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Creating Lazy stream in CSharp

Dhaval Dalal
Dhaval Dalal

This document discusses implementing lazy lists or streams in C# using immutable data structures. It describes representing streams as a class with an eager head and lazy tail, implemented using generics and lazy evaluation. Methods like Take, Drop, Select, Where, Concat are implemented to operate lazily on streams. Streams can be constructed from iterators, generators or by prepending/appending elements.

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Hand-Toss a Stream (Lazy List) in C# Dhaval Dalal https://dhavaldalal.wordpress.com @softwareartisan
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Implementing Lazy List IEnumerable<int> Naturals(int @from) {
 for (var i = @from; true ; i++) {
 yield return i;
 }
 }
 Naturals(0) .Take(3) .ForEach(Console.WriteLine); // 0 1 2 Using generators This is the idiomatic approach. There is yet another one as well.
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Implementing Lazy List
4
Using Lambda Wrap the tail of the list in a closure. 1 ? Implementing Lazy List
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Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
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Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
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Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List Stream implementation shown in these slides is available on: https://github.com/CodeJugalbandi/FunctionalProgramming/blob/master/melodies/lazy_sequences/Stream.cs
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Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Func<Stream<T>> tail;
 
 public Stream(T head, Func<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail(); // Need Memoization (for Perf)
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
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Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 
 public Stream(T head, Lazy<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail.Value; // Cached after first eval
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
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Immutable Stream with eager Head & lazy Tail var empty = new Stream<int>(0, null);
 Console.WriteLine(empty); // Stream<System.Int32>(0, ?)
 Console.WriteLine(empty.Head); // 0
 Console.WriteLine(empty.Tail);
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream<System.Int32>(1, ?)
 Console.WriteLine(singleton.Head); // 1
 Console.WriteLine(singleton.Tail); // Stream<System.Int32>(0, ?)
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream<System.Int32>(2, ?)
 Console.WriteLine(couple.Head); // 2
 Console.WriteLine(couple.Tail); // Stream<System.Int32>(1, ?)
 Console.WriteLine(couple.Tail.Tail); // Stream<System.Int32>(0, ?)
 Console.WriteLine(couple.Tail.Tail.Tail); As Streams are immutable we can structurally share the earlier stream. Boom! Boom!
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Introduce Empty Stream sealed class Stream<T> {
 public static readonly Stream<T> Empty = new Stream<T>(default(T), null);
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 public Stream(T head, Lazy<Stream<T>> tail) { … }
 public T Head { … }
 public Stream<T> Tail { … }
 public bool IsEmpty {
 get => tail == null;
 }
 public override string ToString() {
 if (IsEmpty) 
 return "Empty";
 
 return $"Stream<{typeof(T)}>({head}, ?)";
 }
 }
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Introduce Empty Stream var empty = Stream<int>.Empty;
 Console.WriteLine(empty); // Empty
 Console.WriteLine(empty.IsEmpty); // True
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream(1, ?)
 Console.WriteLine(singleton.IsEmpty); // False
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream(2, ?)
 Console.WriteLine(couple.IsEmpty); // False
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Doing Side-effects sealed class Stream<T> { … …
 public void ForEach(Action<T> action) {
 if (IsEmpty)
 return; 
 action(Head);
 Tail.ForEach(action);
 }
 } var empty = Stream<int>.Empty;
 empty.ForEach(Console.WriteLine); // Prints Nothing
 var stream = new Stream<int>(2, new Lazy<Stream<int>>(new Stream<int>(1, new Lazy<Stream<int>>(() => empty))));
 stream.ForEach(Console.WriteLine); // 2 1
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Consing to Stream sealed class Stream<T> {
 … …
 // Cons using +
 public static Stream<T> operator + (Stream<T> s, T element) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s));
 } var stream = Stream<int>.Empty + 1 + 2;
 Console.WriteLine(stream); // Stream(2, ?)
 Console.WriteLine(stream.Head); // 2
 Console.WriteLine(stream.Tail); // Stream(1, ?) 
 stream.ForEach(Console.WriteLine); // 2 1 Prepend (Cons)
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Append to Stream sealed class Stream<T> { …
 // Append using +
 public static Stream<T> operator + (T element, Stream<T> s) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s.IsEmpty ? Stream<T>.Empty : s));
 } var stream = 1 + Stream<int>.Empty;
 stream.ForEach(Console.WriteLine); // 1
 
 var stream = 1 + (2 + (3 + (4 + Stream<int>.Empty)));
 stream.ForEach(Console.WriteLine); // 1 2 3 4
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sealed class Stream<T> { … public static Stream<R> Of<R>(params R[] rs) {
 var stream = Stream<R>.Empty;
 var indices = rs.Length - 1;
 for (var i = indices; i >= 0; i--) {
 stream = stream + rs[i];
 }
 return stream;
 }
 } Stream<int>.Of<int>() .ForEach(Console.WriteLine); // Prints Nothing Stream<int>.Of(1, 2, 3, 4) .ForEach(Console.WriteLine); // 1 2 3 4 Construct a Stream from few elements
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Concat another Stream sealed class Stream<T> {
 …
 public static Stream<T> operator + (Stream<T> @this, Stream<T> other) { if (@this.IsEmpty)
 return other;
 
 return new Stream<T>(@this.Head, new Lazy<Stream<T>>(() => @this.Tail + other));
 } } var concat1 = Stream<char>.Empty + Stream<char>.Of('a', 'b');
 concat1.ForEach(Console.Write); // ab
 
 var concat2 = Stream<char>.Of('a', 'b') + Stream<char>.Empty;
 concat2.ForEach(Console.Write); // ab
 
 var concat3 = Stream<char>.Of('a', 'b') + Stream<char>.Of('c', 'd', 'e');
 concat3.ForEach(Console.Write); // abcde
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sealed class Stream<T> {
 … public Stream<T> Take(int howMany) {
 if (IsEmpty || howMany <= 0)
 return Stream<T>.Empty;
 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Take(howMany - 1)));
 }
 } Stream<int>.Empty .Take(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Take(2).ForEach(Console.WriteLine); // 1 2
 Stream<int>.Of(1, 2, 3, 4) .Take(12).ForEach(Console.WriteLine); // 1 2 3 4
 Stream<int>.Of(1, 2, 3, 4) .Take(0).ForEach(Console.WriteLine); // Prints Nothing Take few elements
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sealed class Stream<T> {
 … public Stream<T> Drop(int howMany) {
 if (IsEmpty || howMany <= 0)
 return this;
 
 return Tail.Drop(howMany - 1);
 }
 } Stream<int>.Empty .Drop(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(2).ForEach(Console.WriteLine); // 3 4
 Stream<int>.Of(1, 2, 3, 4) .Drop(20).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(0).ForEach(Console.WriteLine); // 1 2 3 4 Drop few elements
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sealed class Stream<T> {
 … … public static Stream<R> Generate<R>(Func<R> fn) => 
 new Stream<R>(fn(), new Lazy<Stream<R>>(() => Generate(fn))); } var random = new Random();
 Stream<int>.Generate(() => random.Next(100, 150)) .Take(4) .ForEach(Console.WriteLine); // Prints 4 random numbers bet [100, 150) Construct a Stream using lambda - 1
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sealed class Stream<T> {
 … … public static Stream<R> Iterate<R>(R initial, Func<R, R> fn) => 
 new Stream<R>(initial, new Lazy<Stream<R>>(() => Iterate(fn(initial), fn)));
 } Stream<int>.Iterate(9, x => x + 2) .Take(4) .ForEach(Console.WriteLine); // 9 11 13 15 Construct a Stream using lambda - 2
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sealed class Stream<T> {
 … … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 } var (head, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
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sealed class Stream<T> {
 … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 public void Deconstruct(out T first, out T second, out Stream<T> rest) => (first, (second, rest)) = this; 
 } var (head, second, rest) = Stream<int>.Of(1, 2, 3, 4); Console.WriteLine("Head = " + head); // 1 Console.WriteLine("Second = " + second); // 2 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
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sealed class Stream<T> {
 … public void Deconstruct(out T first, out T second, out Stream<T> rest) =>
 (first, (second, rest)) = this;
 
 public void Deconstruct(out T first, out T second, out T third, out Stream<T> rest) =>
 (first, second, (third, rest)) = this;
 } var (head, second, third, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Second = " + second); // 2
 Console.WriteLine("Third = " + third); // 3
 Console.WriteLine("Rest = " + rest); // Stream(4, ?) Deconstruct a Stream
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Transform each element sealed class Stream<T> {
 … …
 public Stream<R> Select<R>(Func<T, R> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return new Stream<R>(fn(Head), new Lazy<Stream<R>>(() => Tail.Select(fn)));
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Select(x => x * x)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Select(x => x * x)); // 1 4
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Filtering the Stream sealed class Stream<T> {
 …
 public Stream<T> Where(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head)) 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Where(pred)));
 
 return Tail.Where(pred);
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Where(x => x < 2)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Where(x => x < 2)); // 1
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Flatmap the Stream sealed class Stream<T> { …
 public Stream<T> SelectMany(Func<T, Stream<R>> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return fn(Head) + Tail.SelectMany(fn);
 }
 } Stream<char>.Of('a', 'b')
 .SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // (a, 1)(a, 2)(b, 1)(b, 2)
 
 Stream<int>.Empty.SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // Prints Nothing
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Reverse sealed class Stream<T> {
 … …
 public Stream<T> Reverse() {
 Stream<T> Reverse0(Stream<T> acc, Stream<T> source) {
 if (source.IsEmpty)
 return acc;
 
 return Reverse0(acc + source.Head, source.Tail);
 }
 return Reverse0(Stream<T>.Empty, this);
 }
 } Stream<char>.Of('a', 'b', ‘c') .Reverse().ForEach(Console.Write); // cba 
 Stream<int>.Empty .Reverse().ForEach(Console.WriteLine); // Prints Nothing
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Take while predicate holds sealed class Stream<T> {
 …
 public Stream<T> TakeWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Head + Tail.TakeWhile(pred);
 
 return Stream<T>.Empty;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'a')
 .ForEach(Console.Write); // aa
 
 Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'b')
 .ForEach(Console.Write); // Prints Nothing
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sealed class Stream<T> {
 …
 public Stream<T> DropWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Tail.DropWhile(pred);
 
 return this;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'a')
 .ForEach(Console.Write); // bc
 
 Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'b')
 .ForEach(Console.Write); // aabc Drop while predicate holds
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sealed class Stream<T> {
 …
 public U Aggregate<U>(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return identity;
 
 return Tail.Aggregate(func(identity, Head), func);
 }
 } var sum1 = Stream<int>.Of(1, 2, 3, 4) .Aggregate(0, (acc, elem) => acc + elem);
 Console.WriteLine($"sum = {sum1}"); // 10
 var sum2 = Stream<int>.Of<int>() .Aggregate(0, (acc, elem) => acc + elem); 
 Console.WriteLine($"sum = {sum2}"); // 0 Aggregate or Reduce
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sealed class Stream<T> {
 …
 public bool All(Predicate<T> pred) {
 bool All0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == false)
 return accumulator;
 
 return All0(accumulator && pred(stream.Head), stream.Tail);
 }
 return All0(true, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(2, 4).All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).All(x => x % 2 == 0)); // False All Don’t evaluate the entire Stream, short-circuit if we already determined negation.
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sealed class Stream<T> {
 …
 public bool Any(Predicate<T> pred) {
 bool Any0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == true)
 return accumulator;
 
 return Any0(accumulator || pred(stream.Head), stream.Tail);
 }
 return Any0(false, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().Any(x => x % 2 == 0)); // False
 Console.WriteLine(Stream<int>.Of<int>(2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 3).Any(x => x % 2 == 0)); // False Any Don’t evaluate the entire Stream, short-circuit if we already determined affirmation.
34
sealed class Stream<T> {
 …
 public Stream<T> Scan(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 U newHead = func(identity, Head);
 return newHead + Tail.Scan(newHead, func);
 }
 } // Prints running sum
 Stream<int>.Of(1, 2, 3, 4) .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // 1 3 6 10
 Stream<int>.Of<int>() .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // Prints Nothing Scan
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Zip two Streams sealed class Stream<T> {
 …
 public Stream<(T,U)> Zip<U>(Stream<U> that) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<(T,U)>.Empty;
 
 return (this.Head, that.Head) + this.Tail.Zip(that.Tail);
 }
 } Stream<char>.Of('a', 'b').Zip(Stream<int>.Of(1, 2))
 .ForEach(t => Console.Write(t)); // (a, 1)(b, 2)
 
 Stream<char>.Of('a', 'b').Zip(Stream<int>.Empty)
 .ForEach(t => Console.Write(t)); // Prints Nothing
 
 Stream<int>.Empty.Zip(Stream<char>.Of('a', 'b'))
 .ForEach(t => Console.Write(t)); // Prints Nothing
36
Zip with function sealed class Stream<T> {
 …
 public Stream<R> ZipWith<U, R>(Stream<U> that, Func<T, U, R> fn) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<R>.Empty;
 
 return fn(this.Head, that.Head) + this.Tail.ZipWith(that.Tail, fn);
 }
 } var numbers = Stream<int>.Of(1, 2, 3);
 numbers.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // 1 4 9
 
 numbers.ZipWith(Stream<int>.Empty, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
 
 Stream<int>.Empty.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
37
Splitsealed class Stream<T> {
 …
 public (Stream<T>, Stream<T>) Split(Predicate<T> pred) {
 (Stream<T>, Stream<T>) Split0(Stream<T> yesAcc, Stream<T> noAcc, Stream<T> source) {
 if (source.IsEmpty) 
 return (yesAcc.Reverse(), noAcc.Reverse());
 
 var elem = source.Head;
 if (pred(elem))
 return Split0(yesAcc + elem, noAcc, source.Tail);
 else
 return Split0(yesAcc, noAcc + elem, source.Tail);
 } 
 return Split0(Stream<T>.Empty, Stream<T>.Empty, this);
 }
 } var (evens, odds) = Stream<int>.Iterate(0, x => x + 1).Take(10) .Split(x => x % 2 == 0);
 evens.ForEach(Console.Write); // 02468
 odds.ForEach(Console.Write); // 13579
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To List sealed class Stream<T> {
 … public List<T> ToList() {
 var result = new List<T>();
 ForEach(result.Add);
 return result;
 }
 } var list = Stream<int>.Iterate(1, x => x + 1) .Take(4) .ToList();
 foreach (var item in list) {
 Console.WriteLine(item);
 }
39
Find first 6 primes using the Sieve of Eratosthenes Hint: Use Stream created earlier http://world.mathigon.org/Prime_Numbers
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Sieve Stream<int> From(int start) => Stream<int>.Iterate(start, x => x + 1);
 Stream<int> Sieve(Stream<int> s) {
 var first = s.Head;
 var rest = s.Tail.Where(n => n % first != 0);
 return new Stream<int>(first, new Lazy<Stream<int>>(() => rest));
 }
 
 var primes = Sieve(From(2)).Take(6) primes.ToList() // [2, 3, 5, 7, 11, 13]
41
First 10 Fibonacci Nos. Write a function fibonacci which consumes an integer and produces that many numbers in the fibonacci series. For Example: fibonacci(10) produces [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] Provide Solutions Using Generator Using IEnumerable Using Stream that we developed
42
IEnumerable<int> Fibonacci(int howMany) { var (first, second) = (0, 1);
 for (var i = 0; i < howMany; i++) {
 yield return first;
 (first, second) = (second, first + second);
 }
 }
 
 Fibonacci(10).ToList();
 // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using Generator
43
IEnumerable<int> Fibonacci(int howMany) { return IEnumerableExtensions.Iterate<(int, int)>((0, 1), tuple => {
 var (first, second) = tuple;
 var next = first + second;
 return (second, next);
 })
 .Select(tuple => {
 var (first, second) = tuple;
 return first;
 })
 .Take(howMany);
 } Fibonacci(10).ToList(); // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using IEnumerable Definition as suggested by Christopher Grande
44
First 10 Fibonacci Nos. Using Stream https://www.haskell.org/tutorial/functions.html var seed = From(0).Take(2);
 // Start with seed elements 0 and 1
 Fibonacci(seed)
 .Take(10)
 .ForEach(Console.WriteLine); // 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 Stream<int> Fibonacci(Stream<int> s) {
 var next = s.Zip(s.Tail).Select(tuple => {
 var (first, second) = tuple;
 return first + second;
 });
 return new Stream<int>(s.Head, new Lazy<Stream<int>>(() => Fibonacci(s + next.Head)));
 }
45
Prime Counts Using Lazy Lists, write a program that counts number of primes up to a given number. At every power of 10, it should emit the count of primes obtained thus far. The table shows the output until 10 10 Implement this using: Using Stream we developed earlier. Using IEnumerable Hint: Write an extension method Scan on IEnumerable i/p count 10 4 10 2 25 10 3 168 10 4 1,229 10 5 9,592 10 6 78,498 10 7 6,64,579 10 8 57,61,455 10 9 5,08,47,534 10 10 45,50,52,511
46
class Streams {
 public static Stream<int> Range(int start, int count) {
 if (count < 0)
 throw new ArgumentOutOfRangeException($"{count}");
 
 return Stream<int>.Iterate(start, x => x + 1).Take(count);
 } 
 }
 Streams.Range(1, 5).ForEach(Console.WriteLine); // 1 2 3 4 5 Prime Counts using IEnumerable First, write our own Range
47
Prime Counts Using Stream Stream<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Streams.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return Stream<int>.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Streams.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
48
Prime Counts using IEnumerable First, write our own Scan static class IEnumerableExtensions { public static IEnumerable<U> Scan<T, U>(this IEnumerable<T> @this, U initial, Func<U, T, U> fn) {
 IEnumerable<U> ScannedEnumerable() {
 var acc = seed;
 foreach (var item in @this) {
 acc = fn(acc, item);
 yield return acc;
 } 
 if (@this == null)
 throw new ArgumentNullException("Require non-null list!");
 if (fn == null)
 throw new ArgumentNullException("Require non-null function!”);
 return ScannedEnumerable();
 } }
49
Prime Counts using IEnumerable IEnumerable<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Enumerable.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return IEnumerableExtensions.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Enumerable.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
50
Drawbacks of this Stream Implementation As C# compiler does not support Tail- Recursion, all the APIs that are implemented recursively will cause a stack blow-up at some point for large values of stream. Even-though it uses caching of tail using Lazy<T>, this Stream is not performant like IEnumerable! This is because the recursive APIs don’t run in constant stack space.
51
But still its a good mental exercise to create streams from first principles!
52
Thank-you!
Hand-Toss a Stream (Lazy List) in C# Dhaval Dalal https://dhavaldalal.wordpress.com @softwareartisan
Implementing Lazy List IEnumerable<int> Naturals(int @from) {
 for (var i = @from; true ; i++) {
 yield return i;
 }
 }
 Naturals(0) .Take(3) .ForEach(Console.WriteLine); // 0 1 2 Using generators This is the idiomatic approach. There is yet another one as well.
Implementing Lazy List
Using Lambda Wrap the tail of the list in a closure. 1 ? Implementing Lazy List
Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List Stream implementation shown in these slides is available on: https://github.com/CodeJugalbandi/FunctionalProgramming/blob/master/melodies/lazy_sequences/Stream.cs
Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Func<Stream<T>> tail;
 
 public Stream(T head, Func<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail(); // Need Memoization (for Perf)
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 
 public Stream(T head, Lazy<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail.Value; // Cached after first eval
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
Immutable Stream with eager Head & lazy Tail var empty = new Stream<int>(0, null);
 Console.WriteLine(empty); // Stream<System.Int32>(0, ?)
 Console.WriteLine(empty.Head); // 0
 Console.WriteLine(empty.Tail);
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream<System.Int32>(1, ?)
 Console.WriteLine(singleton.Head); // 1
 Console.WriteLine(singleton.Tail); // Stream<System.Int32>(0, ?)
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream<System.Int32>(2, ?)
 Console.WriteLine(couple.Head); // 2
 Console.WriteLine(couple.Tail); // Stream<System.Int32>(1, ?)
 Console.WriteLine(couple.Tail.Tail); // Stream<System.Int32>(0, ?)
 Console.WriteLine(couple.Tail.Tail.Tail); As Streams are immutable we can structurally share the earlier stream. Boom! Boom!
Introduce Empty Stream sealed class Stream<T> {
 public static readonly Stream<T> Empty = new Stream<T>(default(T), null);
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 public Stream(T head, Lazy<Stream<T>> tail) { … }
 public T Head { … }
 public Stream<T> Tail { … }
 public bool IsEmpty {
 get => tail == null;
 }
 public override string ToString() {
 if (IsEmpty) 
 return "Empty";
 
 return $"Stream<{typeof(T)}>({head}, ?)";
 }
 }
Introduce Empty Stream var empty = Stream<int>.Empty;
 Console.WriteLine(empty); // Empty
 Console.WriteLine(empty.IsEmpty); // True
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream(1, ?)
 Console.WriteLine(singleton.IsEmpty); // False
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream(2, ?)
 Console.WriteLine(couple.IsEmpty); // False
Doing Side-effects sealed class Stream<T> { … …
 public void ForEach(Action<T> action) {
 if (IsEmpty)
 return; 
 action(Head);
 Tail.ForEach(action);
 }
 } var empty = Stream<int>.Empty;
 empty.ForEach(Console.WriteLine); // Prints Nothing
 var stream = new Stream<int>(2, new Lazy<Stream<int>>(new Stream<int>(1, new Lazy<Stream<int>>(() => empty))));
 stream.ForEach(Console.WriteLine); // 2 1
Consing to Stream sealed class Stream<T> {
 … …
 // Cons using +
 public static Stream<T> operator + (Stream<T> s, T element) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s));
 } var stream = Stream<int>.Empty + 1 + 2;
 Console.WriteLine(stream); // Stream(2, ?)
 Console.WriteLine(stream.Head); // 2
 Console.WriteLine(stream.Tail); // Stream(1, ?) 
 stream.ForEach(Console.WriteLine); // 2 1 Prepend (Cons)
Append to Stream sealed class Stream<T> { …
 // Append using +
 public static Stream<T> operator + (T element, Stream<T> s) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s.IsEmpty ? Stream<T>.Empty : s));
 } var stream = 1 + Stream<int>.Empty;
 stream.ForEach(Console.WriteLine); // 1
 
 var stream = 1 + (2 + (3 + (4 + Stream<int>.Empty)));
 stream.ForEach(Console.WriteLine); // 1 2 3 4
sealed class Stream<T> { … public static Stream<R> Of<R>(params R[] rs) {
 var stream = Stream<R>.Empty;
 var indices = rs.Length - 1;
 for (var i = indices; i >= 0; i--) {
 stream = stream + rs[i];
 }
 return stream;
 }
 } Stream<int>.Of<int>() .ForEach(Console.WriteLine); // Prints Nothing Stream<int>.Of(1, 2, 3, 4) .ForEach(Console.WriteLine); // 1 2 3 4 Construct a Stream from few elements
Concat another Stream sealed class Stream<T> {
 …
 public static Stream<T> operator + (Stream<T> @this, Stream<T> other) { if (@this.IsEmpty)
 return other;
 
 return new Stream<T>(@this.Head, new Lazy<Stream<T>>(() => @this.Tail + other));
 } } var concat1 = Stream<char>.Empty + Stream<char>.Of('a', 'b');
 concat1.ForEach(Console.Write); // ab
 
 var concat2 = Stream<char>.Of('a', 'b') + Stream<char>.Empty;
 concat2.ForEach(Console.Write); // ab
 
 var concat3 = Stream<char>.Of('a', 'b') + Stream<char>.Of('c', 'd', 'e');
 concat3.ForEach(Console.Write); // abcde
sealed class Stream<T> {
 … public Stream<T> Take(int howMany) {
 if (IsEmpty || howMany <= 0)
 return Stream<T>.Empty;
 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Take(howMany - 1)));
 }
 } Stream<int>.Empty .Take(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Take(2).ForEach(Console.WriteLine); // 1 2
 Stream<int>.Of(1, 2, 3, 4) .Take(12).ForEach(Console.WriteLine); // 1 2 3 4
 Stream<int>.Of(1, 2, 3, 4) .Take(0).ForEach(Console.WriteLine); // Prints Nothing Take few elements
sealed class Stream<T> {
 … public Stream<T> Drop(int howMany) {
 if (IsEmpty || howMany <= 0)
 return this;
 
 return Tail.Drop(howMany - 1);
 }
 } Stream<int>.Empty .Drop(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(2).ForEach(Console.WriteLine); // 3 4
 Stream<int>.Of(1, 2, 3, 4) .Drop(20).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(0).ForEach(Console.WriteLine); // 1 2 3 4 Drop few elements
sealed class Stream<T> {
 … … public static Stream<R> Generate<R>(Func<R> fn) => 
 new Stream<R>(fn(), new Lazy<Stream<R>>(() => Generate(fn))); } var random = new Random();
 Stream<int>.Generate(() => random.Next(100, 150)) .Take(4) .ForEach(Console.WriteLine); // Prints 4 random numbers bet [100, 150) Construct a Stream using lambda - 1
sealed class Stream<T> {
 … … public static Stream<R> Iterate<R>(R initial, Func<R, R> fn) => 
 new Stream<R>(initial, new Lazy<Stream<R>>(() => Iterate(fn(initial), fn)));
 } Stream<int>.Iterate(9, x => x + 2) .Take(4) .ForEach(Console.WriteLine); // 9 11 13 15 Construct a Stream using lambda - 2
sealed class Stream<T> {
 … … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 } var (head, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
sealed class Stream<T> {
 … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 public void Deconstruct(out T first, out T second, out Stream<T> rest) => (first, (second, rest)) = this; 
 } var (head, second, rest) = Stream<int>.Of(1, 2, 3, 4); Console.WriteLine("Head = " + head); // 1 Console.WriteLine("Second = " + second); // 2 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
sealed class Stream<T> {
 … public void Deconstruct(out T first, out T second, out Stream<T> rest) =>
 (first, (second, rest)) = this;
 
 public void Deconstruct(out T first, out T second, out T third, out Stream<T> rest) =>
 (first, second, (third, rest)) = this;
 } var (head, second, third, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Second = " + second); // 2
 Console.WriteLine("Third = " + third); // 3
 Console.WriteLine("Rest = " + rest); // Stream(4, ?) Deconstruct a Stream
Transform each element sealed class Stream<T> {
 … …
 public Stream<R> Select<R>(Func<T, R> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return new Stream<R>(fn(Head), new Lazy<Stream<R>>(() => Tail.Select(fn)));
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Select(x => x * x)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Select(x => x * x)); // 1 4
Filtering the Stream sealed class Stream<T> {
 …
 public Stream<T> Where(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head)) 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Where(pred)));
 
 return Tail.Where(pred);
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Where(x => x < 2)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Where(x => x < 2)); // 1
Flatmap the Stream sealed class Stream<T> { …
 public Stream<T> SelectMany(Func<T, Stream<R>> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return fn(Head) + Tail.SelectMany(fn);
 }
 } Stream<char>.Of('a', 'b')
 .SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // (a, 1)(a, 2)(b, 1)(b, 2)
 
 Stream<int>.Empty.SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // Prints Nothing
Reverse sealed class Stream<T> {
 … …
 public Stream<T> Reverse() {
 Stream<T> Reverse0(Stream<T> acc, Stream<T> source) {
 if (source.IsEmpty)
 return acc;
 
 return Reverse0(acc + source.Head, source.Tail);
 }
 return Reverse0(Stream<T>.Empty, this);
 }
 } Stream<char>.Of('a', 'b', ‘c') .Reverse().ForEach(Console.Write); // cba 
 Stream<int>.Empty .Reverse().ForEach(Console.WriteLine); // Prints Nothing
Take while predicate holds sealed class Stream<T> {
 …
 public Stream<T> TakeWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Head + Tail.TakeWhile(pred);
 
 return Stream<T>.Empty;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'a')
 .ForEach(Console.Write); // aa
 
 Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'b')
 .ForEach(Console.Write); // Prints Nothing
sealed class Stream<T> {
 …
 public Stream<T> DropWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Tail.DropWhile(pred);
 
 return this;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'a')
 .ForEach(Console.Write); // bc
 
 Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'b')
 .ForEach(Console.Write); // aabc Drop while predicate holds
sealed class Stream<T> {
 …
 public U Aggregate<U>(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return identity;
 
 return Tail.Aggregate(func(identity, Head), func);
 }
 } var sum1 = Stream<int>.Of(1, 2, 3, 4) .Aggregate(0, (acc, elem) => acc + elem);
 Console.WriteLine($"sum = {sum1}"); // 10
 var sum2 = Stream<int>.Of<int>() .Aggregate(0, (acc, elem) => acc + elem); 
 Console.WriteLine($"sum = {sum2}"); // 0 Aggregate or Reduce
sealed class Stream<T> {
 …
 public bool All(Predicate<T> pred) {
 bool All0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == false)
 return accumulator;
 
 return All0(accumulator && pred(stream.Head), stream.Tail);
 }
 return All0(true, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(2, 4).All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).All(x => x % 2 == 0)); // False All Don’t evaluate the entire Stream, short-circuit if we already determined negation.
sealed class Stream<T> {
 …
 public bool Any(Predicate<T> pred) {
 bool Any0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == true)
 return accumulator;
 
 return Any0(accumulator || pred(stream.Head), stream.Tail);
 }
 return Any0(false, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().Any(x => x % 2 == 0)); // False
 Console.WriteLine(Stream<int>.Of<int>(2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 3).Any(x => x % 2 == 0)); // False Any Don’t evaluate the entire Stream, short-circuit if we already determined affirmation.
sealed class Stream<T> {
 …
 public Stream<T> Scan(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 U newHead = func(identity, Head);
 return newHead + Tail.Scan(newHead, func);
 }
 } // Prints running sum
 Stream<int>.Of(1, 2, 3, 4) .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // 1 3 6 10
 Stream<int>.Of<int>() .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // Prints Nothing Scan
Zip two Streams sealed class Stream<T> {
 …
 public Stream<(T,U)> Zip<U>(Stream<U> that) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<(T,U)>.Empty;
 
 return (this.Head, that.Head) + this.Tail.Zip(that.Tail);
 }
 } Stream<char>.Of('a', 'b').Zip(Stream<int>.Of(1, 2))
 .ForEach(t => Console.Write(t)); // (a, 1)(b, 2)
 
 Stream<char>.Of('a', 'b').Zip(Stream<int>.Empty)
 .ForEach(t => Console.Write(t)); // Prints Nothing
 
 Stream<int>.Empty.Zip(Stream<char>.Of('a', 'b'))
 .ForEach(t => Console.Write(t)); // Prints Nothing
Zip with function sealed class Stream<T> {
 …
 public Stream<R> ZipWith<U, R>(Stream<U> that, Func<T, U, R> fn) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<R>.Empty;
 
 return fn(this.Head, that.Head) + this.Tail.ZipWith(that.Tail, fn);
 }
 } var numbers = Stream<int>.Of(1, 2, 3);
 numbers.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // 1 4 9
 
 numbers.ZipWith(Stream<int>.Empty, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
 
 Stream<int>.Empty.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
Splitsealed class Stream<T> {
 …
 public (Stream<T>, Stream<T>) Split(Predicate<T> pred) {
 (Stream<T>, Stream<T>) Split0(Stream<T> yesAcc, Stream<T> noAcc, Stream<T> source) {
 if (source.IsEmpty) 
 return (yesAcc.Reverse(), noAcc.Reverse());
 
 var elem = source.Head;
 if (pred(elem))
 return Split0(yesAcc + elem, noAcc, source.Tail);
 else
 return Split0(yesAcc, noAcc + elem, source.Tail);
 } 
 return Split0(Stream<T>.Empty, Stream<T>.Empty, this);
 }
 } var (evens, odds) = Stream<int>.Iterate(0, x => x + 1).Take(10) .Split(x => x % 2 == 0);
 evens.ForEach(Console.Write); // 02468
 odds.ForEach(Console.Write); // 13579
To List sealed class Stream<T> {
 … public List<T> ToList() {
 var result = new List<T>();
 ForEach(result.Add);
 return result;
 }
 } var list = Stream<int>.Iterate(1, x => x + 1) .Take(4) .ToList();
 foreach (var item in list) {
 Console.WriteLine(item);
 }
Find first 6 primes using the Sieve of Eratosthenes Hint: Use Stream created earlier http://world.mathigon.org/Prime_Numbers
Sieve Stream<int> From(int start) => Stream<int>.Iterate(start, x => x + 1);
 Stream<int> Sieve(Stream<int> s) {
 var first = s.Head;
 var rest = s.Tail.Where(n => n % first != 0);
 return new Stream<int>(first, new Lazy<Stream<int>>(() => rest));
 }
 
 var primes = Sieve(From(2)).Take(6) primes.ToList() // [2, 3, 5, 7, 11, 13]
First 10 Fibonacci Nos. Write a function fibonacci which consumes an integer and produces that many numbers in the fibonacci series. For Example: fibonacci(10) produces [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] Provide Solutions Using Generator Using IEnumerable Using Stream that we developed
IEnumerable<int> Fibonacci(int howMany) { var (first, second) = (0, 1);
 for (var i = 0; i < howMany; i++) {
 yield return first;
 (first, second) = (second, first + second);
 }
 }
 
 Fibonacci(10).ToList();
 // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using Generator
IEnumerable<int> Fibonacci(int howMany) { return IEnumerableExtensions.Iterate<(int, int)>((0, 1), tuple => {
 var (first, second) = tuple;
 var next = first + second;
 return (second, next);
 })
 .Select(tuple => {
 var (first, second) = tuple;
 return first;
 })
 .Take(howMany);
 } Fibonacci(10).ToList(); // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using IEnumerable Definition as suggested by Christopher Grande
First 10 Fibonacci Nos. Using Stream https://www.haskell.org/tutorial/functions.html var seed = From(0).Take(2);
 // Start with seed elements 0 and 1
 Fibonacci(seed)
 .Take(10)
 .ForEach(Console.WriteLine); // 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 Stream<int> Fibonacci(Stream<int> s) {
 var next = s.Zip(s.Tail).Select(tuple => {
 var (first, second) = tuple;
 return first + second;
 });
 return new Stream<int>(s.Head, new Lazy<Stream<int>>(() => Fibonacci(s + next.Head)));
 }
Prime Counts Using Lazy Lists, write a program that counts number of primes up to a given number. At every power of 10, it should emit the count of primes obtained thus far. The table shows the output until 10 10 Implement this using: Using Stream we developed earlier. Using IEnumerable Hint: Write an extension method Scan on IEnumerable i/p count 10 4 10 2 25 10 3 168 10 4 1,229 10 5 9,592 10 6 78,498 10 7 6,64,579 10 8 57,61,455 10 9 5,08,47,534 10 10 45,50,52,511
class Streams {
 public static Stream<int> Range(int start, int count) {
 if (count < 0)
 throw new ArgumentOutOfRangeException($"{count}");
 
 return Stream<int>.Iterate(start, x => x + 1).Take(count);
 } 
 }
 Streams.Range(1, 5).ForEach(Console.WriteLine); // 1 2 3 4 5 Prime Counts using IEnumerable First, write our own Range
Prime Counts Using Stream Stream<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Streams.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return Stream<int>.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Streams.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
Prime Counts using IEnumerable First, write our own Scan static class IEnumerableExtensions { public static IEnumerable<U> Scan<T, U>(this IEnumerable<T> @this, U initial, Func<U, T, U> fn) {
 IEnumerable<U> ScannedEnumerable() {
 var acc = seed;
 foreach (var item in @this) {
 acc = fn(acc, item);
 yield return acc;
 } 
 if (@this == null)
 throw new ArgumentNullException("Require non-null list!");
 if (fn == null)
 throw new ArgumentNullException("Require non-null function!”);
 return ScannedEnumerable();
 } }
Prime Counts using IEnumerable IEnumerable<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Enumerable.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return IEnumerableExtensions.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Enumerable.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
Drawbacks of this Stream Implementation As C# compiler does not support Tail- Recursion, all the APIs that are implemented recursively will cause a stack blow-up at some point for large values of stream. Even-though it uses caching of tail using Lazy<T>, this Stream is not performant like IEnumerable! This is because the recursive APIs don’t run in constant stack space.
But still its a good mental exercise to create streams from first principles!
Thank-you!
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Creating Lazy stream in CSharp

  • 1. Hand-Toss a Stream (Lazy List) in C# Dhaval Dalal https://dhavaldalal.wordpress.com @softwareartisan
  • 2. Implementing Lazy List IEnumerable<int> Naturals(int @from) {
 for (var i = @from; true ; i++) {
 yield return i;
 }
 }
 Naturals(0) .Take(3) .ForEach(Console.WriteLine); // 0 1 2 Using generators This is the idiomatic approach. There is yet another one as well.
  • 4. Using Lambda Wrap the tail of the list in a closure. 1 ? Implementing Lazy List
  • 5. Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
  • 6. Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List
  • 7. Using Lambda Wrap the tail of the list in a closure. When we need the result evaluate the tail by invoking the closure. Additionally for performance - Cache or Memoize the closure output. Evaluate tail 1 ? 1 * 2 ? Implementing Lazy List Stream implementation shown in these slides is available on: https://github.com/CodeJugalbandi/FunctionalProgramming/blob/master/melodies/lazy_sequences/Stream.cs
  • 8. Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Func<Stream<T>> tail;
 
 public Stream(T head, Func<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail(); // Need Memoization (for Perf)
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
  • 9. Immutable Stream with eager Head & lazy Tail sealed class Stream<T> {
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 
 public Stream(T head, Lazy<Stream<T>> tail) {
 this.head = head;
 this.tail = tail;
 }
 public T Head {
 get => head;
 }
 public Stream<T> Tail {
 get => tail.Value; // Cached after first eval
 }
 public override string ToString() => $"Stream<{typeof(T)}>({head}, ?)";
 }
  • 10. Immutable Stream with eager Head & lazy Tail var empty = new Stream<int>(0, null);
 Console.WriteLine(empty); // Stream<System.Int32>(0, ?)
 Console.WriteLine(empty.Head); // 0
 Console.WriteLine(empty.Tail);
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream<System.Int32>(1, ?)
 Console.WriteLine(singleton.Head); // 1
 Console.WriteLine(singleton.Tail); // Stream<System.Int32>(0, ?)
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream<System.Int32>(2, ?)
 Console.WriteLine(couple.Head); // 2
 Console.WriteLine(couple.Tail); // Stream<System.Int32>(1, ?)
 Console.WriteLine(couple.Tail.Tail); // Stream<System.Int32>(0, ?)
 Console.WriteLine(couple.Tail.Tail.Tail); As Streams are immutable we can structurally share the earlier stream. Boom! Boom!
  • 11. Introduce Empty Stream sealed class Stream<T> {
 public static readonly Stream<T> Empty = new Stream<T>(default(T), null);
 private readonly T head;
 private readonly Lazy<Stream<T>> tail;
 public Stream(T head, Lazy<Stream<T>> tail) { … }
 public T Head { … }
 public Stream<T> Tail { … }
 public bool IsEmpty {
 get => tail == null;
 }
 public override string ToString() {
 if (IsEmpty) 
 return "Empty";
 
 return $"Stream<{typeof(T)}>({head}, ?)";
 }
 }
  • 12. Introduce Empty Stream var empty = Stream<int>.Empty;
 Console.WriteLine(empty); // Empty
 Console.WriteLine(empty.IsEmpty); // True
 
 var singleton = new Stream<int>(1, new Lazy<Stream<int>>(() => empty));
 Console.WriteLine(singleton); // Stream(1, ?)
 Console.WriteLine(singleton.IsEmpty); // False
 
 var couple = new Stream<int>(2, new Lazy<Stream<int>>(() => singleton));
 Console.WriteLine(couple); // Stream(2, ?)
 Console.WriteLine(couple.IsEmpty); // False
  • 13. Doing Side-effects sealed class Stream<T> { … …
 public void ForEach(Action<T> action) {
 if (IsEmpty)
 return; 
 action(Head);
 Tail.ForEach(action);
 }
 } var empty = Stream<int>.Empty;
 empty.ForEach(Console.WriteLine); // Prints Nothing
 var stream = new Stream<int>(2, new Lazy<Stream<int>>(new Stream<int>(1, new Lazy<Stream<int>>(() => empty))));
 stream.ForEach(Console.WriteLine); // 2 1
  • 14. Consing to Stream sealed class Stream<T> {
 … …
 // Cons using +
 public static Stream<T> operator + (Stream<T> s, T element) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s));
 } var stream = Stream<int>.Empty + 1 + 2;
 Console.WriteLine(stream); // Stream(2, ?)
 Console.WriteLine(stream.Head); // 2
 Console.WriteLine(stream.Tail); // Stream(1, ?) 
 stream.ForEach(Console.WriteLine); // 2 1 Prepend (Cons)
  • 15. Append to Stream sealed class Stream<T> { …
 // Append using +
 public static Stream<T> operator + (T element, Stream<T> s) => 
 new Stream<T>(element, new Lazy<Stream<T>>(() => s.IsEmpty ? Stream<T>.Empty : s));
 } var stream = 1 + Stream<int>.Empty;
 stream.ForEach(Console.WriteLine); // 1
 
 var stream = 1 + (2 + (3 + (4 + Stream<int>.Empty)));
 stream.ForEach(Console.WriteLine); // 1 2 3 4
  • 16. sealed class Stream<T> { … public static Stream<R> Of<R>(params R[] rs) {
 var stream = Stream<R>.Empty;
 var indices = rs.Length - 1;
 for (var i = indices; i >= 0; i--) {
 stream = stream + rs[i];
 }
 return stream;
 }
 } Stream<int>.Of<int>() .ForEach(Console.WriteLine); // Prints Nothing Stream<int>.Of(1, 2, 3, 4) .ForEach(Console.WriteLine); // 1 2 3 4 Construct a Stream from few elements
  • 17. Concat another Stream sealed class Stream<T> {
 …
 public static Stream<T> operator + (Stream<T> @this, Stream<T> other) { if (@this.IsEmpty)
 return other;
 
 return new Stream<T>(@this.Head, new Lazy<Stream<T>>(() => @this.Tail + other));
 } } var concat1 = Stream<char>.Empty + Stream<char>.Of('a', 'b');
 concat1.ForEach(Console.Write); // ab
 
 var concat2 = Stream<char>.Of('a', 'b') + Stream<char>.Empty;
 concat2.ForEach(Console.Write); // ab
 
 var concat3 = Stream<char>.Of('a', 'b') + Stream<char>.Of('c', 'd', 'e');
 concat3.ForEach(Console.Write); // abcde
  • 18. sealed class Stream<T> {
 … public Stream<T> Take(int howMany) {
 if (IsEmpty || howMany <= 0)
 return Stream<T>.Empty;
 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Take(howMany - 1)));
 }
 } Stream<int>.Empty .Take(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Take(2).ForEach(Console.WriteLine); // 1 2
 Stream<int>.Of(1, 2, 3, 4) .Take(12).ForEach(Console.WriteLine); // 1 2 3 4
 Stream<int>.Of(1, 2, 3, 4) .Take(0).ForEach(Console.WriteLine); // Prints Nothing Take few elements
  • 19. sealed class Stream<T> {
 … public Stream<T> Drop(int howMany) {
 if (IsEmpty || howMany <= 0)
 return this;
 
 return Tail.Drop(howMany - 1);
 }
 } Stream<int>.Empty .Drop(2).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(2).ForEach(Console.WriteLine); // 3 4
 Stream<int>.Of(1, 2, 3, 4) .Drop(20).ForEach(Console.WriteLine); // Prints Nothing
 Stream<int>.Of(1, 2, 3, 4) .Drop(0).ForEach(Console.WriteLine); // 1 2 3 4 Drop few elements
  • 20. sealed class Stream<T> {
 … … public static Stream<R> Generate<R>(Func<R> fn) => 
 new Stream<R>(fn(), new Lazy<Stream<R>>(() => Generate(fn))); } var random = new Random();
 Stream<int>.Generate(() => random.Next(100, 150)) .Take(4) .ForEach(Console.WriteLine); // Prints 4 random numbers bet [100, 150) Construct a Stream using lambda - 1
  • 21. sealed class Stream<T> {
 … … public static Stream<R> Iterate<R>(R initial, Func<R, R> fn) => 
 new Stream<R>(initial, new Lazy<Stream<R>>(() => Iterate(fn(initial), fn)));
 } Stream<int>.Iterate(9, x => x + 2) .Take(4) .ForEach(Console.WriteLine); // 9 11 13 15 Construct a Stream using lambda - 2
  • 22. sealed class Stream<T> {
 … … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 } var (head, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
  • 23. sealed class Stream<T> {
 … public void Deconstruct(out T first, out Stream<T> rest) {
 if (IsEmpty) 
 throw new ArgumentException("Collection is Empty!");
 
 first = Head;
 rest = Drop(1);
 }
 public void Deconstruct(out T first, out T second, out Stream<T> rest) => (first, (second, rest)) = this; 
 } var (head, second, rest) = Stream<int>.Of(1, 2, 3, 4); Console.WriteLine("Head = " + head); // 1 Console.WriteLine("Second = " + second); // 2 Console.WriteLine("Rest = " + rest); // Stream(2, ?) Deconstruct a Stream
  • 24. sealed class Stream<T> {
 … public void Deconstruct(out T first, out T second, out Stream<T> rest) =>
 (first, (second, rest)) = this;
 
 public void Deconstruct(out T first, out T second, out T third, out Stream<T> rest) =>
 (first, second, (third, rest)) = this;
 } var (head, second, third, rest) = Stream<int>.Of(1, 2, 3, 4);
 Console.WriteLine("Head = " + head); // 1
 Console.WriteLine("Second = " + second); // 2
 Console.WriteLine("Third = " + third); // 3
 Console.WriteLine("Rest = " + rest); // Stream(4, ?) Deconstruct a Stream
  • 25. Transform each element sealed class Stream<T> {
 … …
 public Stream<R> Select<R>(Func<T, R> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return new Stream<R>(fn(Head), new Lazy<Stream<R>>(() => Tail.Select(fn)));
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Select(x => x * x)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Select(x => x * x)); // 1 4
  • 26. Filtering the Stream sealed class Stream<T> {
 …
 public Stream<T> Where(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head)) 
 return new Stream<T>(Head, new Lazy<Stream<T>>(() => Tail.Where(pred)));
 
 return Tail.Where(pred);
 }
 } var empty = Stream<int>.Empty; Console.WriteLine(empty.Where(x => x < 2)); // Prints Nothing var stream = Stream<int>.Of(1, 2);
 Console.WriteLine(stream.Where(x => x < 2)); // 1
  • 27. Flatmap the Stream sealed class Stream<T> { …
 public Stream<T> SelectMany(Func<T, Stream<R>> fn) {
 if (IsEmpty)
 return Stream<R>.Empty;
 
 return fn(Head) + Tail.SelectMany(fn);
 }
 } Stream<char>.Of('a', 'b')
 .SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // (a, 1)(a, 2)(b, 1)(b, 2)
 
 Stream<int>.Empty.SelectMany(c => Stream<int>.Of(1, 2).Select(n => (c, n)))
 .ForEach(t => Console.Write(t)); // Prints Nothing
  • 28. Reverse sealed class Stream<T> {
 … …
 public Stream<T> Reverse() {
 Stream<T> Reverse0(Stream<T> acc, Stream<T> source) {
 if (source.IsEmpty)
 return acc;
 
 return Reverse0(acc + source.Head, source.Tail);
 }
 return Reverse0(Stream<T>.Empty, this);
 }
 } Stream<char>.Of('a', 'b', ‘c') .Reverse().ForEach(Console.Write); // cba 
 Stream<int>.Empty .Reverse().ForEach(Console.WriteLine); // Prints Nothing
  • 29. Take while predicate holds sealed class Stream<T> {
 …
 public Stream<T> TakeWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Head + Tail.TakeWhile(pred);
 
 return Stream<T>.Empty;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'a')
 .ForEach(Console.Write); // aa
 
 Stream<char>.Of('a', 'a', 'b', 'c').TakeWhile(c => c == 'b')
 .ForEach(Console.Write); // Prints Nothing
  • 30. sealed class Stream<T> {
 …
 public Stream<T> DropWhile(Predicate<T> pred) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 if (pred(Head))
 return Tail.DropWhile(pred);
 
 return this;
 }
 } Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'a')
 .ForEach(Console.Write); // bc
 
 Stream<char>.Of('a', 'a', 'b', 'c').DropWhile(c => c == 'b')
 .ForEach(Console.Write); // aabc Drop while predicate holds
  • 31. sealed class Stream<T> {
 …
 public U Aggregate<U>(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return identity;
 
 return Tail.Aggregate(func(identity, Head), func);
 }
 } var sum1 = Stream<int>.Of(1, 2, 3, 4) .Aggregate(0, (acc, elem) => acc + elem);
 Console.WriteLine($"sum = {sum1}"); // 10
 var sum2 = Stream<int>.Of<int>() .Aggregate(0, (acc, elem) => acc + elem); 
 Console.WriteLine($"sum = {sum2}"); // 0 Aggregate or Reduce
  • 32. sealed class Stream<T> {
 …
 public bool All(Predicate<T> pred) {
 bool All0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == false)
 return accumulator;
 
 return All0(accumulator && pred(stream.Head), stream.Tail);
 }
 return All0(true, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(2, 4).All(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).All(x => x % 2 == 0)); // False All Don’t evaluate the entire Stream, short-circuit if we already determined negation.
  • 33. sealed class Stream<T> {
 …
 public bool Any(Predicate<T> pred) {
 bool Any0(bool accumulator, Stream<T> stream) {
 if (stream.IsEmpty || accumulator == true)
 return accumulator;
 
 return Any0(accumulator || pred(stream.Head), stream.Tail);
 }
 return Any0(false, this);
 }
 } Console.WriteLine(Stream<int>.Of<int>().Any(x => x % 2 == 0)); // False
 Console.WriteLine(Stream<int>.Of<int>(2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 2, 4).Any(x => x % 2 == 0)); // True
 Console.WriteLine(Stream<int>.Of<int>(1, 3).Any(x => x % 2 == 0)); // False Any Don’t evaluate the entire Stream, short-circuit if we already determined affirmation.
  • 34. sealed class Stream<T> {
 …
 public Stream<T> Scan(U identity, Func<U, T, U> func) {
 if (IsEmpty)
 return Stream<T>.Empty;
 
 U newHead = func(identity, Head);
 return newHead + Tail.Scan(newHead, func);
 }
 } // Prints running sum
 Stream<int>.Of(1, 2, 3, 4) .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // 1 3 6 10
 Stream<int>.Of<int>() .Scan(0, (acc, elem) => acc + elem) .ForEach(Console.WriteLine); // Prints Nothing Scan
  • 35. Zip two Streams sealed class Stream<T> {
 …
 public Stream<(T,U)> Zip<U>(Stream<U> that) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<(T,U)>.Empty;
 
 return (this.Head, that.Head) + this.Tail.Zip(that.Tail);
 }
 } Stream<char>.Of('a', 'b').Zip(Stream<int>.Of(1, 2))
 .ForEach(t => Console.Write(t)); // (a, 1)(b, 2)
 
 Stream<char>.Of('a', 'b').Zip(Stream<int>.Empty)
 .ForEach(t => Console.Write(t)); // Prints Nothing
 
 Stream<int>.Empty.Zip(Stream<char>.Of('a', 'b'))
 .ForEach(t => Console.Write(t)); // Prints Nothing
  • 36. Zip with function sealed class Stream<T> {
 …
 public Stream<R> ZipWith<U, R>(Stream<U> that, Func<T, U, R> fn) {
 if (this.IsEmpty || that.IsEmpty)
 return Stream<R>.Empty;
 
 return fn(this.Head, that.Head) + this.Tail.ZipWith(that.Tail, fn);
 }
 } var numbers = Stream<int>.Of(1, 2, 3);
 numbers.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // 1 4 9
 
 numbers.ZipWith(Stream<int>.Empty, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
 
 Stream<int>.Empty.ZipWith(numbers, (n1, n2) => n1 * n2)
 .ForEach(Console.WriteLine); // Prints Nothing
  • 37. Splitsealed class Stream<T> {
 …
 public (Stream<T>, Stream<T>) Split(Predicate<T> pred) {
 (Stream<T>, Stream<T>) Split0(Stream<T> yesAcc, Stream<T> noAcc, Stream<T> source) {
 if (source.IsEmpty) 
 return (yesAcc.Reverse(), noAcc.Reverse());
 
 var elem = source.Head;
 if (pred(elem))
 return Split0(yesAcc + elem, noAcc, source.Tail);
 else
 return Split0(yesAcc, noAcc + elem, source.Tail);
 } 
 return Split0(Stream<T>.Empty, Stream<T>.Empty, this);
 }
 } var (evens, odds) = Stream<int>.Iterate(0, x => x + 1).Take(10) .Split(x => x % 2 == 0);
 evens.ForEach(Console.Write); // 02468
 odds.ForEach(Console.Write); // 13579
  • 38. To List sealed class Stream<T> {
 … public List<T> ToList() {
 var result = new List<T>();
 ForEach(result.Add);
 return result;
 }
 } var list = Stream<int>.Iterate(1, x => x + 1) .Take(4) .ToList();
 foreach (var item in list) {
 Console.WriteLine(item);
 }
  • 39. Find first 6 primes using the Sieve of Eratosthenes Hint: Use Stream created earlier http://world.mathigon.org/Prime_Numbers
  • 40. Sieve Stream<int> From(int start) => Stream<int>.Iterate(start, x => x + 1);
 Stream<int> Sieve(Stream<int> s) {
 var first = s.Head;
 var rest = s.Tail.Where(n => n % first != 0);
 return new Stream<int>(first, new Lazy<Stream<int>>(() => rest));
 }
 
 var primes = Sieve(From(2)).Take(6) primes.ToList() // [2, 3, 5, 7, 11, 13]
  • 41. First 10 Fibonacci Nos. Write a function fibonacci which consumes an integer and produces that many numbers in the fibonacci series. For Example: fibonacci(10) produces [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] Provide Solutions Using Generator Using IEnumerable Using Stream that we developed
  • 42. IEnumerable<int> Fibonacci(int howMany) { var (first, second) = (0, 1);
 for (var i = 0; i < howMany; i++) {
 yield return first;
 (first, second) = (second, first + second);
 }
 }
 
 Fibonacci(10).ToList();
 // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using Generator
  • 43. IEnumerable<int> Fibonacci(int howMany) { return IEnumerableExtensions.Iterate<(int, int)>((0, 1), tuple => {
 var (first, second) = tuple;
 var next = first + second;
 return (second, next);
 })
 .Select(tuple => {
 var (first, second) = tuple;
 return first;
 })
 .Take(howMany);
 } Fibonacci(10).ToList(); // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] First 10 Fibonacci Nos. Using IEnumerable Definition as suggested by Christopher Grande
  • 44. First 10 Fibonacci Nos. Using Stream https://www.haskell.org/tutorial/functions.html var seed = From(0).Take(2);
 // Start with seed elements 0 and 1
 Fibonacci(seed)
 .Take(10)
 .ForEach(Console.WriteLine); // 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 Stream<int> Fibonacci(Stream<int> s) {
 var next = s.Zip(s.Tail).Select(tuple => {
 var (first, second) = tuple;
 return first + second;
 });
 return new Stream<int>(s.Head, new Lazy<Stream<int>>(() => Fibonacci(s + next.Head)));
 }
  • 45. Prime Counts Using Lazy Lists, write a program that counts number of primes up to a given number. At every power of 10, it should emit the count of primes obtained thus far. The table shows the output until 10 10 Implement this using: Using Stream we developed earlier. Using IEnumerable Hint: Write an extension method Scan on IEnumerable i/p count 10 4 10 2 25 10 3 168 10 4 1,229 10 5 9,592 10 6 78,498 10 7 6,64,579 10 8 57,61,455 10 9 5,08,47,534 10 10 45,50,52,511
  • 46. class Streams {
 public static Stream<int> Range(int start, int count) {
 if (count < 0)
 throw new ArgumentOutOfRangeException($"{count}");
 
 return Stream<int>.Iterate(start, x => x + 1).Take(count);
 } 
 }
 Streams.Range(1, 5).ForEach(Console.WriteLine); // 1 2 3 4 5 Prime Counts using IEnumerable First, write our own Range
  • 47. Prime Counts Using Stream Stream<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Streams.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return Stream<int>.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Streams.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
  • 48. Prime Counts using IEnumerable First, write our own Scan static class IEnumerableExtensions { public static IEnumerable<U> Scan<T, U>(this IEnumerable<T> @this, U initial, Func<U, T, U> fn) {
 IEnumerable<U> ScannedEnumerable() {
 var acc = seed;
 foreach (var item in @this) {
 acc = fn(acc, item);
 yield return acc;
 } 
 if (@this == null)
 throw new ArgumentNullException("Require non-null list!");
 if (fn == null)
 throw new ArgumentNullException("Require non-null function!”);
 return ScannedEnumerable();
 } }
  • 49. Prime Counts using IEnumerable IEnumerable<(int, int)> PrimeCount(int howManyPowerOf10) {
 bool IsPrime(int x) => Enumerable.Range(2, x) .Where(n => n < x) .All(n => x % n != 0); 
 return IEnumerableExtensions.Iterate(2, x => x + 1)
 .TakeWhile(x => x <= Math.Pow(10, howManyPowerOf10))
 .Select(x => (x, IsPrime(x)))
 .Scan((0, 0), (acc, tuple) => {
 var (x, isPrime) = tuple;
 var (_, count) = acc;
 return isPrime ? (x, count + 1): (x, count);
 })
 .Where(tuple => {
 var (x, _) = tuple;
 return Enumerable.Range(1, howManyPowerOf10)
 .Any(n => Math.Pow(10, n) == x);
 });
 } PrimeCount(3).ForEach(t => Console.WriteLine(t)); (10, 4), (100, 25), (1000, 168)
  • 50. Drawbacks of this Stream Implementation As C# compiler does not support Tail- Recursion, all the APIs that are implemented recursively will cause a stack blow-up at some point for large values of stream. Even-though it uses caching of tail using Lazy<T>, this Stream is not performant like IEnumerable! This is because the recursive APIs don’t run in constant stack space.
  • 51. But still its a good mental exercise to create streams from first principles!