algebra StandardAlgebra

+: int x int -> int
+: int x real -> real
+: real x int -> real
+: real x real -> real
+: string x string -> string

-: int x int -> int
-: int x real -> real
-: real x int -> real
-: real x real -> real

*: int x int -> int
*: int x real -> real
*: real x int -> real
*: real x real -> real

/: int x int -> real
/: int x real -> real
/: real x int -> real
/: real x real -> real

mod: int x int -> int
div: int x int -> int

<: int x int -> bool
<: int x real -> bool
<: real x int -> bool
<: real x real -> bool
<: bool x bool -> bool
<: string x string -> string

<=: int x int -> bool
<=: int x real -> bool
<=: real x int -> bool
<=: real x real -> bool
<=: bool x bool -> bool
<=: string x string -> string

>: int x int -> bool
>: int x real -> bool
>: real x int -> bool
>: real x real -> bool
>: bool x bool -> bool
>: string x string -> string

>=: int x int -> bool
>=: int x real -> bool
>=: real x int -> bool
>=: real x real -> bool
>=: bool x bool -> bool
>=: string x string -> string

=: int x int -> bool
=: int x real -> bool
=: real x int -> bool
=: real x real -> bool
=: bool x bool -> bool
=: string x string -> string

starts: string x string -> bool

and: bool x bool -> bool
or: bool x bool -> bool


algebra DateAlgebra

<: date x date -> bool
=: date x date -> bool
>: date x date -> bool


algebra RelationAlgebra

feed: rel(Tuple) -> stream(Tuple)
consume: stream(Tuple) -> rel(Tuple)
filter: stream(Tuple) :: (Tuple -> bool) -> stream(Tuple)
attr: tuple(Attrs) :: Ident -> (Number, Type); 
    attr(Ident, Attrs, Type, Number)
project: stream(tuple(Attrs_1)) :: (Ident_i)+
        -> (Numbers_i, stream(tuple(Attrs_2)));
    attrs(Ident_i, Attrs_1, Types_i, Numbers_i),
    combine(Ident_i, Types_i, Attrs_2),
    distinctAttrs(Attrs_2)

count: stream(Tuple) -> int
count: rel(Tuple) -> int
count: orel(Tuple) -> int
count: trel(Tuple) -> int
rename: stream(Tuple) :: (Tuple -> string) -> stream(Tuple)


algebra ExtRelationAlgebra

hashjoin: stream(tuple(Attrs_1)) x stream(tuple(Attrs_2)) 
        :: Ident_1 x Ident_2
        -> stream(tuple(Attrs_3));
    attr(Ident_1, Attrs_1, Type_1, Number_1),
    attr(Ident_2, Attrs_2, Type_1, Number_2),
    concat(Attrs_1, Attrs_2, Attrs_3),
    distinctAttrs(Attrs_3)

extend: stream(tuple(Attrs_1))
        :: (Ident_i x (tuple(Attrs_2) -> Type_i))+
	-> stream(tuple(Attrs_3));
    combine(Ident_i, Type_i, Attrs_2),
    concat(Attrs_1, Attrs_2, Attrs_3),
    distinctAttrs(Attrs_3)

projectextend: stream(tuple(Attrs_1))
        :: (Ident_i)+ x (Ident_j x (tuple(Attrs_3) -> Type_j))+
	-> stream(tuple(Attrs_4));
    attrs(Ident_i, Attrs_1, Type_i, Number_i),
    combine(Ident_i, Type_i, Attrs_2),
    combine(Ident_j, Type_j, Attrs_3),
    concat(Attrs_2, Attrs_3, Attrs_4),
    distinctAttrs(Attrs_4)

projectextendstream: stream(tuple(Attrs_1))
	:: (Ident_i)+ x (Ident x (tuple(Attrs_3) -> stream(Type)))	
	-> stream(tuple(Attrs_4));
    attrs(Ident_i, Attrs_1, Type_i, Number_i),
    combine(Ident_i, Type_i, Attrs_2),
    combine(Ident, Type, Attrs_3),
    concat(Attrs_2, Attrs_3, Attrs_4),
    distinctAttrs(Attrs_4)

groupby: stream(tuple(Attrs_1))
	:: (Ident_i)+ x (Ident_j x (rel(tuple(Attrs_3)) -> Type_j))+
	-> stream(tuple(Attrs_4));
    attrs(Ident_i, Attrs_1, Type_i, Number_i),
    combine(Ident_i, Type_i, Attrs_2),
    combine(Ident_j, Type_j, Attrs_3),
    concat(Attrs_2, Attrs_3, Attrs_4),
    distinctAttrs(Attrs_4)


algebra TemporalAlgebra

atinstant: moving(T) x instant -> intime(T) 
where T in {int, real, string, bool, point, region}.

deftime: moving(T) -> periods 
where T in {int, real, string, bool, point, region}.



algebra QcV2Test

<: mreal x mreal -> bool
<: real x mreal -> mbool

=: rect x rect -> bool


avg:    (stream)(Empty)(Empty)
	:: (attr)(Space)(int)(Comma)(real)(Empty)(Empty) -> real

bbox:   (point)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect
bbox:   (points)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect
bbox:   (mpoint)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect
bbox:   (line)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect
bbox:   (region)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect
bbox:   (sline)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> rect

collect_points: (stream)(Space)(point)
	:: (bool)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> points

convexhull: (points)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> region

distance: (mpoint)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (mpoint)(Semicolon)(mpoint)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (point)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (point)(Semicolon)(line)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (point)(Semicolon)(rect)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (line)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (line)(Semicolon)(line)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (line)(Semicolon)(rect)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (rect)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (rect)(Semicolon)(line)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal
distance: (rect)(Semicolon)(rect)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> mreal

extendstream: (stream)(Empty)(Empty)
	:: (new)(Space)(stream)(Space)(list)(Empty)(Empty) -> stream

extract: (stream)(Empty)(Empty)
	:: (attr)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> attr

feedproject: rel(Tuple) :: (Tuple -> attrlist) -> stream(Tuple)

head: stream(Tuple) :: (Tuple -> int) -> stream(Tuple)

intstream: int x int -> stream(data)

kbiggest: (stream)(Empty)(Empty)
	:: (int)(Semicolon)(attrlist)(Empty)(Empty)(Empty)(Empty) -> stream

krdup: (stream)(Empty)(Empty)
	:: (attrlist)(Space)(sort)(Empty)(Empty)(Empty)(Empty) -> stream

ksmallest: (stream)(Empty)(Empty)
	:: (int)(Semicolon)(attrlist)(Empty)(Empty)(Empty)(Empty) -> stream

loopjoin: stream(Tuple) :: (Tuple -> fun) -> stream(Tuple)

loopsel: stream(Tuple) :: (Tuple -> fun) -> stream(Tuple)

mergejoin: (stream)(Semicolon)(stream)
	:: (attr)(Comma)(attr)(Empty)(Empty)(Empty)(Empty) -> stream

min:    (stream)(Empty)(Empty)
	:: (attr)(Space)(int)(Comma)(real)(Empty)(Empty) -> real

minimum: (mreal)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> real

namedtransformstream: (stream)(Space)(data)
	:: (string)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> stream

passes: (mpoint)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool
passes: (mpoint)(Semicolon)(line)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool
passes: (mregion)(Semicolon)(point)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool
passes: (mregion)(Semicolon)(line)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool

rdup: stream(Tuple) -> stream(Tuple)

remove: stream(tuple(Attrs_1)) :: (Ident_i)+
        -> (Numbers_i, stream(tuple(Attrs_2)));
    attrs(Ident_i, Attrs_1, Types_i, Numbers_i),
    combine(Ident_i, Types_i, Attrs_2),
    distinctAttrs(Attrs_2)

size: (line)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> real

sometimes: (ubool)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool
sometimes: (mbool)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> bool

sort: (stream)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> stream

sortby: (stream)(Empty)(Empty)
	:: (attrlist)(Space)(dir)(Empty)(Empty)(Empty)(Empty) -> stream

sortmergejoin: (stream)(Semicolon)(stream)
	:: (attr)(Comma)(attr)(Empty)(Empty)(Empty)(Empty) -> stream

spatialjoin: (stream)(Semicolon)(stream)
	:: (attr)(Comma)(attr)(Empty)(Empty)(Empty)(Empty) -> stream

symmjoin: (stream)(Semicolon)(stream)
	:: (bool)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> stream

tail: stream(Tuple) :: (Tuple -> int) -> stream(Tuple)

tconsume: stream(Tuple) -> trel(Tuple)

transformstream: (stream)(Space)(data)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> stream

units: mpoint(Tuple) -> stream(data)

windowintersects: (rtree)(Semicolon)(rel)
	:: (rect)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> stream

year_of: (date)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> int

month_of: (date)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> int

day_of: (date)(Empty)(Empty)
	:: (Empty)(Empty)(Empty)(Empty)(Empty)(Empty)(Empty) -> int