From 715fd33a0fe2317c4f8421e2d0b91cb013e3c346 Mon Sep 17 00:00:00 2001 From: polybeandip Date: Sat, 10 Aug 2024 19:59:18 -0400 Subject: [PATCH] Bug fixes + recompilation - use macros for push, pop, PIEO, PIEOTree, etc - change iff to implies in Defn 1.1, eq (2) --- pieo-trees/notes.pdf | Bin 145383 -> 153263 bytes pieo-trees/notes.tex | 14 ++++++-------- 2 files changed, 6 insertions(+), 8 deletions(-) diff --git a/pieo-trees/notes.pdf b/pieo-trees/notes.pdf index 81050afc572c1a4cd9c90e16513b55047b0bc77e..5d9b33aea266320f31cac3cd483add31c5b35942 100644 GIT binary patch delta 52939 zcmZUYLwKMKux4Z1w#|;!v2EM#7+-8#9d~Tow$riMv7PzvGc&8Zd$+Zz_nfMeYna+< zSX4?SF$qRiCQdlYxuxO1aBQ53D459yowSJxFu;zXNN;glT*R*6;hm^TgG$eDtI9hP zdUXz-O2TYemBTsw_tjF?zD)t>@?~S8L{Sr#SixQgj<6Yn+0%Ln@r;rC1VS&e`}Mk$cFy6pN~JK_XGeX^BKKddpiM$;Gj&dD_GjtwTRz4&DZ zpXuY?H#f=~^MBubg0SC^Jbm&)m;AO!;U5R2AMU-I5?B`wgUq+MCOryWOD)!dz$!K3 zc~A?>e#%6%d4CFdlC%~orQTQ_#fr}SPi0;pkx-%X;+IsA!w2Q*L^K4<_`-7idq$LX 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b/pieo-trees/notes.tex @@ -122,7 +122,7 @@ \section{Structure \& Semantics} These three maps play nicely together: \begin{align} \pop(p, f) \text{ is undefined} &\iff \pop(\proj(p, f)) \text{ is undefined} \label{eq:pieo1}\\ - \pop(p, f) = (\pkt, p^\prime) &\iff \pop(\proj(p, f)) = (\pkt, \proj(p^\prime, f)) \label{eq:pieo2}\\ + \pop(p, f) = (\pkt, p^\prime) &\implies \pop(\proj(p, f)) = (\pkt, \proj(p^\prime, f)) \label{eq:pieo2}\\ \proj(\push(p, s, d, r), f) &= \begin{cases} \push(\proj(p, f), s, r) & f(d) \text{ holds true}\\ @@ -163,7 +163,7 @@ \section{Structure \& Semantics} \forall i \in [1, n]. \; qs[i] \in \mathbf{PIEOTree}(ts[i]) } { - \Internal(qs, p) \in \mathbf{PIEOTree}(\Node(ts)) + \Internal(qs, p) \in \PIEOTree(\Node(ts)) } \end{align*} \end{dfn} @@ -174,7 +174,7 @@ \section{Structure \& Semantics} \begin{align*} \inference{} { - \text{POP}(p, f) = (\pkt, p^\prime) + \pop(p, f) = (\pkt, p^\prime) } { \pop(\Leaf(p), f) = (\pkt, \Leaf(p^\prime)) @@ -182,7 +182,7 @@ \section{Structure \& Semantics} && \inference{} { - \text{POP}(p, f) = (i, p^\prime)\\ + \pop(p, f) = (i, p^\prime)\\ \pop(qs[i], f) = (\pkt, q^\prime) } { @@ -197,7 +197,7 @@ \section{Structure \& Semantics} \begin{align*} \inference{} { - \text{PUSH}(p, \pkt, d, r) = p^\prime + \push(p, \pkt, d, r) = p^\prime } { \push(\Leaf(p), \pkt, d, r) = \Leaf(p^\prime) @@ -205,7 +205,7 @@ \section{Structure \& Semantics} && \inference{} { - \text{PUSH}(p, i, d, r) = p^\prime\\ + \push(p, i, d, r) = p^\prime\\ \push(qs[i], \pkt, d, pt) = q^\prime } { @@ -260,8 +260,6 @@ \section{Well-Formedness} \textcolor{red}{TBD} \end{proof} -\newpage - \section{Projection} \begin{dfn}