diff --git a/src/autgroups.jl b/src/autgroups.jl
index 7c30686..6ac0165 100644
--- a/src/autgroups.jl
+++ b/src/autgroups.jl
@@ -105,16 +105,15 @@ function evaluate!(
     t::NTuple{N,T},
     f::AbstractFPGroupElement{<:AutomorphismGroup{<:Group}},
     tmp = one(first(t)),
-) where {N, T}
+) where {N, T<:FPGroupElement}
     A = alphabet(f)
-    AF = alphabet(object(parent(f)))
     for idx in word(f)
-        t = @inbounds evaluate!(t, A[idx], AF, tmp)::NTuple{N,T}
+        t = @inbounds evaluate!(t, A[idx], tmp)::NTuple{N,T}
     end
     return t
 end
 
-evaluate!(t::NTuple{N, T}, s::GSymbol, A, tmp=one(first(t))) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
+evaluate!(t::NTuple{N, T}, s::GSymbol, tmp=nothing) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
 
 # forward evaluate by substitution
 
@@ -132,7 +131,7 @@ function LettersMap(a::FPGroupElement{<:AutomorphismGroup})
 
     # (dom[i] → img[i] is a map from domain to images)
     # we need a map from alphabet indices → (gens, gens⁻¹) → images
-    # here we do it for elements of the domai
+    # here we do it for elements of the domain
     # (trusting it's a set of generators that define a)
     @assert length(dom) == length(img)
 
diff --git a/src/groups/symplectic_twists.jl b/src/groups/symplectic_twists.jl
index 6951e19..140216c 100644
--- a/src/groups/symplectic_twists.jl
+++ b/src/groups/symplectic_twists.jl
@@ -195,8 +195,7 @@ end
 function evaluate!(
     t::NTuple{N,T},
     smc::SymplecticMappingClass,
-    A::Alphabet,
-    tmp = one(first(t)),
+    tmp=nothing,
 ) where {N,T}
 
     t = smc.f(t[smc.perm])[smc.invperm]
diff --git a/src/groups/transvections.jl b/src/groups/transvections.jl
index 1b9a358..dc56f2f 100644
--- a/src/groups/transvections.jl
+++ b/src/groups/transvections.jl
@@ -45,9 +45,15 @@ Base.:(==)(t::Transvection, s::Transvection) =
     t.id === s.id && t.ij == s.ij && t.inv == s.inv
 Base.hash(t::Transvection, h::UInt) = hash(t.id, hash(t.ij, hash(t.inv, h)))
 
-Base.@propagate_inbounds function evaluate!(v::NTuple{T, N}, t::Transvection, A::Alphabet, tmp=one(first(v))) where {T, N}
+Base.@propagate_inbounds @inline function evaluate!(
+    v::NTuple{T, N},
+    t::Transvection,
+    tmp=one(first(v))
+) where {T, N}
     i, j = indices(t)
-    @assert i ≤ length(v) && j ≤ length(v)
+    @assert 1 ≤ i ≤ length(v) && 1 ≤ j ≤ length(v)
+
+    A = alphabet(parent(first(v)))
 
     @inbounds begin
         if t.id === :ϱ
@@ -101,6 +107,5 @@ Base.inv(p::PermRightAut) = PermRightAut(invperm(p.perm))
 Base.:(==)(p::PermRightAut, q::PermRightAut) = p.perm == q.perm
 Base.hash(p::PermRightAut, h::UInt) = hash(p.perm, hash(PermRightAut, h))
 
-function evaluate!(v::NTuple{T, N}, p::PermRightAut, ::Alphabet, tmp=one(first(v))) where {T, N}
-    return v[p.perm]
+evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp=nothing) where {T,N} = v[p.perm]
 end
diff --git a/test/AutFn.jl b/test/AutFn.jl
index a269163..b8a3f1d 100644
--- a/test/AutFn.jl
+++ b/test/AutFn.jl
@@ -47,7 +47,7 @@
         r = Groups.Transvection(:ϱ,i,j)
         l = Groups.Transvection(:λ,i,j)
 
-        (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t, A4)
+        (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t)
 
         @test      r(deepcopy(D)) == (a*b,   b, c, d)
         @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)