From 66f5758c343546733f7cda281ccff7eafedd6b73 Mon Sep 17 00:00:00 2001
From: Matthijs Kooijman <matthijs@stdin.nl>
Date: Fri, 28 Aug 2009 21:41:15 +0200
Subject: [PATCH] Add a new definition of the normal form.

This definition uses a sort of EBNF.
---
 Chapters/Normalization.tex | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index cbef2c0..b91eb40 100644
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -93,6 +93,44 @@ An example of a program in canonical form would be:
     res
 \stoplambda
 
+\startlambda
+\italic{normal} = \italic{lambda}
+\italic{lambda} = λvar.\italic{lambda} (representable(typeof(var)))
+                | \italic{toplet} 
+\italic{toplet} = let \italic{binding} in \italic{toplet} 
+                | letrec [\italic{binding}] in \italic{toplet}
+                | var (representable(typeof(var)), fvar(var))
+\italic{binding} = var = \italic{rhs} (representable(typeof(rhs)))
+                 -- State packing and unpacking by coercion
+                 | var0 = var1 :: State ty (fvar(var1))
+                 | var0 = var1 :: ty (var0 :: State ty) (fvar(var1))
+\italic{rhs} = userapp
+             | builtinapp
+             -- Extractor case
+             | case var of C a0 ... an -> ai (fvar(var))
+             -- Selector case
+             | case var of (fvar(var))
+                DEFAULT -> var0 (fvar(var0))
+                C w0 ... wn -> resvar (\forall{}i, wi \neq resvar, fvar(resvar))
+\italic{userapp} = \italic{userfunc}
+                 | \italic{userapp} {userarg}
+\italic{userfunc} = var (tvar(var))
+\italic{userarg} = var (fvar(var))
+\italic{builtinapp} = \italic{builtinfunc}
+                    | \italic{builtinapp} \italic{builtinarg}
+\italic{builtinfunc} = var (bvar(var))
+\italic{builtinarg} = \italic{coreexpr}
+\stoplambda
+
+-- TODO: Define tvar, fvar, typeof, representable
+-- TODO: Limit builtinarg further
+
+-- TODO: There can still be other casts around (which the code can handle,
+e.g., ignore), which still need to be documented here.
+
+-- TODO: Note about the selector case. It just supports Bit and Bool
+currently, perhaps it should be generalized in the normal form?
+
 When looking at such a program from a hardware perspective, the top level
 lambda's define the input ports. The value produced by the let expression is
 the output port. Most function applications bound by the let expression
-- 
2.30.2