From: Matthijs Kooijman Date: Wed, 2 Sep 2009 09:17:18 +0000 (+0200) Subject: Remove the example sequence, it was completely out of date. X-Git-Tag: final-thesis~264 X-Git-Url: https://git.stderr.nl/gitweb?a=commitdiff_plain;h=689ceb49f2969d573c77d6f279b5ea90592cd6ca;p=matthijs%2Fmaster-project%2Freport.git Remove the example sequence, it was completely out of date. --- diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex index 1f9f62b..68d48d4 100644 --- a/Chapters/Normalization.tex +++ b/Chapters/Normalization.tex @@ -973,247 +973,3 @@ x = let x = add 1 2 in x \stopbuffer \transexample{Return value simplification}{from}{to} - -\subsection{Example sequence} - -This section lists an example expression, with a sequence of transforms -applied to it. The exact transforms given here probably don't exactly -match the transforms given above anymore, but perhaps this can clarify -the big picture a bit. - -TODO: Update or remove this section. - -\startlambda - λx. - let s = foo x - in - case s of - (a, b) -> - case a of - High -> add - Low -> let - op' = case b of - High -> sub - Low -> λc.λd.c - in - λc.λd.op' d c -\stoplambda - -After top-level η-abstraction: - -\startlambda - λx.λc.λd. - (let s = foo x - in - case s of - (a, b) -> - case a of - High -> add - Low -> let - op' = case b of - High -> sub - Low -> λc.λd.c - in - λc.λd.op' d c - ) c d -\stoplambda - -After (extended) β-reduction: - -\startlambda - λx.λc.λd. - let s = foo x - in - case s of - (a, b) -> - case a of - High -> add c d - Low -> let - op' = case b of - High -> sub - Low -> λc.λd.c - in - op' d c -\stoplambda - -After return value extraction: - -\startlambda - λx.λc.λd. - let s = foo x - r = case s of - (a, b) -> - case a of - High -> add c d - Low -> let - op' = case b of - High -> sub - Low -> λc.λd.c - in - op' d c - in - r -\stoplambda - -Scrutinee simplification does not apply. - -After case binder wildening: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> - case a of - High -> add c d - Low -> let op' = case b of - High -> sub - Low -> λc.λd.c - in - op' d c - in - r -\stoplambda - -After case value simplification - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> r' - rh = add c d - rl = let rll = λc.λd.c - op' = case b of - High -> sub - Low -> rll - in - op' d c - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After let flattening: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> r' - rh = add c d - rl = op' d c - rll = λc.λd.c - op' = case b of - High -> sub - Low -> rll - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After function inlining: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> r' - rh = add c d - rl = (case b of - High -> sub - Low -> λc.λd.c) d c - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After (extended) β-reduction again: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> r' - rh = add c d - rl = case b of - High -> sub d c - Low -> d - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After case value simplification again: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = case s of (_, _) -> r' - rh = add c d - rlh = sub d c - rl = case b of - High -> rlh - Low -> d - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After case removal: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - r = r' - rh = add c d - rlh = sub d c - rl = case b of - High -> rlh - Low -> d - r' = case a of - High -> rh - Low -> rl - in - r -\stoplambda - -After let bind removal: - -\startlambda - λx.λc.λd. - let s = foo x - a = case s of (a, _) -> a - b = case s of (_, b) -> b - rh = add c d - rlh = sub d c - rl = case b of - High -> rlh - Low -> d - r' = case a of - High -> rh - Low -> rl - in - r' -\stoplambda - -Application simplification is not applicable.