task 5 - embedding and lazy generation

assignment3/main.oz

@@ -95,3 +95,10 @@ end
 {System.show {{Quadratic 3 2 1} 2}}
 
 
+% task 5
+fun {LazyNumberGenerator StartValue}
+    StartValue|(fun {$} {LazyNumberGenerator StartValue+1} end)
+end
+{System.show 'should be 5:'}
+{System.show {{{{{{LazyNumberGenerator 0}.2}.2}.2}.2}.2}.1}
+

assignment3/report.md

@@ -139,3 +139,23 @@ end
 
 *: Quadratic is of arity 3, but could be thought of as arity 4 if you consider the argument of it's returned function as well. all functions of arity greater than 1 can be thought of as functions returning functions composed with each other: currying. named after Haskell Curry.
 
+## task 5
+
+### a)
+
+this embedded function simulates lazy function evaluation and represents an infinite list.
+
+```oz
+fun {LazyNumberGenerator StartValue}
+    StartValue|(fun {$} {LazyNumberGenerator StartValue+1} end)
+end
+```
+
+### b)
+
+the idea is that the lazy number generator should return both a current number, and a function that knows how to get to the next number, based on that current number. embedding these two into a data structure allows for lazy evaluation, i.e. "getting the thing you want just when you need it, and not a moment earlier".
+
+this can be useful to save on memory usage by deferring calculations until you need the results.
+
+i suppose a limitation with my above implementation is that it uses recursion as its driving force, thus it uses quite a lot of stack memory for each new number. this could in theory be mitigated by using tail recursion (as we will see in the next task).
+