doc-src/TutorialI/Recdef/document/examples.tex
changeset 10187 0376cccd9118
parent 9933 9feb1e0c4cb3
child 10362 c6b197ccf1f1
     1.1 --- a/doc-src/TutorialI/Recdef/document/examples.tex	Wed Oct 11 09:09:06 2000 +0200
     1.2 +++ b/doc-src/TutorialI/Recdef/document/examples.tex	Wed Oct 11 10:44:42 2000 +0200
     1.3 @@ -7,8 +7,8 @@
     1.4  \end{isamarkuptext}%
     1.5  \isacommand{consts}\ fib\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat\ {\isasymRightarrow}\ nat{\isachardoublequote}\isanewline
     1.6  \isacommand{recdef}\ fib\ {\isachardoublequote}measure{\isacharparenleft}{\isasymlambda}n{\isachardot}\ n{\isacharparenright}{\isachardoublequote}\isanewline
     1.7 -\ \ {\isachardoublequote}fib\ \isadigit{0}\ {\isacharequal}\ \isadigit{0}{\isachardoublequote}\isanewline
     1.8 -\ \ {\isachardoublequote}fib\ \isadigit{1}\ {\isacharequal}\ \isadigit{1}{\isachardoublequote}\isanewline
     1.9 +\ \ {\isachardoublequote}fib\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequote}\isanewline
    1.10 +\ \ {\isachardoublequote}fib\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}\isanewline
    1.11  \ \ {\isachardoublequote}fib\ {\isacharparenleft}Suc{\isacharparenleft}Suc\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ fib\ x\ {\isacharplus}\ fib\ {\isacharparenleft}Suc\ x{\isacharparenright}{\isachardoublequote}%
    1.12  \begin{isamarkuptext}%
    1.13  \noindent
    1.14 @@ -44,14 +44,14 @@
    1.15  Overlapping patterns are disambiguated by taking the order of equations into
    1.16  account, just as in functional programming:%
    1.17  \end{isamarkuptext}%
    1.18 -\isacommand{consts}\ sep\isadigit{1}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.19 -\isacommand{recdef}\ sep\isadigit{1}\ {\isachardoublequote}measure\ {\isacharparenleft}{\isasymlambda}{\isacharparenleft}a{\isacharcomma}xs{\isacharparenright}{\isachardot}\ length\ xs{\isacharparenright}{\isachardoublequote}\isanewline
    1.20 -\ \ {\isachardoublequote}sep\isadigit{1}{\isacharparenleft}a{\isacharcomma}\ x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep\isadigit{1}{\isacharparenleft}a{\isacharcomma}y{\isacharhash}zs{\isacharparenright}{\isachardoublequote}\isanewline
    1.21 -\ \ {\isachardoublequote}sep\isadigit{1}{\isacharparenleft}a{\isacharcomma}\ xs{\isacharparenright}\ \ \ \ \ {\isacharequal}\ xs{\isachardoublequote}%
    1.22 +\isacommand{consts}\ sep{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.23 +\isacommand{recdef}\ sep{\isadigit{1}}\ {\isachardoublequote}measure\ {\isacharparenleft}{\isasymlambda}{\isacharparenleft}a{\isacharcomma}xs{\isacharparenright}{\isachardot}\ length\ xs{\isacharparenright}{\isachardoublequote}\isanewline
    1.24 +\ \ {\isachardoublequote}sep{\isadigit{1}}{\isacharparenleft}a{\isacharcomma}\ x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep{\isadigit{1}}{\isacharparenleft}a{\isacharcomma}y{\isacharhash}zs{\isacharparenright}{\isachardoublequote}\isanewline
    1.25 +\ \ {\isachardoublequote}sep{\isadigit{1}}{\isacharparenleft}a{\isacharcomma}\ xs{\isacharparenright}\ \ \ \ \ {\isacharequal}\ xs{\isachardoublequote}%
    1.26  \begin{isamarkuptext}%
    1.27  \noindent
    1.28  This defines exactly the same function as \isa{sep} above, i.e.\
    1.29 -\isa{sep\isadigit{1}\ {\isacharequal}\ sep}.
    1.30 +\isa{sep{\isadigit{1}}\ {\isacharequal}\ sep}.
    1.31  
    1.32  \begin{warn}
    1.33    \isacommand{recdef} only takes the first argument of a (curried)
    1.34 @@ -62,18 +62,18 @@
    1.35    arguments as in the following definition:
    1.36  \end{warn}%
    1.37  \end{isamarkuptext}%
    1.38 -\isacommand{consts}\ sep\isadigit{2}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.39 -\isacommand{recdef}\ sep\isadigit{2}\ {\isachardoublequote}measure\ length{\isachardoublequote}\isanewline
    1.40 -\ \ {\isachardoublequote}sep\isadigit{2}\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}a{\isachardot}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep\isadigit{2}\ zs\ a{\isacharparenright}{\isachardoublequote}\isanewline
    1.41 -\ \ {\isachardoublequote}sep\isadigit{2}\ xs\ \ \ \ \ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}a{\isachardot}\ xs{\isacharparenright}{\isachardoublequote}%
    1.42 +\isacommand{consts}\ sep{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.43 +\isacommand{recdef}\ sep{\isadigit{2}}\ {\isachardoublequote}measure\ length{\isachardoublequote}\isanewline
    1.44 +\ \ {\isachardoublequote}sep{\isadigit{2}}\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}a{\isachardot}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep{\isadigit{2}}\ zs\ a{\isacharparenright}{\isachardoublequote}\isanewline
    1.45 +\ \ {\isachardoublequote}sep{\isadigit{2}}\ xs\ \ \ \ \ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}a{\isachardot}\ xs{\isacharparenright}{\isachardoublequote}%
    1.46  \begin{isamarkuptext}%
    1.47  Because of its pattern-matching syntax, \isacommand{recdef} is also useful
    1.48  for the definition of non-recursive functions:%
    1.49  \end{isamarkuptext}%
    1.50 -\isacommand{consts}\ swap\isadigit{1}\isadigit{2}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.51 -\isacommand{recdef}\ swap\isadigit{1}\isadigit{2}\ {\isachardoublequote}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequote}\isanewline
    1.52 -\ \ {\isachardoublequote}swap\isadigit{1}\isadigit{2}\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ y{\isacharhash}x{\isacharhash}zs{\isachardoublequote}\isanewline
    1.53 -\ \ {\isachardoublequote}swap\isadigit{1}\isadigit{2}\ zs\ \ \ \ \ \ \ {\isacharequal}\ zs{\isachardoublequote}%
    1.54 +\isacommand{consts}\ swap{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
    1.55 +\isacommand{recdef}\ swap{\isadigit{1}}{\isadigit{2}}\ {\isachardoublequote}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequote}\isanewline
    1.56 +\ \ {\isachardoublequote}swap{\isadigit{1}}{\isadigit{2}}\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ y{\isacharhash}x{\isacharhash}zs{\isachardoublequote}\isanewline
    1.57 +\ \ {\isachardoublequote}swap{\isadigit{1}}{\isadigit{2}}\ zs\ \ \ \ \ \ \ {\isacharequal}\ zs{\isachardoublequote}%
    1.58  \begin{isamarkuptext}%
    1.59  \noindent
    1.60  For non-recursive functions the termination measure degenerates to the empty