From 6f4601d5bd245e99831cedb12b732d77501a16e1 Mon Sep 17 00:00:00 2001
From: Masaya Tojo <masaya@tojo.tokyo>
Date: Sun, 16 Jun 2024 18:39:20 +0900
Subject: Add usages section to README.md

---
 examples/mod7.scm                | 51 ++++++++++++++++++++++++++++++++++++++++
 examples/pythagorean-triples.scm | 11 +++++++++
 2 files changed, 62 insertions(+)
 create mode 100644 examples/mod7.scm
 create mode 100644 examples/pythagorean-triples.scm

(limited to 'examples')

diff --git a/examples/mod7.scm b/examples/mod7.scm
new file mode 100644
index 0000000..cfdce61
--- /dev/null
+++ b/examples/mod7.scm
@@ -0,0 +1,51 @@
+(import (algebraic-structures semigroup)
+        (algebraic-structures monoid)
+        (algebraic-structures group)
+        (algebraic-structures monoid fold)
+        (algebraic-structures list foldable))
+
+(module (mod7 semigroup) = (algebraic-structures semigroup)
+  (import scheme
+          (chicken module)
+          (chicken base))
+  (export <>)
+
+  (define (<> x y)
+    (assert (integer? x))
+    (assert (integer? y))
+    (assert (not (zero? x)))
+    (assert (not (zero? y)))
+    (modulo (* x y) 7)))
+
+(module (mod7 monoid) = (algebraic-structures monoid)
+  (import scheme
+          (chicken module)
+          (chicken base))
+  (reexport (mod7 semigroup))
+  (export unit)
+
+  (define unit 1))
+
+(module (mod7 group) = (algebraic-structures group)
+  (import scheme
+          (chicken base)
+          (chicken module)
+          matchable)
+  (reexport (mod7 monoid))
+  (export inv)
+
+  (define (inv n)
+    (assert (integer? n))
+    (assert (not (zero? n)))
+    (match (modulo n 7)
+      (1 1)
+      (2 4)
+      (3 5)
+      (4 2)
+      (5 3)
+      (6 6))))
+
+(module (mod7 fold) = ((algebraic-structures monoid fold) (mod7 monoid) (algebraic-structures list foldable)))
+
+(import (prefix (mod7 group) mod7:)
+        (prefix (mod7 fold) mod7:))
diff --git a/examples/pythagorean-triples.scm b/examples/pythagorean-triples.scm
new file mode 100644
index 0000000..4f620af
--- /dev/null
+++ b/examples/pythagorean-triples.scm
@@ -0,0 +1,11 @@
+(import (srfi 41)
+        (prefix (algebraic-structures stream monad) stream:)
+        (prefix (algebraic-structures stream alternative) stream:))
+
+(define (pythagorean-triples)
+  (stream:do (b <- (stream-from 1))
+             (a <- (stream-range 1 b))
+             (let c^2 = (+ (* a a) (* b b)))
+             (let-values (c r) = (exact-integer-sqrt c^2))
+             (stream:guard (zero? r))
+             (stream (list a b c))))
-- 
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