3.5 with notes

3-5.org

@@ -1,4 +1,5 @@
 #+TITLE: 3.5 - Streams
+#+STARTUP: indent
 
 #+BEGIN_HTML
   <script type="text/javascript"
@@ -7,6 +8,30 @@
 #+END_HTML
 
 * Streams are Delayed Lists
+** Notes
+#+BEGIN_SRC scheme
+  (define x (delay 5))
+
+  ;; is equivalent to
+
+  (define x (lambda () 5))
+
+  ;; A "thunk" (a function of no arguments, used to delay evaluation of its return value)
+
+  (force x)
+  ;; => 5
+#+END_SRC
+
+The MIT implementation of =delay= returns a =promise= value. Force
+will evaluate a =promise= if it hasn't yet been computed. The result
+of the evaluation will be memoized for future calls to force.
+
+Stream processing explanation: [[https://www.youtube.com/watch?v%3Da2Qt9uxhNSM#t%3D48m00s][MIT OpenCourseWare Lecture 6A]]
+
+A stream a sequence built as a pair of an initial value, and a
+procedure to generate the next value and the next procedure to
+continue the sequence.
+** Code
 #+begin_src scheme
   (define (cons-stream a b)
     (cons a (delay b)))
@@ -66,7 +91,8 @@
 
   #+end_src
 
-** Exercise 3.50
+** Exercises
+*** Exercise 3.50
 Complete the following definition, which generalizes `stream-map' to
 allow procedures that take multiple arguments, analogous to `map' in
 section *Note 2-2-3::, footnote *Note Footnote 12::.
@@ -97,7 +123,7 @@ section *Note 2-2-3::, footnote *Note Footnote 12::.
                 (cons proc (map stream-cdr argstreams))))))
 #+end_src
 
-** Exercise 3.51
+*** Exercise 3.51
 In order to take a closer look at delayed
 evaluation, we will use the following procedure, which simply
 returns its argument after printing it:
@@ -123,26 +149,24 @@ expression in the following sequence?(7)
 
 #+begin_src scheme
   (define x (stream-map show (stream-enumerate-interval 0 10)))
-  ; 9
-  ; 8
-  ; 7
-  ; 6
-  ; 5
-  ; 4
-  ; 3
-  ; 2
-  ; 1
   ; 0
   ;Value: x
    
   (stream-ref x 5)
+  1
+  2
+  3
+  4
+  5
   ;Value: 5
 
   (stream-ref x 7)
+  6
+  7
   ;Value: 7
 
 #+end_src
-** Exercise 3.52
+*** Exercise 3.52
 Consider the sequence of expressions
 
 #+begin_src scheme
@@ -198,7 +222,13 @@ case if delay were not memoized, as without being so it would be
 recalculated each time the items in the node were resolved, adding to
 the value of =sum= each time, and changing the results captured by =y=
 and =z=.
-* 3.5.2 Infinite Streams
+* Infinite Streams
+** Notes
+Streams can continue forever if the promise never returns an empty
+stream.
+
+Streams can be combined to model complex sequences.
+** Code
 #+begin_src scheme :tangle yes
   ;; ===================================================================
   ;; 3.5.2: Infinite Streams
@@ -230,7 +260,7 @@ and =z=.
 
   (define primes (sieve (integers-starting-from 2)))
 #+end_src
-** Defining streams implicitly
+*** Defining streams implicitly
 #+begin_src scheme :tangle yes
   (define ones (cons-stream 1 ones))
 
@@ -261,6 +291,7 @@ and =z=.
             (else (iter (stream-cdr ps)))))
     (iter primes))
 #+end_src
+** Exercises
 *** Exercise 3.53
 Without running the program, describe the elements of the stream
 defined by
@@ -298,3 +329,66 @@ Define a procedure `partial-sums' that takes as argument a stream S
 and returns the stream whose elements are S_0, S_0 + S_1, S_0 + S_1 +
 S_2, ....  For example, `(partial-sums integers)' should be the stream
 1, 3, 6, 10, 15, ....
+* Exploiting the Stream Paradigm
+** Notes
+Streams and their property of delayed evaluation can be used to build
+abstractions over the sequences and computations used to generate
+them. The examples are the square-root stream and the pi streams being
+accelerated via a generic stream transformation method.
+
+* Streams and Delayed Evaluation
+** Notes
+#+BEGIN_QUOTE
+...stream models of systems with loops may require uses of delay
+beyond the “hidden” delay supplied by cons-stream.
+#+END_QUOTE
+
+#+BEGIN_QUOTE
+Unfortunately, including delays in procedure calls wreaks havoc with
+our ability to design programs that depend on the order of events,
+such as programs that use assignment, mutate data, or perform input or
+output.
+
+...
+
+As far as anyone knows, mutability and delayed evaluation do not mix
+well in programming languages, and devising ways to deal with both of
+these at once is an active area of research.
+#+END_QUOTE
+
+* Modularity of Functional Programs and Modularity of Objects
+
+** Notes
+Random number generation can be implemented as an infinite stream
+instantiated with some seed.
+
+*** A functional-programming view of time
+#+BEGIN_QUOTE
+We can model a changing quantity, such as the local state of some
+object, using a stream that represents the time history of successive
+states. In essence, we represent time explicitly, using streams, so
+that we decouple time in our simulated world from the sequence of
+events that take place during evaluation.
+#+END_QUOTE
+
+Events over time can be merged / serialized (deterministically?) into
+a stream of events.
+
+#+BEGIN_QUOTE
+This is precisely the same constraint that we had to deal with in
+3.4.1, where we found the need to introduce explicit synchronization
+to ensure a “correct” order of events in concurrent processing of
+objects with state. Thus, in an attempt to support the functional
+style, the need to merge inputs from different agents reintroduces the
+same problems that the functional style was meant to eliminate.
+#+END_QUOTE
+
+With a working merge solution, a system can be designed in a
+functional way, operating on a stream of state and inputs.
+
+The Erlang/OTP generic server, generic fsm and other behaviours are
+implemented in such a way that input streams received concurrently are
+merged by the vm and combined with the state of the process as a
+single stream pairing the current state with the next input to
+process, allowing an Erlang developer to build a functional interface
+with the complexities of concurrency abstracted away.