By Harrison J.
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Additional info for Introduction to functional programming
The first alternative is to stick with normal order reduction, but attempt to optimize the implementation so multiple subexpressions arising in this way are shared, and never evaluated more than once. Internally, expressions are represented as directed acyclic graphs rather than as trees. This is known as lazy or call-by-need evaluation, since expressions are only evaluated when absolutely necessary. The second approach is to turn the theoretical considerations about reduction strategy on their head and evaluate arguments to functions before passing the values to the function.
It is remarkable that this device is enough to bring us to the point where we can write the definition of the factorial function almost in the way we can in ML. In what sense, though, is the lambda calculus augmented with these notational conventions really a programming language? Ultimately, a program is just a single expression. g: let rec fact(n) = if ISZERO n then 1 else n ∗ fact(PRE n) in ··· f act(6) We can read these definitions of auxiliary functions as equations in the mathematical sense.
Others, like PL/I, have only weak typing, with the compiler allowing some mixtures of different types and casting them appropriately. There are also languages like LISP that perform typechecking dynamically, during execution, rather than statically during compilation. This can (at least in principle) degrade runtime performance, since it means that the computer is spending some time on making sure types are respected during execution — compare checking of array bounds during execution, another common runtime overhead.