last changes

sofp-src/book_cover/sofp-cover-parameters.tex

@@ -18,7 +18,7 @@
 % -- Ingram: page count MUST be divisible by 2.
 % -- Blurb : page count MUST be divisible by 6.
 % Add blank pages as needed in final PDF generations!
-\pgfmathsetmacro\TotalPageCount{831}% Must be manually entered
+\pgfmathsetmacro\TotalPageCount{830}% Must be manually entered
 \pgfmathsetmacro\PaperWidthPt{7.444in}%
 \pgfmathsetmacro\PaperHeightPt{9.68in}%
 

sofp-src/check_and_make_draft.sh

@@ -8,10 +8,10 @@ name="sofp"
 # When changing the title of any chapter, make sure it is correctly updated in `draft_title_*` and in the `chapters` array below.
 
 # Expected total number of pages in the book draft:
-draft_pages=799
+draft_pages=798
 
 # The number of pages in each chapter:
-pagecounts=(3 17 42 34 24 49 43 12 63 54 63 62 54 27 148 5 5 6 3 6 6 3 6 48 21 1 2 1 1 7)
+pagecounts=(3 17 42 34 24 49 43 12 63 54 63 62 53 27 148 5 5 6 3 6 6 3 6 48 21 1 2 1 1 7)
 
 # To create the draft version that contains only proofread chapters:
 # cut out from here, including:

sofp-src/sofp-traversable.lyx

@@ -21431,11 +21431,11 @@ width "26col%"
 status open
 
 \begin_layout Plain Layout
-\begin_inset VSpace -100baselineskip%
+\begin_inset VSpace -130baselineskip%
 \end_inset
 
 
-\begin_inset Formula $\xymatrix{\xyScaleY{2.0pc}\xyScaleX{5.0pc}L^{A}\ar[rd]\sb(0.4){\text{trav}_{L}^{G,A,B}(g\bef f)~~}\ar[r]\sp(0.5){\text{trav}_{L}^{F,A,B}(g)} & F^{L^{B}}\ar[d]\sp(0.45){f}\\
+\begin_inset Formula $\xymatrix{\xyScaleY{1.7pc}\xyScaleX{5.0pc}L^{A}\ar[rd]\sb(0.4){\text{trav}_{L}^{G,A,B}(g\bef f)~~}\ar[r]\sp(0.5){\text{trav}_{L}^{F,A,B}(g)} & F^{L^{B}}\ar[d]\sp(0.45){f}\\
  & G^{L^{B}}
 }
 $
@@ -22390,10 +22390,9 @@ noprefix "false"
 ).
  To verify the identity law:
 \begin_inset Formula 
-\begin{align*}
- & \text{pu}_{F}(\text{wu}_{\text{Id}})\overset{?}{=}\text{wu}_{F}\\
-\text{definition of }\text{wu}_{F}:\quad & =\text{pu}_{F}(1)=\text{pu}_{F}(\text{wu}_{\text{Id}})\quad.
-\end{align*}
+\[
+\text{pu}_{F}(\text{wu}_{\text{Id}})\overset{?}{=}\text{wu}_{F}=\text{pu}_{F}(1)=\text{pu}_{F}(\text{wu}_{\text{Id}})\quad.
+\]
 
 \end_inset
 
@@ -22522,19 +22521,7 @@ p.traverse(f)
 \end_inset
 
 -effect.
- If 
-\begin_inset listings
-inline true
-status open
-
-\begin_layout Plain Layout
-
-p.traverse(f)
-\end_layout
-
-\end_inset
-
- does not skip any data stored in 
+ We expect that the data structure of 
 \begin_inset listings
 inline true
 status open
@@ -22546,19 +22533,19 @@ p
 
 \end_inset
 
-, the full data structure of 
+ should be preserved in the final result of 
 \begin_inset listings
 inline true
 status open
 
 \begin_layout Plain Layout
 
-p
+p.traverse(f)
 \end_layout
 
 \end_inset
 
- should be preserved in the final result.
+.
 
 \end_layout
 
@@ -23045,20 +23032,16 @@ noprefix "false"
 \end_layout
 
 \begin_layout Standard
-The identity law of 
-\begin_inset listings
-inline true
-status open
-
-\begin_layout Plain Layout
-
-traverse
-\end_layout
+Apart from visiting every stored value exactly once, we expect that all
+
+\begin_inset Formula $F$
+\end_inset
 
+-effects returned by 
+\begin_inset Formula $f$
 \end_inset
 
- guarantees that all stored values are visited exactly once.
- Another expected property of 
+ are collected by 
 \begin_inset listings
 inline true
 status open
@@ -23070,15 +23053,7 @@ traverse
 
 \end_inset
 
- is that all 
-\begin_inset Formula $F$
-\end_inset
-
--effects returned by 
-\begin_inset Formula $f$
-\end_inset
-
- are collected exactly once.
+ exactly once.
  To see an example where that expectation fails, consider a simple traversable
  functor 
 \begin_inset Formula $L^{A}=A\times A$
@@ -23254,6 +23229,10 @@ traverse
 \end_inset
 
 , and compute the following composition:
+\begin_inset VSpace -15baselineskip%
+\end_inset
+
+
 \begin_inset Formula 
 \[
 p\triangleright\text{trav}_{L}^{F,A,B}(f)\triangleright\big(\text{trav}_{L}^{G,B,C}(g)\big)^{\uparrow F}:F^{G^{L^{C}}}\quad.
@@ -23262,7 +23241,7 @@ p\triangleright\text{trav}_{L}^{F,A,B}(f)\triangleright\big(\text{trav}_{L}^{G,B
 \end_inset
 
 
-\begin_inset VSpace -50baselineskip%
+\begin_inset VSpace -65baselineskip%
 \end_inset
 
 
@@ -23347,11 +23326,7 @@ traverse
 
 \end_inset
 
- operation using that functor and obtain a value of the same type 
-\begin_inset Formula $F^{G^{L^{C}}}$
-\end_inset
-
-:
+ operation using that functor and obtain:
 \begin_inset VSpace -50baselineskip%
 \end_inset
 
@@ -23375,7 +23350,7 @@ width "38col%"
 status open
 
 \begin_layout Plain Layout
-\begin_inset VSpace -150baselineskip%
+\begin_inset VSpace -160baselineskip%
 \end_inset
 
 
@@ -30216,12 +30191,9 @@ def access[N: Finite, A](s: SqSize[N, A], i: Int, j: Int): A = s match {
 }
 \end_layout
 
-\end_inset
+\begin_layout Plain Layout
 
-Let us test this code:
-\begin_inset listings
-inline false
-status open
+\end_layout
 
 \begin_layout Plain Layout
 
@@ -30278,7 +30250,7 @@ Sq
 \end_inset
 
 .
- To test this code (Figure
+ For testing (Figure
 \begin_inset space ~
 \end_inset
 

sofp-src/sofp-traversable.tex

@@ -2880,8 +2880,8 @@ \subsection{Laws of \texttt{traverse}}
 $F$ to another arbitrary applicative functor $G$:
 
 \begin{wrapfigure}{l}{0.26\columnwidth}%
-\vspace{-1\baselineskip}
-$\xymatrix{\xyScaleY{2.0pc}\xyScaleX{5.0pc}L^{A}\ar[rd]\sb(0.4){\text{trav}_{L}^{G,A,B}(g\bef f)~~}\ar[r]\sp(0.5){\text{trav}_{L}^{F,A,B}(g)} & F^{L^{B}}\ar[d]\sp(0.45){f}\\
+\vspace{-1.3\baselineskip}
+$\xymatrix{\xyScaleY{1.7pc}\xyScaleX{5.0pc}L^{A}\ar[rd]\sb(0.4){\text{trav}_{L}^{G,A,B}(g\bef f)~~}\ar[r]\sp(0.5){\text{trav}_{L}^{F,A,B}(g)} & F^{L^{B}}\ar[d]\sp(0.45){f}\\
  & G^{L^{B}}
 }
 $\vspace{0.5\baselineskip}
@@ -3118,10 +3118,9 @@ \subsubsection{Example \label{subsec:Example-pure-is-applicative-morphism}\ref{s
 \]
 We need to show that $\text{pu}_{F}$ obeys the laws~(\ref{eq:identity-law-of-applicative-morphism})\textendash (\ref{eq:composition-law-of-applicative-morphism}).
 To verify the identity law:
-\begin{align*}
- & \text{pu}_{F}(\text{wu}_{\text{Id}})\overset{?}{=}\text{wu}_{F}\\
-{\color{greenunder}\text{definition of }\text{wu}_{F}:}\quad & =\text{pu}_{F}(1)=\text{pu}_{F}(\text{wu}_{\text{Id}})\quad.
-\end{align*}
+\[
+\text{pu}_{F}(\text{wu}_{\text{Id}})\overset{?}{=}\text{wu}_{F}=\text{pu}_{F}(1)=\text{pu}_{F}(\text{wu}_{\text{Id}})\quad.
+\]
 To verify the composition law:
 \begin{align*}
  & \text{zip}_{F}\big(\text{pu}_{F}(p^{:A})\times\text{pu}_{F}(q^{:B})\big)\overset{?}{=}\text{pu}_{F}(\text{zip}_{\text{Id}}(p\times q))=\text{pu}_{F}(p\times q)\\
@@ -3138,9 +3137,8 @@ \subsubsection{Example \label{subsec:Example-pure-is-applicative-morphism}\ref{s
 as a law, consider for simplicity a function $f$ of type $A\rightarrow F^{A}$.
 Then the final result of \lstinline!p.traverse(f)! has type $F^{L^{A}}$,
 which can be visualized as a value of type $L^{A}$ wrapped under
-an $F$-effect. If \lstinline!p.traverse(f)! does not skip any data
-stored in \lstinline!p!, the full data structure of \lstinline!p!
-should be preserved in the final result. 
+an $F$-effect. We expect that the data structure of \lstinline!p!
+should be preserved in the final result of \lstinline!p.traverse(f)!. 
 
 To formulate this condition in a simple way, we may choose functions
 $f$ that always return an \emph{empty} $F$-effect (that is, a result
@@ -3193,11 +3191,10 @@ \subsubsection{Statement \label{subsec:Statement-identity-law-traverse-simplifie
 At the same time, we have: $\text{trav}_{L}(\text{id}\bef f)=\text{trav}_{L}(f)=\text{trav}_{L}(\text{pu}_{F})$.
 So, Eq.~(\ref{eq:traverse-identity-law-with-pure}) holds. $\square$
 
-The identity law of \lstinline!traverse! guarantees that all stored
-values are visited exactly once. Another expected property of \lstinline!traverse!
-is that all $F$-effects returned by $f$ are collected exactly once.
-To see an example where that expectation fails, consider a simple
-traversable functor $L^{A}=A\times A$ and write the \lstinline!traverse!
+Apart from visiting every stored value exactly once, we expect that
+all $F$-effects returned by $f$ are collected by \lstinline!traverse!
+exactly once. To see an example where that expectation fails, consider
+a simple traversable functor $L^{A}=A\times A$ and write the \lstinline!traverse!
 method like this:
 \begin{lstlisting}
 def trav2[A, B, F[_]: WuZip : Functor](f: A => F[B])(la: (A, A)): F[(B, B)] = {
@@ -3216,25 +3213,24 @@ \subsubsection{Statement \label{subsec:Statement-identity-law-traverse-simplifie
 found by composing two \lstinline!traverse! operations. Consider
 two different applicative functors ($F$ and $G$), two functions
 $f:A\rightarrow F^{B}$ and $g:B\rightarrow G^{C}$, and compute the
-following composition:
+following composition:\vspace{-0.15\baselineskip}
 \[
 p\triangleright\text{trav}_{L}^{F,A,B}(f)\triangleright\big(\text{trav}_{L}^{G,B,C}(g)\big)^{\uparrow F}:F^{G^{L^{C}}}\quad.
 \]
-\vspace{-0.5\baselineskip}
+\vspace{-0.65\baselineskip}
 
 \noindent The second \lstinline!traverse! operation needs to be lifted
 to \lstinline!F! for the types to match. The result (of type $F^{G^{L^{C}}}$)
 looks like a \lstinline!traverse! operation with respect to the functor
 $F\circ G$. By Statement~\ref{subsec:Statement-applicative-composition},
 the functor $F\circ G$ is applicative. So, we may apply a single
-\lstinline!traverse! operation using that functor and obtain a value
-of the same type $F^{G^{L^{C}}}$:\vspace{-0.5\baselineskip}
+\lstinline!traverse! operation using that functor and obtain:\vspace{-0.5\baselineskip}
 \[
 p\triangleright\text{trav}_{L}^{F\circ G,A,C}(f\bef g^{\uparrow F}):F^{G^{L^{C}}}\quad.
 \]
 
 \begin{wrapfigure}{l}{0.38\columnwidth}%
-\vspace{-1.5\baselineskip}
+\vspace{-1.6\baselineskip}
 $\xymatrix{\xyScaleY{1.5pc}\xyScaleX{3.4pc}L^{A}\ar[dr]\sb(0.35){\text{trav}_{L}^{F\circ G,A,C}(f\bef g^{\uparrow F})~~}\ar[r]\sp(0.5){\text{trav}_{L}^{F,A,B}(f)} & F^{L^{B}}\ar[d]\sp(0.4){\big(\text{trav}_{L}^{G,B,C}(g)\big)^{\uparrow F}}\\
  & F^{G^{L^{C}}}
 }
@@ -4477,16 +4473,14 @@ \subsubsection{Statement \label{subsec:Statement-nested-recursive-type-traversab
   case Matrix(byIndex) => byIndex((Finite[N].apply(i), Finite[N].apply(j)))
   case Next(next) => access[Option[N], A](next, i, j)
 }
-\end{lstlisting}
-Let us test this code:
-\begin{lstlisting}
+
 scala> access(matrix2x2, 0, 1)
 res0: Int = 12
 \end{lstlisting}
 
 Figure~\ref{fig:Full-code-implementing-traverse-for-square-matrix}
 shows the complete code of \lstinline!sequence! for \lstinline!Sq!.
-To test this code (Figure~\ref{fig:Full-code-implementing-traverse-for-square-matrix-tests}),
+For testing (Figure~\ref{fig:Full-code-implementing-traverse-for-square-matrix-tests}),
 we define a value \lstinline!matrix2x2List! that represents a square
 matrix of lists:
 \[

sofp-src/sofp.tex

@@ -283,9 +283,9 @@
 ~\\
 ISBN: 978-0-359-76877-6\\
 \\
-{\scriptsize{}Source hash (sha256): b0cb97196cd4d30add1b48365c08df1401bf4a23b96981957b509b93e72d71d8}\\
-{\scriptsize{}Git commit: 803a909f36526cbd50cd1bd0a1ed7c7820241a52}\\
-{\scriptsize{}PDF file built by pdfTeX 3.14159265-2.6-1.40.20 (TeX Live 2019) on Wed, 29 Dec 2021 22:06:18 +0100 by Darwin 20.6.0}\\
+{\scriptsize{}Source hash (sha256): f32d019833d71d9040b4b392919610a144a44b825477124ef0ce4e2d40a0c14f}\\
+{\scriptsize{}Git commit: 9720c487a495e72da004be190a940eb9e41ae867}\\
+{\scriptsize{}PDF file built by pdfTeX 3.14159265-2.6-1.40.20 (TeX Live 2019) on Wed, 29 Dec 2021 23:00:15 +0100 by Darwin 20.6.0}\\
 ~\\
 {\scriptsize{}Permission is granted to copy, distribute and/or modify
 this document under the terms of the GNU Free Documentation License,
@@ -320,7 +320,7 @@
 type constructions.}\\
 {\small{}}\\
 {\small{}Long and difficult, yet boring explanations are logically
-developed in excruciating detail through 1732 Scala
+developed in excruciating detail through 1731 Scala
 code snippets, 185 statements with step-by-step derivations,
 101 diagrams, 212 solved examples with tested
 Scala code, and 266 exercises. Discussions further build