partial evaluation

(compiler, algorithm)partial evaluation - (Or "specialisation") An optimisation technique where the compiler evaluates some subexpressions at compile-time. For example,

pow x 0 = 1 pow x n = if even n then pxn2 * pxn2 else x * pow x (n-1) where pxn2 = pow x (n/2) f x = pow x 5

Since n is known we can specialise pow in its second argument and unfold the recursive calls:

pow5 x = x * x4 where x4 = x2 * x2 x2 = x * x f x = pow5 x

pow5 is known as the residual. We could now also unfold pow5 giving:

f x = x * x4 where x4 = x2 * x2 x2 = x * x

It is important that the partial evaluation algorithm should terminate. This is not guaranteed in the presence of recursive function definitions. For example, if partial evaluation were applied to the right hand side of the second clause for pow above, it would never terminate because the value of n is not known.

Partial evaluation might change the termination properties of the program if, for example, the expression (x * 0) was reduced to 0 it would terminate even if x (and thus x * 0) did not.

It may be necessary to reorder an expression to partially evaluate it, e.g.

f x y = (x + y) + 1 g z = f 3 z

If we rewrite f:

f x y = (x + 1) + y

then the expression x+1 becomes a constant for the function g and we can say

g z = f 3 z = (3 + 1) + z = 4 + z

Partial evaluation of built-in functions applied to constant arguments is known as constant folding.

See also full laziness.
Parthian arrow
parti pris
partial abortion
partial breach
partial correlation
partial denture
partial derivative
Partial differential
partial differential equation
Partial Differential Equation LANguage
Partial differentials
partial eclipse
partial equivalence relation
-- partial evaluation --
Partial fractions
partial function
partial key
partial ordering
Partial Response Maximum Likelihood
partial tone
Partial tones
partial veil
partial verdict
partially ordered set
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