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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{src/algebra aggcat2.spad}
\author{Robert S. Sutor}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{package FLAGG2 FiniteLinearAggregateFunctions2}
<<package FLAGG2 FiniteLinearAggregateFunctions2>>=
import Type
import FiniteLinearAggregate
)abbrev package FLAGG2 FiniteLinearAggregateFunctions2
--% FiniteLinearAggregateFunctions2
++ Author: ???
++ Date Created: ???
++ Date Last Updated: ???
++ Description:
++ FiniteLinearAggregateFunctions2 provides functions involving two
++ FiniteLinearAggregates where the underlying domains might be
++ different. An example of this might be creating a list of rational
++ numbers by mapping a function across a list of integers where the
++ function divides each integer by 1000.
FiniteLinearAggregateFunctions2(S, A, R, B):
Exports == Implementation where
S, R: Type
A : FiniteLinearAggregate S
B : FiniteLinearAggregate R
Exports ==> with
map : (S -> R, A) -> B ++ map(f,a) applies function f to each member of aggregate
++ \spad{a} resulting in a new aggregate over a
++ possibly different underlying domain.
reduce : ((S, R) -> R, A, R) -> R ++ reduce(f,a,r) applies function f to each
++ successive element of the
++ aggregate \spad{a} and an accumulant initialized to r.
++ For example,
++ \spad{reduce(_+$Integer,[1,2,3],0)}
++ does \spad{3+(2+(1+0))}. Note: third argument r
++ may be regarded as the
++ identity element for the function f.
scan : ((S, R) -> R, A, R) -> B ++ scan(f,a,r) successively applies
++ \spad{reduce(f,x,r)} to more and more leading sub-aggregates
++ x of aggregrate \spad{a}.
++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
++ \spad{scan(f,a,r)} returns
++ \spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
Implementation ==> add
getRSample(): R ==
R has sample: R => sample$R
R has random: () -> R => random()$R
NIL$Lisp -- R got to be non-trivial.
if A has ListAggregate(S) then -- A is a list-oid
reduce(fn, l, ident) ==
empty? l => ident
reduce(fn, rest l, fn(first l, ident))
if B has ListAggregate(R) or not(B has shallowlyMutable) then
-- A is a list-oid, and B is either list-oids or not mutable
map(f, l) == construct [f s for s in entries l]
scan(fn, l, ident) ==
empty? l => empty()
val := fn(first l, ident)
concat(val, scan(fn, rest l, val))
else -- A is a list-oid, B a mutable array-oid
map(f, l) ==
i := minIndex(w := new(#l,getRSample())$B)
for a in entries l repeat (qsetelt!(w, i, f a); i := inc i)
w
scan(fn, l, ident) ==
i := minIndex(w := new(#l,getRSample())$B)
vl := ident
for a in entries l repeat
vl := qsetelt!(w, i, fn(a, vl))
i := inc i
w
else -- A is an array-oid
reduce(fn, v, ident) ==
val := ident
for i in minIndex v .. maxIndex v repeat
val := fn(qelt(v, i), val)
val
if B has ListAggregate(R) then -- A is an array-oid, B a list-oid
map(f, v) ==
construct [f qelt(v, i) for i in minIndex v .. maxIndex v]
scan(fn, v, ident) ==
w := empty()$B
for i in minIndex v .. maxIndex v repeat
ident := fn(qelt(v, i), ident)
w := concat(ident, w)
reverse! w
else -- A and B are array-oid's
if B has shallowlyMutable then -- B is also mutable
map(f, v) ==
w := new(#v,getRSample())$B
for i in minIndex w .. maxIndex w repeat
qsetelt!(w, i, f qelt(v, i))
w
scan(fn, v, ident) ==
w := new(#v,getRSample())$B
vl := ident
for i in minIndex v .. maxIndex v repeat
vl := qsetelt!(w, i, fn(qelt(v, i), vl))
w
else -- B non mutable array-oid
map(f, v) ==
construct [f qelt(v, i) for i in minIndex v .. maxIndex v]
scan(fn, v, ident) ==
w := empty()$B
for i in minIndex v .. maxIndex v repeat
ident := fn(qelt(v, i), ident)
w := concat(w, ident)
w
@
\section{package FSAGG2 FiniteSetAggregateFunctions2}
<<package FSAGG2 FiniteSetAggregateFunctions2>>=
import SetCategory
import FiniteSetAggregate
)abbrev package FSAGG2 FiniteSetAggregateFunctions2
--% FiniteSetAggregateFunctions2
++ Author: Robert S. Sutor
++ Date Created: 15 May 1990
++ Date Last Updated: 14 Oct 1993
++ Description:
++ FiniteSetAggregateFunctions2 provides functions involving two
++ finite set aggregates where the underlying domains might be
++ different. An example of this is to create a set of rational
++ numbers by mapping a function across a set of integers, where the
++ function divides each integer by 1000.
FiniteSetAggregateFunctions2(S, A, R, B): Exports == Implementation where
S, R: SetCategory
A : FiniteSetAggregate S
B : FiniteSetAggregate R
Exports ==> with
map : (S -> R, A) -> B ++ map(f,a) applies function f to each member of
++ aggregate \spad{a}, creating a new aggregate with
++ a possibly different underlying domain.
reduce : ((S, R) -> R, A, R) -> R ++ reduce(f,a,r) applies function f to each
++ successive element of the aggregate \spad{a} and an
++ accumulant initialised to r.
++ For example,
++ \spad{reduce(_+$Integer,[1,2,3],0)}
++ does a \spad{3+(2+(1+0))}.
++ Note: third argument r may be regarded
++ as an identity element for the function.
scan : ((S, R) -> R, A, R) -> B ++ scan(f,a,r) successively applies \spad{reduce(f,x,r)}
++ to more and more leading sub-aggregates x of
++ aggregate \spad{a}.
++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
++ \spad{scan(f,a,r)} returns
++ \spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
Implementation ==> add
map(fn, a) ==
set(map(fn, members a)$ListFunctions2(S, R))$B
reduce(fn, a, ident) ==
reduce(fn, members a, ident)$ListFunctions2(S, R)
scan(fn, a, ident) ==
set(scan(fn, members a, ident)$ListFunctions2(S, R))$B
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2009, Gabriel Dos Reis.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>
<<package FLAGG2 FiniteLinearAggregateFunctions2>>
<<package FSAGG2 FiniteSetAggregateFunctions2>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
