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.
Symbol | LATEX | troff | category | name |
![]() | \arithmos | arithmos | type of all numbers | |
![]() | \nat | nn | natural numbers | |
succ | succ | succ | successor function | |
+ | + | + | function 30 leftassoc | addition |
* | * | * | function 40 leftassoc | multiplication |
Symbol | LATEX | troff | category | name |
![]() | \divides | divides | function 40 leftassoc | real division |
![]() | \nat_1 | nn^1 | positives | |
![]() | \rat_+ | fraction | fractions | |
![]() | \rat | rat | rationals | |
- | \negate | ~ | integer negation | |
- | - | - | function 30 leftassoc | subtraction |
< | < | < | relation (infix) | less than |
![]() | \real | real | reals | |
![]() | \leq | <= | relation (infix) | less than or equal |
![]() | \geq | >= | relation (infix) | greater than or equal |
> | > | > | relation (infix) | greater than |
![]() | \num | ints | integers | |
div | \div | div | function 40 leftassoc | division |
mod | \mod | mod | function 40 leftassoc | modulus |
Symbol | LATEX | troff | category | name |
![]() | \neq | <> | relation (infix) | inequality |
![]() | \notin | notmem | relation (infix) | not member |
![]() | \emptyset | empty | empty set | |
![]() | \subseteq | sinc | relation (infix) | subset |
![]() | \subset | ssinc | relation (infix) | strict subset |
![]() | \power_1 | ps^1 | generic (prefix) | non-empty subsets |
![]() | \cup | sor | function 30 leftassoc | set union |
![]() | \cap | sand | function 40 leftassoc | set intersection |
\ | \setminus | sdiff | function 30 leftassoc | set difference |
![]() | \symdiff | symdiff | function 25 leftassoc | symmetric set difference |
![]() | \bigcup | dor | distributed set union | |
![]() | \bigcap | dand | distributed set intersection | |
![]() | \finset | fss | generic (prefix) | finite subsets |
![]() | \finset_1 | fss^1 | generic (prefix) | non-empty finite subsets |
![]() | \rel | rel | generic 5 rightassoc | relation |
![]() | \mapsto | mlet | function 10 leftassoc | maplet |
first | first | first | project first from pair | |
second | second | second | project second from pair |
Symbol | LATEX | troff | category | name |
dom | \dom | dom | domain | |
ran | \ran | ran | range | |
id | \id | id | generic (prefix) | identity |
![]() | \comp | frc | function 40 leftassoc | forward relational composition |
![]() | \circ | rc | function 40 leftassoc | relational composition |
![]() | \dres | dres | function 61 leftassoc | domain restriction |
![]() | \rres | rres | function 60 leftassoc | range restriction |
![]() | \ndres | dsub | function 61 leftassoc | domain subtraction |
![]() | \nrres | rsub | function 60 leftassoc | range subtraction |
~ | \inv | inv | function (postfix) | relational inverse |
![]() | \limg | opimg | function (postfix) | open image bracket |
![]() | \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 | fxov | function 50 leftassoc | overriding |
Symbol | LATEX | 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 | LATEX | troff | category | name |
+ | \plus | nrtc | function (postfix) | transitive closure |
* | \star | rtc | function (postfix) | reflexive transitive closure |
do | do | do | repetition | |
![]() | \pfun | pfx | generic 5 rightassoc | partial function |
![]() | \fun | fx | generic 5 rightassoc | function |
![]() | \pinj | pinj | generic 5 rightassoc | partial injection |
![]() | \inj | inj | generic 5 rightassoc | injection |
![]() | \psurj | psurj | generic 5 rightassoc | partial surjection |
![]() | \surj | surj | generic 5 rightassoc | surjection |
![]() | \bij | bij | generic 5 rightassoc | bijection |
![]() | \ffun | pffx | generic 5 rightassoc | partial finite function |
![]() | \finj | pfinj | generic 5 rightassoc | partial finite injection |
Symbol | LATEX | 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 | opseq | function (nofix) | open sequence bracket |
![]() | \rangle | clseq | function (nofix) | close sequence bracket |
Symbol | LATEX | troff | category | name |
![]() | \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 | srres | function 40 leftassoc | sequence filtering |
![]() | \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 | distributed concatenation | |
iter | iter | iter | relational iteration | |
^{ | iterup | function (postfix) | begin superscripted relational iteration | |
) | iterdown | function (postfix) | end superscripted relational iteration |
Symbol | LATEX | troff | category | name |
bag | \bag | bag | generic (prefix) | set of bags |
count | count | count | multiplicity | |
![]() | \bcount | bagoccurs | function 50 leftassoc | infix multiplicity |
![]() | \otimes | bagscale | function 40 leftassoc | bag scaling |
![]() | \lbag | opbag | function (nofix) | open bag bracket |
![]() | \rbag | clbag | function (nofix) | close bag bracket |
![]() | \inbag | bagmem | relation (infix) | bag membership |
![]() | \subbageq | baginc | relation (infix) | sub-bag relation |
![]() | \uplus | unionbag | function 30 leftassoc | bag union |
![]() | \uminus | diffbag | function 30 leftassoc | bag difference |
relation | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
generic | 5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
function | 8 | ![]() |
function | 10 | ![]() |
function | 20 | .. |
function | 25 | ![]() |
function | 30 | + - ![]() ![]() ![]() ![]() |
function | 40 | * ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
function | 50 | ![]() |
function | 60 | ![]() ![]() |
function | 61 | ![]() ![]() |
generic (prefix) | ![]() ![]() ![]() ![]() | |
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) | ~ ![]() ![]() | |
function (nofix) | ![]() ![]() ![]() ![]() |