License	MIT
Safe Haskell	None
Language	GHC2021

Language.Egison.Type.Index

Description

This module defines tensor index types for the Egison type system. Indices can be superscript (contravariant, ~i) or subscript (covariant, _i).

Synopsis

data IndexKind
- = Superscript
- | Subscript
data Index
- = IndexSym IndexKind String
- | IndexPlaceholder IndexKind
- | IndexVar String
type IndexSpec = [Index]
newtype IndexTyVar = IndexTyVar String
isSupSubPair :: Index -> Index -> Bool
isSuperscript :: Index -> Bool
isSubscript :: Index -> Bool
isPlaceholder :: Index -> Bool
indexSymbol :: Index -> Maybe String
flipIndexKind :: IndexKind -> IndexKind

Documentation

data IndexKind Source #

The kind of tensor index

Constructors

Superscript	Contravariant index, written as ~i
Subscript	Covariant index, written as _i

Instances

Instances details

Generic IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

Associated Types

type Rep IndexKind
Instance details Defined in Language.Egison.Type.Index type Rep IndexKind = D1 ('MetaData "IndexKind" "Language.Egison.Type.Index" "egison-5.0.0-IKLJXBVxR779jp4wYu1Icq" 'False) (C1 ('MetaCons "Superscript" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Subscript" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

from :: IndexKind -> Rep IndexKind x #

to :: Rep IndexKind x -> IndexKind #

Show IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

showsPrec :: Int -> IndexKind -> ShowS #

show :: IndexKind -> String #

showList :: [IndexKind] -> ShowS #

Eq IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

(==) :: IndexKind -> IndexKind -> Bool #

(/=) :: IndexKind -> IndexKind -> Bool #

Ord IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

compare :: IndexKind -> IndexKind -> Ordering #

(<) :: IndexKind -> IndexKind -> Bool #

(<=) :: IndexKind -> IndexKind -> Bool #

(>) :: IndexKind -> IndexKind -> Bool #

(>=) :: IndexKind -> IndexKind -> Bool #

max :: IndexKind -> IndexKind -> IndexKind #

min :: IndexKind -> IndexKind -> IndexKind #

Hashable IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

hashWithSalt :: Int -> IndexKind -> Int #

hash :: IndexKind -> Int #

type Rep IndexKind Source #

Instance details

Defined in Language.Egison.Type.Index

type Rep IndexKind = D1 ('MetaData "IndexKind" "Language.Egison.Type.Index" "egison-5.0.0-IKLJXBVxR779jp4wYu1Icq" 'False) (C1 ('MetaCons "Superscript" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Subscript" 'PrefixI 'False) (U1 :: Type -> Type))

data Index Source #

A tensor index

Constructors

IndexSym IndexKind String	Named index, e.g., _i, ~j
IndexPlaceholder IndexKind	Placeholder index, e.g., _#, ~#
IndexVar String	Index variable (for type-level computation)

Instances

Instances details

Generic Index Source #

Instance details

Defined in Language.Egison.Type.Index

Associated Types

type Rep Index

Instance details

Defined in Language.Egison.Type.Index

type Rep Index = D1 ('MetaData "Index" "Language.Egison.Type.Index" "egison-5.0.0-IKLJXBVxR779jp4wYu1Icq" 'False) (C1 ('MetaCons "IndexSym" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IndexKind) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)) :+: (C1 ('MetaCons "IndexPlaceholder" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IndexKind)) :+: C1 ('MetaCons "IndexVar" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String))))

Methods

from :: Index -> Rep Index x #

to :: Rep Index x -> Index #

Show Index Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

showsPrec :: Int -> Index -> ShowS #

show :: Index -> String #

showList :: [Index] -> ShowS #

Eq Index Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

(==) :: Index -> Index -> Bool #

(/=) :: Index -> Index -> Bool #

Ord Index Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

compare :: Index -> Index -> Ordering #

(<) :: Index -> Index -> Bool #

(<=) :: Index -> Index -> Bool #

(>) :: Index -> Index -> Bool #

(>=) :: Index -> Index -> Bool #

max :: Index -> Index -> Index #

min :: Index -> Index -> Index #

Hashable Index Source #

Instance details

Defined in Language.Egison.Type.Index

Methods

hashWithSalt :: Int -> Index -> Int #

hash :: Index -> Int #

type Rep Index Source #

Instance details

Defined in Language.Egison.Type.Index

type Rep Index = D1 ('MetaData "Index" "Language.Egison.Type.Index" "egison-5.0.0-IKLJXBVxR779jp4wYu1Icq" 'False) (C1 ('MetaCons "IndexSym" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IndexKind) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)) :+: (C1 ('MetaCons "IndexPlaceholder" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IndexKind)) :+: C1 ('MetaCons "IndexVar" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String))))

type IndexSpec = [Index] Source #

A sequence of indices

newtype IndexTyVar Source #

Index variable for type schemes (type-level)

Constructors

IndexTyVar String

Instances

Instances details

Generic IndexTyVar Source #

Instance details

Defined in Language.Egison.Type.Index

Associated Types

type Rep IndexTyVar
Instance details Defined in Language.Egison.Type.Index type Rep IndexTyVar = D1 ('MetaData "IndexTyVar" "Language.Egison.Type.Index" "egison-5.0.0-IKLJXBVxR779jp4wYu1Icq" 'True) (C1 ('MetaCons "IndexTyVar" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)))