oleg at okmij.org oleg at okmij.org
Sat Feb 23 04:05:08 EST 2008

```Call-by-name lambda-calculus is strictly more expressive (in Felleisen
sense) than call-by-value lambda-calculus, and the call-by-need (aka, lazy)
lambda-calculus is observationally equivalent to the call-by-name.
One can add shift/reset to any of these calculi (CBV shift/reset is
most known; there are several CBN shift/reset, including the one I'm
particularly attached to; in principle one can add shift/reset to
call-by-need).

Adding control effects (shift/reset) changes the expressivity
results. Now all three calculi are distinct and none subsumes the
other. For example, the expression
reset( (\x -> 1) (abort 2))
evaluates to 1 in call-by-name and evaluate to 2 in call-by-value.
The expression
reset ((\x -> x + x) (shift f f))
has the type int->int in call-by-need (it is a function \x -> x + x)
and it has the type int->int->int in call-by-name (and it is the

The fact that call-by-need is no longer observationally equivalent to
call-by-name and sharing becomes observable is the most
distressing. It disables many optimizations GHC is allowed to
do. Types help: there are call-by-name calculi with shift/reset with
effect typing; one can look at the type and see what control effect an
expression may make. That will still permit GHC optimize pure
expressions and leave effectful expressions as they are. Alas, that
type system is complex and I don't think inference is decidable there
due to the presence of subtyping (one must annotate at least some of
the binders with types, in particular, the binders of shift). It seems
the simplest solution is to confine shift/reset to a monad.

Regarding purity: the obligatory reference is

Amr Sabry. What is a Purely Functional Language?
In J. Functional Programming, 8(1), 1-22, Jan. 1998.
http://www.cs.indiana.edu/~sabry/papers/purelyFunctional.ps

Please see the definition 4.7. As Matthias Blume said, a bit
informally, evaluation of a pure expression should not depend on CBN
or CBV or some other such strategy. By this definition, an expression
that involves shift/reset is not pure, as the above examples
demonstrate.
```