Marlow, Simon David
Deforestation for higher-order functional programs.
PhD thesis, University of Glasgow.
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Functional programming languages are an ideal medium for program optimisations based
on source-to-source transformation techniques. Referential transparency affords opportunities
for a wide range of correctness-preserving transformations leading to potent optimisation
This thesis builds on deforestation, a program transformation technique due to Wadler
that removes intermediate data structures from first-order functional programs.
Our contribution is to reformulate deforestation for higher-order functional programming
languages, and to show that the resulting algorithm terminates given certain syntactic and
typing constraints on the input. These constraints are entirely reasonable, indeed it is
possible to translate any typed program into the required syntactic form. We show how
this translation can be performed automatically and optimally.
The higher-order deforestation algorithm is transparent. That is, it is possible to determine
by examination of the source program where the optimisation will be applicable.
We also investigate the relationship of deforestation to cut-elimination, the normalisation
property for the logic of sequent calculus. By combining a cut-elimination algorithm and
first-order deforestation, we derive an improved higher-order deforestation algorithm.
The higher-order deforestation algorithm has been implemented in the Glasgow Haskell
Compiler. We describe how deforestation fits into the framework of Haskell, and design
a model for the implementation that allows automatic list removal, with additional deforestation
being performed on the basis of programmer supplied annotations. Results from
applying the deforestation implementation to several example Haskell programs are given.
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