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Diffstat (limited to 'src/algebra/aggcat.spad.pamphlet')
| -rw-r--r-- | src/algebra/aggcat.spad.pamphlet | 49 |
1 files changed, 49 insertions, 0 deletions
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index ab9eb619..938a09fb 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -61,6 +61,8 @@ Aggregate: Category == Type with @ +\section{} + \section{category HOAGG HomogeneousAggregate} <<category HOAGG HomogeneousAggregate>>= @@ -154,6 +156,52 @@ HomogeneousAggregate(S:Type): Category == Aggregate with @ +\section{Aggregates of finite extent} + +<<category FINAGG FiniteAggregate>>= +)abbrev category FINAGG FiniteAggregate +++ Author: Gabriel Dos Reis +++ Date Created: May 15, 2013 +++ Date Last Modified: May 15, 2013 +++ Description: +++ A finite aggregate is a homogeneous aggregate with a finite +++ number of elements. +FiniteAggregate(S: Type): Category == Exports where + Exports == HomogeneousAggregate S with + #: % -> NonNegativeInteger + ++ \spad{#u} returns the number of items in u. + any?: (S->Boolean,%) -> Boolean + ++ \spad{any?(p,u)} tests if \spad{p(x)} is true for + ++ any element \spad{x} of \spad{u}. + ++ Note: for collections, + ++ \axiom{any?(p,u) = reduce(or,map(f,u),false,true)}. + every?: (S->Boolean,%) -> Boolean + ++ \spad{every?(f,u)} tests if p(x) holds for all + ++ elements \spad{x} of \spad{u}. + ++ Note: for collections, + ++ \axiom{every?(p,u) = reduce(and,map(f,u),true,false)}. + count: (S->Boolean,%) -> NonNegativeInteger + ++ \spad{count(p,u)} returns the number of elements \spad{x} + ++ in \spad{u} such that \axiom{p(x)} holds. For collections, + ++ \axiom{count(p,u) = reduce(+,[1 for x in u | p(x)],0)}. + members: % -> List S + ++ \spad{members(u)} returns a list of the consecutive elements of u. + ++ For collections, \axiom{parts([x,y,...,z]) = (x,y,...,z)}. + if S has SetCategory then + count: (S,%) -> NonNegativeInteger + ++ \spad{count(x,u)} returns the number of occurrences + ++ of \spad{x} in \spad{u}. + ++ For collections, \axiom{count(x,u) = reduce(+,[x=y for y in u],0)}. + member?: (S,%) -> Boolean + ++ \spad{member?(x,u)} tests if \spad{x} is a member of \spad{u}. + ++ For collections, + ++ \axiom{member?(x,u) = reduce(or,[x=y for y in u],false)}. + +@ + + + + \section{category CLAGG Collection} <<category CLAGG Collection>>= @@ -2753,6 +2801,7 @@ BitAggregate(): Category == <<category AGG Aggregate>> <<category HOAGG HomogeneousAggregate>> +<<category FINAGG FiniteAggregate>> <<category CLAGG Collection>> <<category BGAGG BagAggregate>> <<category SKAGG StackAggregate>> |