type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the Tuple{Real}, x); julia> f(2) 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) IntegerCHAPTER 41. ESSENTIALS 569

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the Tuple{Real}, x); julia> f(2) 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) IntegerCHAPTER 41. ESSENTIALS 569

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the Tuple{Real}, x); julia> f(2) 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) IntegerCHAPTER 43. ESSENTIALS 646

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}

type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., dtype is np.float64, [('f1', np.uint64), ('f2', np.int32)], etc.) can be rep- resented by Array{T} where T is a concrete, immutable states that calling with certain argtypes is a part of public API. For example, the change between f1 and f2 in the example below is usually considered compatible because the change is invisible by the 5 julia> f1(::Integer) = Integer f1(::Real) = Real; julia> f2(x::Real) = _f2(x) _f2(::Integer) = Integer _f2(_) = Real; julia> f1(1) Integer julia> f2(1) Integer julia> invoke(f1, Tuple{Real}