Update README.md

README.md

@@ -8,6 +8,9 @@ SPDX-License-Identifier: BSD-3-Clause
 [![CI](https://github.com/pgujjula/apply-merge/actions/workflows/ci.yml/badge.svg?branch=main)](https://github.com/pgujjula/apply-merge/actions/workflows/ci.yml)
 [![REUSE status](https://api.reuse.software/badge/github.com/pgujjula/apply-merge)](https://api.reuse.software/info/github.com/pgujjula/apply-merge)
 
+⚠️ Under construction. No stability guarantees, even commit history may be
+overwritten.
+
 This library provides a function
 
 ```haskell
@@ -21,16 +24,6 @@ a sorted list of all `f x y`, for each `x` in `xs` and `y` in `ys`.
 With `applyMerge`, we can implement a variety of complex algorithms succinctly.
 For example, the Sieve of Erastosthenes[^1] to generate prime numbers:
 
-[^1]: Note that this is really the Sieve of Erastosthenes, as defined in the
-classic [The Genuine Sieve of Eratosthenes](https://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf).
-Constrast this to other simple prime generation implementations, such as
-```
-primes = sieve [2..]
-sieve (p : xs) = p : sieve [x | x <− xs, x ‘mod‘ p > 0]
-```
-which is actually trial division, and not a faithful implementation of the Sieve
-of Erastosthenes.
-
 ```haskell
 primes :: [Int]
 primes = 2 : ([3..] `minus` composites)    -- `minus` from data-ordlist
@@ -39,24 +32,37 @@ composites :: [Int]
 composites = applyMerge (*) primes [2..]
 ```
 
+3-smooth numbers ([Wikipedia](https://en.wikipedia.org/wiki/Smooth_number)):
+
 ```haskell
--- Square-free integers
-squarefrees :: [Int]
-squarefrees = [1..] `minus` applyMerge (*) (map (^2) primes) [1..]
+smooth3 :: [Integer]
+smooth3 = applyMerge (*) (iterate (*2) 1) (iterate (*3) 1)
+```
+
+Gaussian integers, ordered by norm ([Wikipedia](https://en.wikipedia.org/wiki/Gaussian_integer)):
+```haskell
+zs :: [Int]
+zs = 0 : concatMap (\i -> [i, -i]) [1..]
 
--- Gaussian integers in the first quadrant, ordered by norm
 gaussianInts :: [Complex Int]
-gaussianInts = applyMergeBy (comparing (\a b -> a*a + b*b)) (:+) [1..] [1..]
+gaussianInts = applyMergeBy (comparing (\a b -> a*a + b*b)) (:+) ints ints
 ```
 
+Square-free integers ([Wikipedia](https://en.wikipedia.org/wiki/Square-free_integer)):
 
-⚠️ Under construction. No stability guarantees, even commit history may be
-overwritten.
-
-See [ALGORITHM.md](docs/ALGORITHM.md) for a full description of the algorithm.
+```haskell
+squarefrees :: [Int]
+squarefrees = [1..] `minus` applyMerge (*) (map (^2) primes) [1..]
+```
 
+See [ALGORITHM.md](docs/ALGORITHM.md) for a full exposition of the `applyMerge` function and its implementation.
 
 ## Licensing
 This project licensed under BSD-3-Clause (except for `.gitignore`, which is
 under CC0-1.0), and follows [REUSE](https://reuse.software) licensing
 principles.
+
+[^1]: Note that this is really the Sieve of Erastosthenes, as defined in the classic [The Genuine Sieve of Eratosthenes](https://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf). Constrast this to other simple prime generation implementations, such as <pre>
+primes = sieve [2..]
+sieve (p : xs) = p : sieve [x | x <- xs, x \`rem\` p > 0]</pre>
+which are actually trial division and not faithful implementations of the Sieve of Erastosthenes.