Use "let mutable" to introduce mutable variables in algorithms.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

protocol/protocol.tex

@@ -5895,15 +5895,15 @@ be the \incomingViewingKey corresponding to $\AuthPrivate$, and let $\TransmitPu
 
 \vspace{1ex}
 \begin{algorithm}
-  \item Initialize $\ReceivedSet \typecolon \powerset{\NoteTypeSprout \times \MemoType} = \setof{}$.
+  \item let mutable $\ReceivedSet \typecolon \powerset{\NoteTypeSprout \times \MemoType} := \setof{}$
-  \item Initialize $\SpentSet \typecolon \powerset{\NoteTypeSprout} = \setof{}$.
+  \item let mutable $\SpentSet \typecolon \powerset{\NoteTypeSprout} := \setof{}$
-  \item Initialize $\NullifierMap \typecolon \PRFOutputSprout \rightarrow \NoteTypeSprout$ to the empty mapping.
+  \item let mutable $\NullifierMap \typecolon \PRFOutputSprout \rightarrow \NoteTypeSprout :=$ the empty mapping
         \vspace{1ex}
-  \item For each \transaction $\tx$,
+  \item for each \transaction $\tx$:
-  \item \tab For each \joinSplitDescription in $\tx$,
+  \item \tab for each \joinSplitDescription in $\tx$:
-  \item \tab \tab Let $(\EphemeralPublic, \TransmitCiphertext{\allNew})$ be the \notesCiphertext
+  \item \tab \tab let $(\EphemeralPublic, \TransmitCiphertext{\allNew})$ be the \notesCiphertext
-                  of the \joinSplitDescription.
+                  of the \joinSplitDescription
-  \item \tab \tab For $i$ in $\allNew$,
+  \item \tab \tab for $i$ in $\allNew$:
   \item \tab \tab \tab Attempt to decrypt the \notesCiphertext component
                        $(\EphemeralPublic, \TransmitCiphertext{i})$ using $\InViewingKey$ with the
                        \vspace{-1.2ex}
@@ -5916,12 +5916,12 @@ be the \incomingViewingKey corresponding to $\AuthPrivate$, and let $\TransmitPu
                             as described in \crossref{notes}.
   \item \tab \tab \tab \tab Add the mapping $\nf \rightarrow \NoteTuple{}$ to $\NullifierMap$.
   \item \blank
-  \item \tab \tab Let $\nf_{\allOld}$ be the \nullifiers of the \joinSplitDescription.
+  \item \tab \tab let $\nf_{\allOld}$ be the \nullifiers of the \joinSplitDescription
-  \item \tab \tab For $i$ in $\allOld$,
+  \item \tab \tab for $i$ in $\allOld$:
-  \item \tab \tab \tab If $\nf_i$ is present in $\NullifierMap$, add $\NullifierMap(\nf_i)$
+  \item \tab \tab \tab if $\nf_i$ is present in $\NullifierMap$, add $\NullifierMap(\nf_i)$
-                       to $\SpentSet$.
+                       to $\SpentSet$
   \item \blank
-  \item Return $(\ReceivedSet, \SpentSet)$.
+  \item return $(\ReceivedSet, \SpentSet)$.
 \end{algorithm}
 
 
@@ -5950,26 +5950,26 @@ and its final status (spent or unspent).
 
 \vspace{1ex}
 \begin{algorithm}
-  \item Initialize $\ReceivedSet \typecolon \powerset{\NoteTypeSapling \times \MemoType} = \setof{}$.
+  \item let mutable $\ReceivedSet \typecolon \powerset{\NoteTypeSapling \times \MemoType} := \setof{}$
-  \item Initialize $\SpentSet \typecolon \powerset{\NoteTypeSapling} = \setof{}$.
+  \item let mutable $\SpentSet \typecolon \powerset{\NoteTypeSapling} := \setof{}$
-  \item Initialize $\NullifierMap \typecolon \PRFOutputNfSapling \rightarrow \NoteTypeSapling$ to the empty mapping.
+  \item let mutable $\NullifierMap \typecolon \PRFOutputNfSapling \rightarrow \NoteTypeSapling :=$ the empty mapping
         \vspace{1ex}
-  \item For each \transaction $\tx$,
+  \item for each \transaction $\tx$:
-  \item \tab For each \outputDescription in $\tx$ with \notePosition $\NotePosition$,
+  \item \tab for each \outputDescription in $\tx$ with \notePosition $\NotePosition$:
   \item \tab \tab Attempt to decrypt the \noteCiphertext components
                   $\EphemeralPublic$ and $\TransmitCiphertext{}$ using $\InViewingKey$ with the algorithm\vspace{-1.2ex}%
   \item \tab \tab in \crossref{saplingdecryptivk}. If this succeeds giving $\NotePlaintext{}$:
-  \item \tab \tab \tab Extract $\NoteTuple{}$ and $\Memo \typecolon \MemoType$ from $\NotePlaintext{}$.
+  \item \tab \tab \tab Extract $\NoteTuple{}$ and $\Memo \typecolon \MemoType$ from $\NotePlaintext{}$
-  \item \tab \tab \tab Add $(\NoteTuple{}, \Memo)$ to $\ReceivedSet$.
+  \item \tab \tab \tab Add $(\NoteTuple{}, \Memo)$ to $\ReceivedSet$
   \item \tab \tab \tab Calculate the nullifier $\nf$ of $\NoteTuple{}$ using $\AuthProvePublic$
                        and $\NotePosition$ as described in \crossref{notes}.
   \item \tab \tab \tab Add the mapping $\nf \rightarrow \NoteTuple{}$ to $\NullifierMap$.
   \item \blank
-  \item \tab For each \spendDescription in $\tx$,
+  \item \tab for each \spendDescription in $\tx$:
-  \item \tab \tab Let $\nf$ be the \nullifier of the \spendDescription.
+  \item \tab \tab let $\nf$ be the \nullifier of the \spendDescription
-  \item \tab \tab If $\nf$ is present in $\NullifierMap$, add $\NullifierMap(\nf)$ to $\SpentSet$.
+  \item \tab \tab if $\nf$ is present in $\NullifierMap$, add $\NullifierMap(\nf)$ to $\SpentSet$
   \item \blank
-  \item Return $(\ReceivedSet, \SpentSet)$.
+  \item return $(\ReceivedSet, \SpentSet)$.
 \end{algorithm}
 
 \begin{nnotes}
@@ -10789,7 +10789,7 @@ Filippo Valsorda, Zaki Manian, Tracy Hu, Brian Warner, Mary Maller,
 Michael Dixon, Andrew Poelstra, Eirik Ogilvie-Wigley, Benjamin Winston,
 Kobi Gurkan, Weikeng Chen, Henry de Valence, Deirdre Connolly, Chelsea Komlo,
 Zancas Wilcox, Jane Lusby, Teor, Izaak Meckler, Zac Williamson, Vitalik Buterin,
-and no doubt others.
+Jakub Zalewski. and no doubt others.
 We would also like to thank the designers and developers of \Bitcoin.
 
 \Zcash has benefited from security audits performed by NCC Group, Coinspect,
@@ -10855,9 +10855,10 @@ Peter Newell's illustration of the Jubjub bird, from \cite{Carroll1902}.
           possibilities is prefix-free. (The human-readable forms are prefix-free but the
           raw encodings are not; for example, the \rawEncoding of a \Sapling \spendingKey
           can be a prefix of several of the other encodings.)
+    \item Use ``let mutable'' to introduce mutable variables in algorithms.
     \item Include a reference to \cite{BFIJSV2010} for batch pairing verification techniques.
     \item Acknowledge Jack Gavigan as a co-designer of \Sapling and of the \Zcash protocol.
-    \item Acknowledge Izaak Meckler, Zac Williamson, and Vitalik Buterin.
+    \item Acknowledge Izaak Meckler, Zac Williamson, Vitalik Buterin, and Jakub Zalewski.
     \item Acknowledge Alexandra Elbakyan.
 \end{itemize}
 
@@ -13426,11 +13427,11 @@ Define $\BlakeTwos{256} \typecolon (p \typecolon \byteseq{8}) \times (x \typecol
   \item \blank
   \item let $h \typecolon \typeexp{\binaryrange{32}}{8} =
              \listcomp{\LEOStoIPOf{32}{\BlakeParamBlock_{\barerange{4 \mult i}{4 \mult i\,+\,3}}} \xor \BlakeIV_i \for i \from 0 \upto 7}$
-  \item let $v \typecolon \typeexp{\binaryrange{32}}{16} =
-             h \bconcat\,[\,\BlakeIV_0, \BlakeIV_1, \BlakeIV_2, \BlakeIV_3,
-                            t_0 \xor \BlakeIV_4, t_1 \xor \BlakeIV_5, f_0 \xor \BlakeIV_6, f_1 \xor \BlakeIV_7\,]$
   \item let $m \typecolon \typeexp{\binaryrange{32}}{16} =
              \listcomp{\LEOStoIPOf{32}{x_{\barerange{4 \mult i}{4 \mult i\,+\,3}}} \for i \from 0 \upto 15}$
+  \item let mutable $v \typecolon \typeexp{\binaryrange{32}}{16} :=
+             h \bconcat\,[\,\BlakeIV_0, \BlakeIV_1, \BlakeIV_2, \BlakeIV_3,
+                            t_0 \xor \BlakeIV_4, t_1 \xor \BlakeIV_5, f_0 \xor \BlakeIV_6, f_1 \xor \BlakeIV_7\,]$
         \vspace{1ex}
   \item for $r$ from $0$ up to $9$:
         \vspace{-2ex}