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fully lazy lambda lifting
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John Hughes's optimisation of lambda lifting to give fulllaziness. Maximal free expressions are shared to minimise
the amount of recalculation. Each inner sub-expression is
replaced by a function of its maximal free expressions
(expressions not containing any bound variable) applied to
those expressions. E.g.
f = x . ( y . (+) (sqrt x) y)
((+) (sqrt x)) is a maximal free expression in
( y . (+) (sqrt x) y) so this inner abstraction is replaced
( g . y . g y) ((+) (sqrt x))
Now, if a partial application of f is shared, the result of
evaluating (sqrt x) will also be shared rather than
re-evaluated on each application of f. As Chin notes, the
same benefit could be achieved without introducing the new
higher-order function, g, if we just extracted out (sqrt x).