Handout 7: Call by Name and Call by Value

In Handout 4, we have examined the reduction semantics of lambda calculus, and noted the difference between the normal order reduction, which chooses leftmost-outermost redexes for reduction at every stage, and the applicative order reduction, which chooses innermost redexes for reduction at every stage. We noted that the normal order reduction strategy is always able to find the normal form of a lambda calculus term, but the applicative order strategy may fail to find the normal form by carrying out reductions that are “unnecessary” for the normal form. In programming languages, the evaluation order that corresponds to normal order reduction is termed call by name. The evaluation order that corresponds to the applicative order reduction is termed call-by-value. Algol 60 was the first programming language to use the call-by-name evaluation order. However, at this early stage in the evolution of programming languages, the implications of call-by-name were not fully understood and it is said that many implementations of Algol 60 failed to implement it correctly. Many of the Algol derivatives, such as Simula 67, also used the call-by-name evaluation mechanism. Pascal and C, which were also derivatives of Algol, chose to use the call by value evaluation order because it was simpler and it was also felt that it was a more efficient execution mechanism. In functional programming, Miranda and Haskell use call-by-name evaluation order. (They actually use a variant of call-by-name order called call by need.) Other languages, including Lisp, Pop-11 and ML use the call-by-value evaluation order. In this handout, we look at the two evaluation mechanisms more closely and formalize their behaviour.