,0,1,2] [x0,x1,x2] = [x1,x0,x1,x2] (not a permutation because not invertible).

Agda typing would be: Perm : {m : Nat}(n : Nat) -> Vec (Fin n) m -> Permutation m is the size of the permutation.

Constructors

Perm 

Fields

Instances

Instances details
KillRange Permutation Source # 
Instance details

Defined in Agda.Syntax.Position

DropArgs Permutation Source # 
Instance details

Defined in Agda.TypeChecking.DropArgs

PrettyTCM Permutation Source # 
Instance details

Defined in Agda.TypeChecking.Pretty

EmbPrj Permutation Source # 
Instance details

Defined in Agda.TypeChecking.Serialise.Instances.Internal

Abstract Permutation Source # 
Instance details

Defined in Agda.TypeChecking.Substitute

Apply Permutation Source # 
Instance details

Defined in Agda.TypeChecking.Substitute

Null Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

DoDrop Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

Sized Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

size :: Permutation -> Int Source #

Data Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Permutation -> c Permutation #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Permutation #

toConstr :: Permutation -> Constr #

dataTypeOf :: Permutation -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Permutation) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Permutation) #

gmapT :: (forall b. Data b => b -> b) -> Permutation -> Permutation #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Permutation -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Permutation -> r #

gmapQ :: (forall d. Data d => d -> u) -> Permutation -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Permutation -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Permutation -> m Permutation #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Permutation -> m Permutation #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Permutation -> m Permutation #

Generic Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

Associated Types

type Rep Permutation :: Type -> Type #

Show Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

NFData Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

rnf :: Permutation -> () #

Eq Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

type Rep Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

type Rep Permutation = D1 ('MetaData "Permutation" "Agda.Utils.Permutation" "Agda-2.6.2.1.20220320-inplace" 'False) (C1 ('MetaCons "Perm" 'PrefixI 'True) (S1 ('MetaSel ('Just "permRange") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int) :*: S1 ('MetaSel ('Just "permPicks") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [Int])))

permute :: Permutation -> [a] -> [a] Source #

permute [1,2,0] [x0,x1,x2] = [x1,x2,x0] More precisely, permute indices list = sublist, generates sublist from list by picking the elements of list as indicated by indices. permute [1,3,0] [x0,x1,x2,x3] = [x1,x3,x0]

Agda typing: permute (Perm {m} n is) : Vec A m -> Vec A n

class InversePermute a b where Source #

Invert a Permutation on a partial finite int map. inversePermute perm f = f' such that permute perm f' = f

Example, with map represented as [Maybe a]: f = [Nothing, Just a, Just b ] perm = Perm 4 [3,0,2] f' = [ Just a , Nothing , Just b , Nothing ] Zipping perm with f gives [(0,a),(2,b)], after compression with catMaybes. This is an IntMap which can easily written out into a substitution again.

Methods

inversePermute :: Permutation -> a -> b Source #

Instances

Instances details
InversePermute [Maybe a] (IntMap a) Source # 
Instance details

Defined in Agda.Utils.Permutation

InversePermute [Maybe a] [Maybe a] Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

inversePermute :: Permutation -> [Maybe a] -> [Maybe a] Source #

InversePermute [Maybe a] [(Int, a)] Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

inversePermute :: Permutation -> [Maybe a] -> [(Int, a)] Source #

InversePermute (Int -> a) [Maybe a] Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

inversePermute :: Permutation -> (Int -> a) -> [Maybe a] Source #

idP :: Int -> Permutation Source #

Identity permutation.

takeP :: Int -> Permutation -> Permutation Source #

Restrict a permutation to work on n elements, discarding picks >=n.

droppedP :: Permutation -> Permutation Source #

Pick the elements that are not picked by the permutation.

liftP :: Int -> Permutation -> Permutation Source #

liftP k takes a Perm {m} n to a Perm {m+k} (n+k). Analogous to liftS, but Permutations operate on de Bruijn LEVELS, not indices.

composeP :: Permutation -> Permutation -> Permutation Source #

permute (compose p1 p2) == permute p1 . permute p2

invertP :: Int -> Permutation -> Permutation Source #

invertP err p is the inverse of p where defined, otherwise defaults to err. composeP p (invertP err p) == p

compactP :: Permutation -> Permutation Source #

Turn a possible non-surjective permutation into a surjective permutation.

reverseP :: Permutation -> Permutation Source #

permute (reverseP p) xs ==
    reverse $ permute p $ reverse xs

Example: permute (reverseP (Perm 4 [1,3,0])) [x0,x1,x2,x3] == permute (Perm 4 $ map (3-) [0,3,1]) [x0,x1,x2,x3] == permute (Perm 4 [3,0,2]) [x0,x1,x2,x3] == [x3,x0,x2] == reverse [x2,x0,x3] == reverse $ permute (Perm 4 [1,3,0]) [x3,x2,x1,x0] == reverse $ permute (Perm 4 [1,3,0]) $ reverse [x0,x1,x2,x3]

With reverseP, you can convert a permutation on de Bruijn indices to one on de Bruijn levels, and vice versa.

flipP :: Permutation -> Permutation Source #

permPicks (flipP p) = permute p (downFrom (permRange p)) or permute (flipP (Perm n xs)) [0..n-1] = permute (Perm n xs) (downFrom n)

Can be use to turn a permutation from (de Bruijn) levels to levels to one from levels to indices.

See numberPatVars.

expandP :: Int -> Int -> Permutation -> Permutation Source #

expandP i n π in the domain of π replace the ith element by n elements.

topoSort :: (a -> a -> Bool) -> [a] -> Maybe Permutation Source #

Stable topologic sort. The first argument decides whether its first argument is an immediate parent to its second argument.

topoSortM :: Monad m => (a -> a -> m Bool) -> [a] -> m (Maybe Permutation) Source #

Drop (apply) and undrop (abstract)

data Drop a Source #

Delayed dropping which allows undropping.

Constructors

Drop 

Fields

  • dropN :: Int

    Non-negative number of things to drop.

  • dropFrom :: a

    Where to drop from.

Instances

Instances details
Foldable Drop Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

fold :: Monoid m => Drop m -> m #

foldMap :: Monoid m => (a -> m) -> Drop a -> m #

foldMap' :: Monoid m => (a -> m) -> Drop a -> m #

foldr :: (a -> b -> b) -> b -> Drop a -> b #

foldr' :: (a -> b -> b) -> b -> Drop a -> b #

foldl :: (b -> a -> b) -> b -> Drop a -> b #

foldl' :: (b -> a -> b) -> b -> Drop a -> b #

foldr1 :: (a -> a -> a) -> Drop a -> a #

foldl1 :: (a -> a -> a) -> Drop a -> a #

toList :: Drop a -> [a] #

null :: Drop a -> Bool #

length :: Drop a -> Int #

elem :: Eq a => a -> Drop a -> Bool #

maximum :: Ord a => Drop a -> a #

minimum :: Ord a => Drop a -> a #

sum :: Num a => Drop a -> a #

product :: Num a => Drop a -> a #

Traversable Drop Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

traverse :: Applicative f => (a -> f b) -> Drop a -> f (Drop b) #

sequenceA :: Applicative f => Drop (f a) -> f (Drop a) #

mapM :: Monad m => (a -> m b) -> Drop a -> m (Drop b) #

sequence :: Monad m => Drop (m a) -> m (Drop a) #

Functor Drop Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

fmap :: (a -> b) -> Drop a -> Drop b #

(<$) :: a -> Drop b -> Drop a #

KillRange a => KillRange (Drop a) Source # 
Instance details

Defined in Agda.Syntax.Position

EmbPrj a => EmbPrj (Drop a) Source # 
Instance details

Defined in Agda.TypeChecking.Serialise.Instances.Internal

Methods

icode :: Drop a -> S Int32 Source #

icod_ :: Drop a -> S Int32 Source #

value :: Int32 -> R (Drop a) Source #

DoDrop a => Abstract (Drop a) Source # 
Instance details

Defined in Agda.TypeChecking.Substitute

Methods

abstract :: Telescope -> Drop a -> Drop a Source #

DoDrop a => Apply (Drop a) Source # 
Instance details

Defined in Agda.TypeChecking.Substitute

Methods

apply :: Drop a -> Args -> Drop a Source #

applyE :: Drop a -> Elims -> Drop a Source #

Data a => Data (Drop a) Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Drop a -> c (Drop a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Drop a) #

toConstr :: Drop a -> Constr #

dataTypeOf :: Drop a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Drop a)) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Drop a)) #

gmapT :: (forall b. Data b => b -> b) -> Drop a -> Drop a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Drop a -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Drop a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Drop a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Drop a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Drop a -> m (Drop a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Drop a -> m (Drop a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Drop a -> m (Drop a) #

Show a => Show (Drop a) Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

showsPrec :: Int -> Drop a -> ShowS #

show :: Drop a -> String #

showList :: [Drop a] -> ShowS #

Eq a => Eq (Drop a) Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

(==) :: Drop a -> Drop a -> Bool #

(/=) :: Drop a -> Drop a -> Bool #

Ord a => Ord (Drop a) Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

compare :: Drop a -> Drop a -> Ordering #

(<) :: Drop a -> Drop a -> Bool #

(<=) :: Drop a -> Drop a -> Bool #

(>) :: Drop a -> Drop a -> Bool #

(>=) :: Drop a -> Drop a -> Bool #

max :: Drop a -> Drop a -> Drop a #

min :: Drop a -> Drop a -> Drop a #

class DoDrop a where Source #

Things that support delayed dropping.

Minimal complete definition

doDrop

Methods

doDrop Source #

Arguments

:: Drop a 
-> a

Perform the dropping.

dropMore Source #

Arguments

:: Int 
-> Drop a 
-> Drop a

Drop more.

unDrop Source #

Arguments

:: Int 
-> Drop a 
-> Drop a

Pick up dropped stuff.

Instances

Instances details
DoDrop Permutation Source # 
Instance details

Defined in Agda.Utils.Permutation

DoDrop [a] Source # 
Instance details

Defined in Agda.Utils.Permutation

Methods

doDrop :: Drop [a] -> [a] Source #

dropMore :: Int -> Drop [a] -> Drop [a] Source #

unDrop :: Int -> Drop [a] -> Drop [a] Source #