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 ## fairstream
 
 [Simple fair and terminating backtracking Monad Transformer](https://okmij.org/ftp/Computation/monads.html#fair-bt-stream)
+[Backtracking, Interleaving, and Terminating Monad Transformers](https://okmij.org/ftp/Computation/LogicT.pdf)
+
+### Motivation
+
+The problem with depth-first search `flatMap` of fs2.Stream and standard library's collection is that when you nest infinite streams, it gets stuck exploring the first branch forever:
+
+```scala
+val number = fs2.Stream.iterate(1)(_ + 1) // 1, 2, 3, ...
+
+val triples = for {
+  i <- number
+  j <- number // stuck here: tries j=1,2,3,... for i=1 forever
+  k <- number
+  if i * i + j * j == k * k
+} yield (i, j, k)
+
+triples.take(1).toList // never terminates
+```
+
+`Fair` uses fair disjunction (`mplus`) instead of simple concatenation. It interleaves branches so that every candidate is eventually reached:
+
+```scala
+import com.codiff.fairstream.Fair
+import com.codiff.fairstream.Fair._
+
+lazy val number: Fair[Int] = mplus(unit(0), number.map(_ + 1))
+
+val triples = for {
+  i <- number
+  _ <- guard(i > 0)
+  j <- number
+  _ <- guard(j > 0)
+  k <- number
+  _ <- guard(k > 0)
+  _ <- guard(i * i + j * j == k * k)
+} yield (i, j, k)
+
+Fair.runM(None, Some(5), triples)
+// List((3,4,5), (4,3,5), (6,8,10), (8,6,10), (5,12,13))
+```
+
+The `fairstream-fs2` allows converting `Fair`/`FairT` to `fs2.Stream`:
+
+```scala
+import com.codiff.fairstream.fs2.syntax._
+
+// Fair[A] => fs2.Stream[Pure, A]
+val stream = triples.toFs2.take(10).toList
+
+// FairT[IO, A] => fs2.Stream[IO, A]
+val ioStream = compatible.toFs2.take(5).compile.toList
+```