From bfec4ec2fb4ea629cd0f93234ff4fd04f097ff5d Mon Sep 17 00:00:00 2001
From: Zebulun Arendsee <arendsee@iastate.edu>
Date: Sat, 24 Feb 2018 22:20:15 -0600
Subject: [PATCH] Add notes on parameterized Bool and Chance

---
 docs/types.md | 52 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 52 insertions(+)

diff --git a/docs/types.md b/docs/types.md
index d2aa5105..0a274010 100644
--- a/docs/types.md
+++ b/docs/types.md
@@ -209,3 +209,55 @@ Syntactically, I will probably use a '?' for Maybe, for example: `?Int`
  * ? column metadata
  * ? row metadata
  * ? cell metadata
+
+### Parameterized Boolean
+
+This is a odd type, but something important I want to express: a boolean with
+semantic annotation. For example:
+
+```
+Filename -> Is Readable
+Image    -> Is Dog
+String   -> Is Integer
+Integer  -> Is Odd
+Audio    -> Is HipHop
+```
+
+```
+-- general
+filterImage :: (Image -> Is Thing) -> [Image] -> [Image]
+
+-- more specific
+filterImage :: (Image -> Is Airplane) -> [Image] -> [Image]
+
+-- most specific
+filterImage :: (Image -> Is Boeing747) -> [Image] -> [Image]
+```
+
+These would have the more general types:
+
+```
+Filename -> Bool
+Image    -> Bool
+String   -> Bool
+Integer  -> Bool
+Audio    -> Bool
+```
+
+But these lack semantic meaning.
+
+'Is' implies an equivalence of some sort. 'Has' implies a `has_part` relation.
+For example: 
+
+```
+[Integer] -> Has 45
+Image -> Has Dog
+```
+
+### Parameterized Probability
+
+First there is the `ChanceOf` type
+
+```
+FeatureTable -> ChanceOf Win
+```