author paulson Thu, 06 Dec 2001 13:00:25 +0100 changeset 12407 70ebb59264f1 parent 12406 c9775847ed66 child 12408 2884148a9fe9
record extend and truncate exercises
--- a/doc-src/TutorialI/Types/Records.thy	Thu Dec 06 00:46:24 2001 +0100
+++ b/doc-src/TutorialI/Types/Records.thy	Thu Dec 06 13:00:25 2001 +0100
@@ -62,15 +62,13 @@

text {* Basic simplifications. *}

-lemma "point.make a b = (| Xcoord = a, Ycoord = b |)"
-by (simp add: point.make_def) -- "needed?? forget it"
-
lemma "Xcoord (| Xcoord = a, Ycoord = b |) = a"
by simp -- "selection"

lemma "(| Xcoord = a, Ycoord = b |) (| Xcoord:= 0 |) = (| Xcoord = 0, Ycoord = b |)"
by simp -- "update"

+
subsection {* Coloured points: record extension *}

@@ -119,9 +117,7 @@
"getX r == Xcoord r"
setX :: "['a point_scheme, int] \<Rightarrow> 'a point_scheme"
"setX r a == r (| Xcoord := a |)"
-  extendpt :: "'a \<Rightarrow> 'a point_scheme"
-   "extendpt ext == (| Xcoord = 15, Ycoord = 0, ... = ext |)"
-     text{*not sure what this is for!*}  (* FIXME use new point.make/extend/truncate *)
+

text {*
@@ -247,4 +243,26 @@
apply record_split --{* @{subgoals[display,indent=0,margin=65]} *}
by simp

+constdefs
+  cpt2 :: cpoint
+   "cpt2 \<equiv> point.extend pt1 (cpoint.fields Green)"
+
+text {*
+@{thm[display] point.defs}
+*};
+
+text {*
+@{thm[display] cpoint.defs}
+*};
+
+text{*cpt2 is the same as cpt1, but defined by extending point pt1*}
+lemma "cpt1 = cpt2"
+apply (simp add: cpt1_def cpt2_def point.defs cpoint.defs)
+	--{* @{subgoals[display,indent=0,margin=65]} *}
+
+
+lemma "point.truncate cpt2 = pt1"
+by (simp add: pt1_def cpt2_def point.defs)
+
end
--- a/doc-src/TutorialI/Types/records.tex	Thu Dec 06 00:46:24 2001 +0100
+++ b/doc-src/TutorialI/Types/records.tex	Thu Dec 06 13:00:25 2001 +0100
@@ -40,7 +40,7 @@
\end{isabelle}
We see above the ASCII notation for record brackets.  You can also use
the symbolic brackets \isa{\isasymlparr} and  \isa{\isasymrparr}.
-Record types can be written directly, rather than referring to
+Record types can be written directly, without referring to
previously declared names:
\begin{isabelle}
\isacommand{constdefs}\ \ \ pt2\ ::\ "(|\ Xcoord\ ::\ int,\ Ycoord\ ::\ int\
@@ -98,14 +98,9 @@
=\ Green\ |)"
\end{isabelle}

-Unfortunately, there are no built-in conversions between types
-\isa{point} and \isa{cpoint}: to add a colour to
-a point,  or to convert a \isa{cpoint} to a \isa{point} by forgetting
-its colour, we must define operations that copy across the other
-fields.  However,  we can define generic operations
-that work on type
-\isa{point} and all extensions of it.

+We can define generic operations that work on type \isa{point} and all
+extensions of it.
Every record structure has an implicit field, \cdx{more}, to allow
extension.  Its type is completely polymorphic:~\isa{'a}.  When a
record value is expressed using just its standard fields, the value of
@@ -117,7 +112,7 @@
\end{isabelle}
This lemma (trivially proved using \isa{simp}) applies to any
record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}.  Field
-\isa{more} can be selected in the usual way, but as all records share
+\isa{more} can be selected in the usual way, but as all records have
this field, the identifier must be qualified:
\begin{isabelle}
\isacommand{lemma}\ "point.more\ cpt1\ =\ \isasymlparr col\ =\ Green\isasymrparr "\isanewline
@@ -263,8 +258,88 @@
been split, the updates can be applied and the record equality can be
replaced by equality of the corresponding fields.

+
+\subsection{Extending and Truncating Records}
+
+Each record declaration introduces functions to refer collectively to a
+record's fields and to convert between related record types.  They can, for
+instance, convert between types \isa{point} and \isa{cpoint}.  We can add a
+colour to a point or to convert a \isa{cpoint} to a \isa{point} by forgetting
+its colour.
+
+\begin{itemize}
+\item Function \isa{make} takes as arguments all of the record's fields.
+  It returns the corresponding record.
+\item If the record type is an extension of another,
+      function \isa{fields} takes the record's new fields
+      and returns a record consisting of just those fields.
+\item Function \isa{extend} takes two arguments: a record to be extended and a
+  record containing the new fields.
+\item Function \isa{truncate} takes a record (possibly an extension of the
+  original record type) and returns a record of the original type, deleting
+\end{itemize}
+
+For example, here are the versions of those functions generated for record
+\isa{point}.  We omit \isa{point.fields}, which is the same as
+\isa{point.make}.
+\begin{isabelle}
+point.make\ ?Xcoord\ ?Ycoord\ \isasymequiv \isanewline\smallskip
+\ \ \isasymlparr Xcoord\ =\ ?Xcoord,\ Ycoord\ =\ ?Ycoord\isasymrparr \isanewline
+point.extend\ ?r\ ?more\ \isasymequiv \isanewline\smallskip
+\ \ \isasymlparr Xcoord\ =\ Xcoord\ ?r,\ Ycoord\ =\ Ycoord\ ?r,\ \isasymdots \ =\ ?more\isasymrparr \isanewline\smallskip
+point.truncate\ ?r\ \isasymequiv \ \isasymlparr Xcoord\ =\ Xcoord\ ?r,\ Ycoord\ =\ Ycoord\ ?r\isasymrparr
+\end{isabelle}
+
+Contrast those with the corresponding functions for record \isa{cpoint}.
+Observe \isa{cpoint.fields} in particular.
+\begin{isabelle}
+cpoint.make\ ?Xcoord\ ?Ycoord\ ?col\ \isasymequiv \isanewline
+\ \ \isasymlparr Xcoord\ =\ ?Xcoord,\ Ycoord\ =\ ?Ycoord,\ col\ =\ ?col\isasymrparr \par\smallskip
+cpoint.fields\ ?col\ \isasymequiv \ \isasymlparr col\ =\ ?col\isasymrparr \par\smallskip
+cpoint.extend\ ?r\ ?more\ \isasymequiv \par
+\ \ \isasymlparr Xcoord\ =\ Xcoord\ ?r,\ Ycoord\ =\ Ycoord\ ?r,\ col\ =\ col\ ?r,\isanewline
+\isaindent{\ \ \ }\isasymdots \ =\ ?more\isasymrparr \par\smallskip
+cpoint.truncate\ ?r\ \isasymequiv \par
+\ \ \isasymlparr Xcoord\ =\ Xcoord\ ?r,\ Ycoord\ =\ Ycoord\ ?r,\ col\ =\ col\ ?r\isasymrparr
+\end{isabelle}
+
+To demonstrate these functions, we declare a new coloured point by extending
+an ordinary point.  Function \isa{point.extend} augments \isa{pt1} with a
+colour, which is converted into a record by \isa{cpoint.fields}.
+\begin{isabelle}
+\isacommand{constdefs}\isanewline
+\ \ cpt2\ ::\ cpoint\isanewline
+\ \ \ "cpt2\ \isasymequiv\ point.extend\ pt1\ (cpoint.fields\ Green)"\isamarkupfalse%
+\end{isabelle}
+
+The coloured points \isa{cpt1} and \isa{cpt2} are equal.  The proof is
+trivial, by unfolding all the definitions.  We deliberately omit the
+definition of~\isa{pt1} in order to reveal the underlying comparison on type
+\isa{point}.
+\begin{isabelle}
+\isacommand{lemma}\ "cpt1\ =\ cpt2"\isanewline
+\isacommand{apply}\ (simp\ add:\ cpt1_def\ cpt2_def\ point.defs\ cpoint.defs)\isanewline
+\ 1.\ Xcoord\ pt1\ =\ 999\ \isasymand \ Ycoord\ pt1\ =\ 23
+\par\smallskip
+\end{isabelle}
+
+In the example below, a coloured point is truncated to leave a point.
+We must use the \isa{truncate} function of the shorter record.
+\begin{isabelle}
+\isacommand{lemma}\ "point.truncate\ cpt2\ =\ pt1"\isanewline
+\isacommand{by}\ (simp\ add:\ pt1_def\ cpt2_def\ point.defs)
+\end{isabelle}
+
\begin{exercise}
-\REMARK{There should be some, but I can't think of any.}
+Extend record \isa{cpoint} to have a further field, \isa{intensity}, of
+type~\isa{nat}.  Experiment with coercions among the three record types.
+\end{exercise}
+
+\begin{exercise}
+(For Java programmers.)
+Model a small class hierarchy using records.
\end{exercise}
\index{records|)}