What are Haskell's strictness points?

Question

We all know (or should know) that Haskell is lazy by default. Nothing is evaluated until it must be evaluated. So when must something be evaluated? There are points where Haskel

Answer 1

C has the concept of sequence points, which are guarantees for particular operations that one operand will be evaluated before the other. I think that's the closest existing concept, but the essentially equivalent term strictness point (or possibly force point) is more in line with Haskell thinking.

In practice Haskell is not a purely lazy language: for instance pattern matching is usually strict (So trying a pattern match forces evaluation to happen at least far enough to accept or reject the match.

…

Programmers can also use the seq primitive to force an expression to evaluate regardless of whether the result will ever be used.

$! is defined in terms of seq.

—Lazy vs. non-strict.

So your thinking about !/$! and seq is essentially right, but pattern matching is subject to subtler rules. You can always use ~ to force lazy pattern matching, of course. An interesting point from that same article:

The strictness analyzer also looks for cases where sub-expressions are always required by the outer expression, and converts those into eager evaluation. It can do this because the semantics (in terms of "bottom") don't change.

Let's continue down the rabbit hole and look at the docs for optimisations performed by GHC:

Strictness analysis is a process by which GHC attempts to determine, at compile-time, which data definitely will 'always be needed'. GHC can then build code to just calculate such data, rather than the normal (higher overhead) process for storing up the calculation and executing it later.

—GHC Optimisations: Strictness Analysis.

In other words, strict code may be generated anywhere as an optimisation, because creating thunks is unnecessarily expensive when the data will always be needed (and/or may only be used once).

…no more evaluation can be performed on the value; it is said to be in normal form. If we are at any of the intermediate steps so that we've performed at least some evaluation on a value, it is in weak head normal form (WHNF). (There is also a 'head normal form', but it's not used in Haskell.) Fully evaluating something in WHNF reduces it to something in normal form…

—Wikibooks Haskell: Laziness

(A term is in head normal form if there is no beta-redex in head position¹. A redex is a head redex if it is preceded only by lambda abstractors of non-redexes ².) So when you start to force a thunk, you're working in WHNF; when there are no more thunks left to force, you're in normal form. Another interesting point:

…if at some point we needed to, say, print z out to the user, we'd need to fully evaluate it…

Which naturally implies that, indeed, any IO action performed from main does force evaluation, which should be obvious considering that Haskell programs do, in fact, do things. Anything that needs to go through the sequence defined in main must be in normal form and is therefore subject to strict evaluation.

C. A. McCann got it right in the comments, though: the only thing that's special about main is that main is defined as special; pattern matching on the constructor is sufficient to ensure the sequence imposed by the IO monad. In that respect only seq and pattern-matching are fundamental.