[Haskell-cafe] About the lazy pattern

[张旭]

Hi, I am really new to haskell. I am reading "A gentle instruction to haskell" now. And I just cannot understand the chapter below. Is there anybody who can gives me some hints about why the pattern matching for "client" is so early? How does the pattern matching works here? 
Thank you so much for answering my questions!

 

Sincerely, 

nemo

4.4  Lazy Patterns
There is one other kind of pattern allowed in Haskell. It is called a lazy pattern, and has the form ~pat. Lazy patterns are irrefutable: matching a value v against ~pat always succeeds, regardless of pat. Operationally speaking, if an identifier in pat is later "used" on the right-hand-side, it will be bound to that portion of the value that would result if v were to successfully match pat, and _|_ otherwise. 
Lazy patterns are useful in contexts where infinite data structures are being defined recursively. For example, infinite lists are an excellent vehicle for writing simulation programs, and in this context the infinite lists are often called streams. Consider the simple case of simulating the interactions between a server process server and a client process client, where client sends a sequence of requests to server, and server replies to each request with some kind of response. This situation is shown pictorially in Figure 2. (Note that client also takes an initial message as argument.) 
 
Figure 2Using streams to simulate the message sequences, the Haskell code corresponding to this diagram is: 

reqs                     = client init resps
resps                    = server reqs

These recursive equations are a direct lexical transliteration of the diagram. 
Let us further assume that the structure of the server and client look something like this: 

client init (resp:resps) = init : client (next resp) resps
server      (req:reqs)   = process req : server reqs

where we assume that next is a function that, given a response from the server, determines the next request, and process is a function that processes a request from the client, returning an appropriate response. 
Unfortunately, this program has a serious problem: it will not produce any output! The problem is that client, as used in the recursive setting of reqs and resps, attempts a match on the response list before it has submitted its first request! In other words, the pattern matching is being done "too early." One way to fix this is to redefine client as follows: 

client init resps         = init : client (next (head resps)) (tail resps)

Although workable, this solution does not read as well as that given earlier. A better solution is to use a lazy pattern: 

client init ~(resp:resps) = init : client (next resp) resps

Because lazy patterns are irrefutable, the match will immediately succeed, allowing the initial request to be "submitted", in turn allowing the first response to be generated; the engine is now "primed", and the recursion takes care of the rest.

 

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