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fully lazy lambda lifting

fully lazy lambda lifting in Technology

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.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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