CADiZ

Reference manual / Symbols defined in the toolkit


Here are the symbols defined in cadiz's extended toolkit, each with its LATEX and troff mark-up, the category of operator it denotes, and a longer name for the symbol. All symbols of the ISO Standard Z toolkit are present amongst these symbols, though the section structure differs.

section prelude

 

Symbol LATE troff category name
 
\arithmos \arithmos arithmos type of all numbers
\nat \nat nn natural numbers
succ succ succ successor function
+ + + function 30 leftassoc addition
* * * function 40 leftassoc multiplication

section numdefs

 

Symbol LATE troff category name
 
\divides \divides divides function 40 leftassoc real division
\nat1 \nat_1 nn^1 positives
\rat+ \rat_+ fraction fractions
\rat \rat rat rationals
- \negate ~ integer negation
- - - function 30 leftassoc subtraction
< < < relation (infix) less than
\real \real real reals
\leq \leq <= relation (infix) less than or equal
\geq \geq >= relation (infix) greater than or equal
> > > relation (infix) greater than
\num \num ints integers
div \div div function 40 leftassoc division
mod \mod mod function 40 leftassoc modulus

section fundefs

 

Symbol LATE troff category name
 
\neq \neq <> relation (infix) inequality
\notin \notin notmem relation (infix) not member
\emptyset \emptyset empty empty set
\subseteq \subseteq sinc relation (infix) subset
\subset \subset ssinc relation (infix) strict subset
\power1 \power_1 ps^1 generic (prefix) non-empty subsets
\cup \cup sor function 30 leftassoc set union
\cap \cap sand function 40 leftassoc set intersection
\ \setminus sdiff function 30 leftassoc set difference
\symdiff \symdiff symdiff function 25 leftassoc symmetric set difference
\bigcup \bigcup dor distributed set union
\bigcap \bigcap dand distributed set intersection
\finset \finset fss generic (prefix) finite subsets
\finset1 \finset_1 fss^1 generic (prefix) non-empty finite subsets
\rel \rel rel generic 5 rightassoc relation
\mapsto \mapsto mlet function 10 leftassoc maplet
first first first project first from pair
second second second project second from pair

Symbol LATE troff category name
 
dom \dom dom domain
ran \ran ran range
id \id id generic (prefix) identity
\comp \comp frc function 40 leftassoc forward relational composition
\circ \circ rc function 40 leftassoc relational composition
\dres \dres dres function 61 leftassoc domain restriction
\rres \rres rres function 60 leftassoc range restriction
\ndres \ndres dsub function 61 leftassoc domain subtraction
\nrres \nrres rsub function 60 leftassoc range subtraction
~ \inv inv function (postfix) relational inverse
\limg \limg opimg function (postfix) open image bracket
\rimg \rimg climg function (postfix) close image bracket
upperBound upperBound upperBound upper bound
disjoint \disjoint disjoint relation (prefix) disjointness
partition \partition partition relation (infix) partitions
\oplus \oplus fxov function 50 leftassoc overriding

Symbol LATE troff category name
 
transitive transitive transitive generic (prefix) transitive relations
antisymmetric antisymmetric antisymmetric generic (prefix) antisymmetric relations
reflexive reflexive reflexive generic (prefix) reflexive relations
irreflexive irreflexive irreflexive generic (prefix) irreflexive relations
preOrder preOrder preOrder generic (prefix) preorders
order order order generic (prefix) partial orders
reflexiveOrder reflexiveOrder reflexiveOrder generic (prefix) reflexive partial orders
irreflexiveOrder irreflexiveOrder irreflexiveOrder generic (prefix) irreflexive partial orders
totalOrder totalOrder totalOrder generic (prefix) total orders
reflexiveTotalOrder reflexiveTotalOrder reflexiveTotalOrder generic (prefix) reflexive total orders
irreflexiveTotalOrder irreflexiveTotalOrder irreflexiveTotalOrder generic (prefix) irreflexive total orders
reflexiveChain reflexiveChain reflexiveChain generic (prefix) reflexive chains
irreflexiveChain irreflexiveChain irreflexiveChain generic (prefix) irreflexive chains

Symbol LATE troff category name
 
+ \plus nrtc function (postfix) transitive closure
* \star rtc function (postfix) reflexive transitive closure
do do do repetition
\pfun \pfun pfx generic 5 rightassoc partial function
\fun \fun fx generic 5 rightassoc function
\pinj \pinj pinj generic 5 rightassoc partial injection
\inj \inj inj generic 5 rightassoc injection
\psurj \psurj psurj generic 5 rightassoc partial surjection
\surj \surj surj generic 5 rightassoc surjection
\bij \bij bij generic 5 rightassoc bijection
\ffun \ffun pffx generic 5 rightassoc partial finite function
\finj \finj pfinj generic 5 rightassoc partial finite injection

section seqdefs

 

Symbol LATE troff category name
 
.. \upto .. function 20 leftassoc number interval
# \# length function (prefix) cardinality
items items items bag of elements of a sequence
min min min minimum
max max max maximum
sequence \sequence sequence generic (prefix) set of infinite sequences
sequence1 \sequence_1 sequence^1 generic (prefix) set of non-empty infinite sequences
isequence \isequence isequence generic (prefix) set of injective infinite sequences
isequence1 \isequence_1 isequence^1 generic (prefix) set of non-empty injective infinite sequences
seq \seq seq generic (prefix) set of finite sequences
seq1 \seq_1 seq^1 generic (prefix) set of non-empty finite sequences
iseq \iseq iseq generic (prefix) set of injective finite sequences
iseq1 \iseq_1 iseq^1 generic (prefix) set of injective non-empty finite sequences
\langle \langle opseq function (nofix) open sequence bracket
\rangle \rangle clseq function (nofix) close sequence bracket

Symbol LATE troff category name
 
\cat \cat cat function 30 leftassoc sequence concatenation
rev rev rev reverse of sequence
head head head project first from sequence
last last last project last from sequence
tail tail tail sequence without head
front front front sequence without last
squash squash squash compaction
\filter \filter srres function 40 leftassoc sequence filtering
\extract \extract sres function 40 leftassoc sequence extraction
prefix \prefix prefix relation (infix) sequence prefix relation
suffix \suffix suffix relation (infix) sequence suffix relation
infix \infix in relation (infix) sequence segment relation
+/ \dsum dsum distributed sum
\dcat \dcat dcat distributed concatenation
iter iter iter relational iteration
^{ iterup function (postfix) begin superscripted relational iteration
) iterdown function (postfix) end superscripted relational iteration

section bagkit

 

Symbol LATE troff category name
 
bag \bag bag generic (prefix) set of bags
count count count multiplicity
\bcount \bcount bagoccurs function 50 leftassoc infix multiplicity
\otimes \otimes bagscale function 40 leftassoc bag scaling
\lbag \lbag opbag function (nofix) open bag bracket
\rbag \rbag clbag function (nofix) close bag bracket
\inbag \inbag bagmem relation (infix) bag membership
\subbageq \subbageq baginc relation (infix) sub-bag relation
\uplus \uplus unionbag function 30 leftassoc bag union
\uminus \uminus diffbag function 30 leftassoc bag difference

Toolkit operator precedences

 

relation \neq \notin \subseteq \subset < \leq \geq > prefix suffix infix partition \inbag \subbageq disjoint
generic 5 \rel \pfun \fun \pinj \inj \psurj \surj \bij \ffun \finj
function 8 \cross
function 10 \mapsto
function 20 ..
function 25 \symdiff
function 30 + - \cup \ \cat \uplus \uminus
function 40 * \divides div mod \bigcap \comp \circ \extract \filter \otimes
function 50 \oplus #
function 60 \rres \nrres
function 61 \dres \ndres
generic (prefix) \power \power1 id \finset \finset1
generic (prefix) sequence sequence1 isequence isequence1 seq seq1 iseq iseq1 bag
generic (prefix) transitive antisymmetric reflexive irreflexive preOrder order
generic (prefix) reflexiveOrder irreflexiveOrder totalOrder reflexiveTotalOrder
generic (prefix) irreflexiveTotalOrder reflexiveChain irreflexiveChain
function (postfix) ~ \limg \rimg + *
function (nofix) \langle \rangle \lbag \rbag

IT 5-Jan-2002