diff --git a/.gitignore b/.gitignore
index ca0c122b..f34e1150 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,6 +2,7 @@ Manifest.toml
 *.jl.cov
 *.jl.*.cov
 *.jl.mem
+.vscode
 
 generated
 .vscode
diff --git a/src/indices.jl b/src/indices.jl
index 10ca5727..0ecb2b0a 100644
--- a/src/indices.jl
+++ b/src/indices.jl
@@ -1,30 +1,33 @@
-# Index of representation element of type ElemT
+# ParmaPolyhedra has its own index type so we have an `AbstractIndex`
+# so that it can use default implementations defined here
+abstract type AbstractIndex{T,ElemT} end
+
 """
-    Index{T, ElemT}
+    Index{T,ElemT} <: AbstractIndex{T,ElemT}
 
 Index of an element of type `ElemT` in a `Rep{T}`.
 """
-struct Index{T, ElemT}
+struct Index{T,ElemT} <: AbstractIndex{T,ElemT}
     value::Int
 end
 
 # Type of the value associated to this index
-valuetype(::Union{Index{T, ElemT}, Type{Index{T, ElemT}}}) where {T, ElemT} = ElemT
+valuetype(::Union{AbstractIndex{T,ElemT},Type{<:AbstractIndex{T,ElemT}}}) where {T,ElemT} = ElemT
 
-const HyperPlaneIndex{T} = Index{T, <:HyperPlane{T}}
-const HalfSpaceIndex{T} = Index{T, <:HalfSpace{T}}
-const HIndex{T} = Union{HyperPlaneIndex{T}, HalfSpaceIndex{T}}
+const HyperPlaneIndex{T} = AbstractIndex{T,<:HyperPlane{T}}
+const HalfSpaceIndex{T} = AbstractIndex{T,<:HalfSpace{T}}
+const HIndex{T} = Union{HyperPlaneIndex{T},HalfSpaceIndex{T}}
 
 #const SymPointIndex{T} = Index{T, <:SymPoint{T}}
-const PointIndex{T} = Index{T, <:AbstractVector{T}}
+const PointIndex{T} = AbstractIndex{T,<:AbstractVector{T}}
 #const PIndex{T} = Union{SymPointIndex{T}, PointIndex{T}}
 const PIndex{T} = PointIndex{T}
-const LineIndex{T} = Index{T, <:Line{T}}
-const RayIndex{T} = Index{T, <:Ray{T}}
-const RIndex{T} = Union{LineIndex{T}, RayIndex{T}}
-const VIndex{T} = Union{PIndex{T}, RIndex{T}}
-islin(::Union{Index{T, ElemT}, Type{Index{T, ElemT}}}) where {T, ElemT} = islin(ElemT)
-ispoint(::Union{Index{T, ElemT}, Type{Index{T, ElemT}}}) where {T, ElemT} = ispoint(ElemT)
+const LineIndex{T} = AbstractIndex{T,<:Line{T}}
+const RayIndex{T} = AbstractIndex{T,<:Ray{T}}
+const RIndex{T} = Union{LineIndex{T},RayIndex{T}}
+const VIndex{T} = Union{PIndex{T},RIndex{T}}
+islin(::Union{AbstractIndex{T, ElemT},Type{<:AbstractIndex{T,ElemT}}}) where {T,ElemT} = islin(ElemT)
+ispoint(::Union{AbstractIndex{T, ElemT},Type{<:AbstractIndex{T,ElemT}}}) where {T,ElemT} = ispoint(ElemT)
 
 """
     Indices{T, ElemT, RepT<:Rep{T}}
@@ -54,15 +57,17 @@ const RayIndices{T, RepT} = Indices{T, <:Ray{T}, RepT}
 const RIndices{T, RepT} = Union{LineIndices{T, RepT}, RayIndices{T, RepT}}
 const VIndices{T, RepT} = Union{PIndices{T, RepT}, RIndices{T, RepT}}
 
-undouble_it(idx::Nothing) = nothing
-double_it(idx::Nothing) = nothing
-undouble_it(idx::NTuple{2, Index}) = idx[1]
-double_it(idx::Index) = idx, idx
+undouble_it(::Nothing) = nothing
+double_it(::Nothing) = nothing
+undouble_it(idx::NTuple{2,AbstractIndex}) = idx[1]
+double_it(idx::AbstractIndex) = idx, idx
 function Base.iterate(idxs::Indices)
     return double_it(startindex(idxs))
 end
-function Base.iterate(idxs::Indices{T, ElemT},
-                      idx::Index{T, ElemT}) where {T, ElemT}
+function Base.iterate(
+    idxs::Indices{T,ElemT},
+    idx::AbstractIndex{T,ElemT},
+) where {T, ElemT}
     return double_it(nextindex(idxs.rep, idx))
 end
 
diff --git a/src/iterators.jl b/src/iterators.jl
index c2221fed..97627b30 100644
--- a/src/iterators.jl
+++ b/src/iterators.jl
@@ -30,15 +30,15 @@ function Base.eachindex(it::AbstractSingleRepIterator{<:Any, ElemT,
                                               RepT}) where {T, ElemT, RepT<:Rep{T}}
     return Indices{T, similar_type(ElemT, FullDim(RepT), T)}(it.p)
 end
-element_and_index(it, idx::Nothing) = nothing
-function element_and_index(it::AbstractSingleRepIterator, idx::Index)
+element_and_index(::AbstractSingleRepIterator, ::Nothing) = nothing
+function element_and_index(it::AbstractSingleRepIterator, idx::AbstractIndex)
     return mapitem(it, get(it.p, idx)), idx
 end
 function Base.iterate(it::AbstractSingleRepIterator)
     idx = undouble_it(iterate(eachindex(it)))
     return element_and_index(it, idx)
 end
-function Base.iterate(it::AbstractSingleRepIterator, idx::Index)
+function Base.iterate(it::AbstractSingleRepIterator, idx::AbstractIndex)
     idx = undouble_it(iterate(eachindex(it), idx))::Union{Nothing, typeof(idx)}
     return element_and_index(it, idx)
 end
diff --git a/src/lphrep.jl b/src/lphrep.jl
index fedcd8ca..e6ce99ec 100644
--- a/src/lphrep.jl
+++ b/src/lphrep.jl
@@ -31,7 +31,7 @@ function LPHRep(model::MOI.ModelLike, T::Type = Float64)
     _model = _MOIModel{T}()
     bridged = MOI.Bridges.LazyBridgeOptimizer(_model)
     # Only enable constraint bridges that don't create variables and don't add
-    # any variable bridge so that there is an identity mapping betwenen
+    # any variable bridge so that there is an identity mapping between
     # variables of `model` and polyhedra dimensions.
     MOI.Bridges.add_bridge(bridged, MOI.Bridges.Constraint.GreaterToLessBridge{T})
     MOI.Bridges.add_bridge(bridged, MOI.Bridges.Constraint.LessToGreaterBridge{T})