Alphabets

Alphabet(letters::AbstractVector[, inversions])

An alphabet consists of the symbols of a common type T.

An Alphabet defines a bijection between consecutive integers and its letters, i.e. it can be queried for the index of a letter, or the letter corresponding to a given index.

Example

julia> al = Alphabet([:a, :b, :c])
Alphabet of Symbol
  1. a
  2. b
  3. c

julia> al[2]
:b

julia> al[:c]
3

julia> Alphabet([:a, :A, :b], [2, 1, 0])
Alphabet of Symbol
  1. a    (inverse of: A)
  2. A    (inverse of: a)
  3. b

setinverse!(A::Alphabet{T}, x::T, X::T) where T

Set the inversion of x to X (and vice versa).

Example

julia> al = Alphabet([:a, :b, :c])
Alphabet of Symbol
  1. a
  2. b
  3. c

julia> KnuthBendix.setinverse!(al, :a, :c)
Alphabet of Symbol
  1. a    (inverse of: c)
  2. b
  3. c    (inverse of: a)

julia> KnuthBendix.setinverse!(al, :a, :b)
┌ Warning: a already has an inverse: c; overriding
└ @ KnuthBendix ~/.julia/dev/KnuthBendix/src/alphabets.jl:161
Alphabet of Symbol
  1. a    (inverse of: b)
  2. b    (inverse of: a)
  3. c

hasinverse(idx::Integer, A::Alphabet)
hasinverse(letter, A::Alphabet)

Check if alphabet A defines the inverse of letter.

inv(idx::Integer, A::Alphabet)
inv(letter::T, A::Alphabet{T}) where T

Return the inverse of a letter letter in the context of alphabet A.

If hasinverse(letter, A) == false a DomainError is thrown.

inv(w::AbstractWord, A::Alphabet)

Return the inverse of a word w in the context of alphabet A.