clojure lazy sequence

I asked a question in SO some months ago, to get a explaination towards lazy sequence:

(def fib-seq (lazy-cat [0 1]  (map + (rest fib-seq) fib-seq )))

Thanks @omiel provide many useful information, but still did not touch the most sensitive point, after thinking a while, I figure out what happened in the generation of lazy sequence.
May clojure sage in SO please correct me if I am actually wrong.

What I mean step by step actually foci on the generation of lazy-sequence item one by one, I already know some of the logic of clojure language.

As we know the fib-seq is defined as a lazy-seq and its first two items is 0 and 1, the rest of its items still left unevaluated, which is the most interesting feature of clojure.
While it is rather easy to understand that accessing the first two item just means to touch those two things, and they are in memory or cached, thus they could be directly return and print out.

As fib-seq do not have third item for now, it need to generate it when thread need to accessing the 3rd item, here is where my assumption start:


Since (map + (rest fib-seq) fib-seq ) is a lazy-seq itself, it contain no item in it currently and waiting for calling more command on it.
Here calling the 3rd item of fib-seq means calling the first item of lazy sequence (map...), hence it need to generate and real execute the code.
By simply replace variable name with list, the code of map seems like this:

(map + (rest [0 1 ..]) [0 1 ..] ); the '..' means it is a lazy sequence

then this code is become below after rest executed:

(map + [1 ..] [0 1 ..] )

As map generate lazy sequence, it is instructed to generate the first item of it, so by map these two lists, we got an item 1=(+ 1 0) which is the result of both the first item of these two lists add together.
Then the map stop generate item as it have no instruction to do so. Now after generate the new item 1 and concatenate it with [0 1], our fib-seq now look like this:

[0 1 1 ..]

Pretty good. Now let’s touch the 4th item of fib-seq by (nth fib-seq 4).
fib-seq find it contain no item with index 4, but it found the third is cached so it will generate the 4th item from 3rd one.

Now thread move to (map ...) function and instruct map to hand out the second item of it.
map found it did not have No.2 item so it have to generate it. and replace fib-seq with real lazy seq:

(map + (rest [0 1 1..]) [0 1 1..] )

Then of course rest get the rest of seq:

(map + [1 1..] [0 1 1..] )

Here the most tricky thing happened I think.
Map add both the second rather than the first item of these lists:

(map + [1 1..] [0 1 1..] )
          ^       ^
          | ----- |

So the map could return 2 as its 2nd item so as to complete the instruction.

The lazy-seq follow the same strategy in the follow item while instructed, and cache every generated item in memory for faster accessibility.

For this Fibonacci number generator, it just shift two list and add them one by one and recursively to generate required Fibonacci number like below:

0 1 1 2 3 5 ..   
1 1 2 3 5 ..

Which of course is a very deft way to generate Fibo.


To sum up, from human’s view, lazy seq will generate item always from its last status/position rather than starting from its initial state.

Please correct me if I am wrong, I am a newbie in clojure and I am eagerly to learn it well.

clojure lazy sequence
Rugal Bernstein
Posted on
September 4, 2014
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