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Formal Specification and Documentation Using Z: a Text Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Z Z Z Z Z Z Z Z Z Z Formal Specification and Documentation using Z: A Case Study Approach A Text Formatting Tool (Case Study) Jonathan Bowen Department of Computer Science University of Reading Email: [email protected] URL: http://www.comlab.ox.ac.uk/oucl/users/jonathan.bowen/zbook.html Z Z Z Z Z Z Z Z Z Z Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 A Text Formatting Tool Simple text processing tool for UNIX called pos. Allows left, centred and right justification of lines. Assumes an ASCII text file. Tab characters and newline must be considered. Cf. UNIX manual page 1 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Basic Concepts UNIX text files consist of ASCII characters. ] [ CHAR space : CHAR seq LINE == CHAR seq DOC == LINE 2 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Repeating a sequence ] [X (seq ) N ! seq rep : X X 8 : seq ; : N s X n 1 = hi ^ srep0 a = ( 1)) srepn s (srep n Some laws about rep: seq ` 0 = hi s : X srep seq ` 1 = s : X srep s N ` hi = hi n : rep n seq ; : N ` #( ) = # s : X n srepn s n : seq ; : N ` ran( ) = ran s X n 1 srepn s seq ; : N ` 8 : N j < s : X n m m n ) (# ) = (srepn after s m for n s 3 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Processing the Input Removing leading spaces from a line: ! clipleft : LINE LINE = hi clipleft hi : j 6= hi 8 l LINE l = ) = ^ head l 6 space clipleft l l ) = ( ) head l = space clipleft l clipleft tail l Removing trailing spaces: ! clipright : LINE LINE o o = 9 clipright rev 9 clipleft rev Removing leading and trailing spaces: ! clip : LINE LINE o = clip clipleft 9 clipright Spaces may be removed in either order: o o ` = 9 clipleft 9 clipright clipright clipleft 4 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Indenting to a given column position: Column alignment : N ! ! left0 LINE LINE : N ; : 8 n l LINE a = (h i ) left0 nl space rep n l Centering a line: : N ! ! centre0 LINE LINE : N ; : 8 n l LINE 2 ) #l n a = (h i ( (# 2))) ^ centre0 nl space rep n l div l > 2 ) #l n = centre0 nl l 5 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Right-alignment of a line: : N ! ! right0 LINE LINE : N ; : 8 n l LINE # ) = l n right0 nl a h i ( # )) ^ ( space rep n l l # > ) = l n right0 nl l Clipping lines first: left ; centre; N ! ! right : LINE LINE : N ; : 8 n l LINE = ( ) ^ left n l left0 n clip l = ( ) ^ centre n l centre0 n clip l = ( ) right n l right0 n clip l 6 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Documents TEXT text : DOC Changes in this document: 0 d = ^ TEXT TEXT TEXT Change selected using an option: Option ::= j LeftOption j CentreOption RightOption POS0 TEXT : option? Option : N column? = ) option? LeftOption 0 o = ( ?) text text 9 left column = ) option? CentreOption 0 o = ( ?) text text 9 centre column = ) option? RightOption 0 o = ( ?) text text 9 right column 7 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Implementation Details Previous assumption: all printable characters of the same width. Tabs Horizontal tab: tab : CHAR = tab 6 space ‘Tabulate’ to the next tab column position. N tabsize : 1 tabsize > Introduces additional complication into the specification. 8 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Split a sequence into a series of segments. ] [X : (seq ) N ! seq(seq ) split X 1 X 8 : seq ; : N ; : seq (seq ) s X n 1 ss X 1 1 1 = hi ^ hi split n , s split n = ss a = ^ = ss s 8 : seq j 2 ran( ) # = ) ^ ( t X t front ss t n < #( ) 0 last ss n Convert trailing spaces to a tab. !7 addtab : LINE LINE : j 2= ran 8 l LINE tab l = ^ #( ) < # 1) ) (#l tabsize clipright l l a ( ) h i ^ addtab l = clipright l tab 6= _ #( ) # 1) ) (#l tabsize clipright l l addtab l = l 9 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Converting spaces to tabs Convert spaces in a line to tabs where appropriate: !7 unexpand : LINE LINE : j 2= ran 8 l LINE tab l a o = = (( ) ) unexpand l l split tabsize 9 addtab ooo Only use on lines not containing tabs. Can only reduce the length of the line: 8 : j 2= ran #( ) # ` l LINE tab l unexpand l l 10 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Converting tabs to spaces First cut a sequence into segments (a sequence of sequences) using another sequence (e.g., a tab): ] [X (seq ) (seq ) !7 seq(seq ) cut : X X X 1 a : seq ; ; : seq j : ( ( )) 8 p X s t X p front s p 1 = hi ^ hi cut p = hi ) = h i ^ s 6 s cut p s a a a a ) = h i ( ) (s p t cut p s p t cut p Recombining the segments gives the original sequence: a : seq ` =( ) = a; b X a cut b a 11 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 A trailing tab can be substituted with spaces: ! addspace : LINE LINE = hi addspacehi : j 6= hi 8 l LINE l ) last l = tab a ( ) (h i addspace l = front l space rep +1 (# ))) ^ (tabsize l mod tabsize = ) = last l 6 tab addspace l l Expanding tabs to spaces ! expand : LINE LINE : 8 l LINE a o = =(( h i) ) expand l l cut tab 9 addspace 12 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Properties of expanding lines Expanding tabs to spaces can only increase the length: ` #( ) # l : LINE expand l l Converting spaces to tabs and back gives the same line: 8 : j 2= ran ( ) = ` l LINE tab l expand unexpand l l But converting tabs to spaces and back may not: 9 : ( ) 6= ` l LINE unexpand expand l l Column width of a line ! N width : LINE : 8 l LINE #( ) width l = expand l Adding tabs does not affect the width of a line: ` ( ) = l : LINE width unexpand l width l 13 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Lines A non-empty unique newline character sequence may be used to terminate lines: seq nl : CHAR 1 ; g; ran i disjoint hfspace tab nl Under UNIX this sequence is the ASCII line-feed ‘control’ character. ooo The characters should not occur within any line. 14 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Combine a sequence of segments using another sequence as a terminator: ] [X (seq(seq )) (seq ) ! seq comb : X X X ; : seq ; : seq (seq ) 8 s p X ss X = hi ^ hi comb p a i = ^ hs comb p s p a a a (h i ) = ) s ss comb p s p (ss comb p ooo With a terminator rather than a separator, an empty document and a single empty line can be distinguished: seq ` hi = hi p : X comb p seq ` hhii = p : X comb p p 15 Slides for Formal Specification and Documentation using Z. Copyright c 1996,1998 Jonathan Bowen. All rights reserved. A Text Formatting Tool (Case Study). Last updated: July 3, 1998 Separate a sequence into a series of segments using a non-empty pattern. ] [X (seq ) (seq ) ! seq(seq ) sep : X X X 1 : seq ; : seq ; : seq(seq ) 8 s X p X ss X 1 , s sep p = ss ^ ss comb p = s 8 : seq j 2 ran : ( )) ( t X t ss p t N.B.: the sequence to be separated must be terminated with the pattern or be empty to be valid.
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