1 files changed, 102 insertions, 0 deletions
diff --git a/std/Logic/Binary.bruijn b/std/Logic/Binary.bruijn
new file mode 100644
index 0000000..b16595c
--- /dev/null
+++ b/std/Logic/Binary.bruijn
@@ -0,0 +1,102 @@
+# MIT License, Copyright (c) 2022 Marvin Borner
+
+:import std/Combinator .
+
+# true
+true k ⧗ Boolean
+
+# false
+false ki ⧗ Boolean
+
+# inverts boolean value
+# equivalent of [0 ⇒ false]
+not! c ⧗ Boolean → Boolean
+
+¬‣ not!
+
+:test (¬true) (false)
+:test (¬false) (true)
+
+# true if both args are true
+and? [[0 1 0]] ⧗ Boolean → Boolean → Boolean
+
+…⋀?… and?
+
+:test (true ⋀? true) (true)
+:test (true ⋀? false) (false)
+:test (false ⋀? true) (false)
+:test (false ⋀? false) (false)
+
+# true if not both args are true
+nand? [[1 0 1 false true]] ⧗ Boolean → Boolean → Boolean
+
+:test (nand? true true) (false)
+:test (nand? true false) (true)
+:test (nand? false true) (true)
+:test (nand? false false) (true)
+
+# true if one of the args is true
+or? m ⧗ Boolean → Boolean → Boolean
+
+…⋁?… or?
+
+:test (true ⋁? true) (true)
+:test (true ⋁? false) (true)
+:test (false ⋁? true) (true)
+:test (false ⋁? false) (false)
+
+# true if both args are false
+nor? [[1 1 0 false true]] ⧗ Boolean → Boolean → Boolean
+
+:test (nor? true true) (false)
+:test (nor? true false) (false)
+:test (nor? false true) (false)
+:test (nor? false false) (true)
+
+# true if args are not same bools
+xor? [[0 (1 false 0) 1]] ⧗ Boolean → Boolean → Boolean
+
+:test (xor? true true) (false)
+:test (xor? true false) (true)
+:test (xor? false true) (true)
+:test (xor? false false) (false)
+
+# true if both args are same bools
+xnor? [[0 1 (1 0 true)]] ⧗ Boolean → Boolean → Boolean
+
+:test (xnor? true true) (true)
+:test (xnor? true false) (false)
+:test (xnor? false true) (false)
+:test (xnor? false false) (true)
+
+# if first arg is true, exec first exp; else second exp
+# this function is generally redundant
+# I personally just write (exp? case-T case-F) directly
+if [[[2 1 0]]] ⧗ Boolean → a → b → c
+
+…?…:… if
+
+:test (if true true false) (true)
+:test (true ? true : false) (true)
+:test (if false true false) (false)
+:test (false ? true : false) (false)
+
+# mathematical implies definition
+implies [[1 0 true]] ⧗ Boolean → Boolean → Boolean
+
+…⇒?… implies
+
+:test (true ⇒? true) (true)
+:test (true ⇒? false) (false)
+:test (false ⇒? true) (true)
+:test (false ⇒? false) (true)
+
+# mathematical iff (if and only if) definition
+iff xnor? ⧗ Boolean → Boolean → Boolean
+
+…⇔?… iff
+
+:test (true ⇔? true) (true)
+:test (true ⇔? false) (false)
+:test (false ⇔? true) (false)
+:test (false ⇔? false) (true)