fully lazy lambda lifting
fully lazy lambda lifting
John Hughes's optimisation of lambda lifting to give full laziness. 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 with
(\ 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).
This is similar to the code motion optimisation in procedural languages where constant expressions are moved outside a loop or procedure.
f = \ x . (\ y . (+) (sqrt x) y)
((+) (sqrt x)) is a maximal free expression in (\ y . (+) (sqrt x) y) so this inner abstraction is replaced with
(\ 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).
This is similar to the code motion optimisation in procedural languages where constant expressions are moved outside a loop or procedure.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)