  Jay and Given-Wilson have recently introduced the Factorisation (or SF-)
calculus as a minimal fundamental model of intensional computation. It is a
combinatory calculus containing a special combinator, F, which is able to
examine the internal structure of its first argument. The calculus is
significant in that as well as being combinatorially complete it also exhibits
the property of structural completeness, i.e. it is able to represent any
function on terms definable using pattern matching on arbitrary normal forms.
In particular, it admits a term that can decide the structural equality of any
two arbitrary normal forms.
  Since SF-calculus is combinatorially complete, it is clearly at least as
powerful as the more familiar and paradigmatic Turing-powerful computational
models of Lambda Calculus and Combinatory Logic. Its relationship to these
models in the converse direction is less obvious, however. Jay and Given-Wilson
have suggested that SF-calculus is strictly more powerful than the
aforementioned models, but a detailed study of the connections between these
models is yet to be undertaken.
  This paper begins to bridge that gap by presenting a faithful encoding of the
Factorisation Calculus into the Lambda Calculus preserving both reduction and
strong normalisation. The existence of such an encoding is a new result. It
also suggests that there is, in some sense, an equivalence between the former
model and the latter. We discuss to what extent our result constitutes an
equivalence by considering it in the context of some previously defined
frameworks for comparing computational power and expressiveness.
