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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra sex.spad}
\author{Stephen M. Watt}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{category SEXCAT SExpressionCategory}
<<category SEXCAT SExpressionCategory>>=
)abbrev category SEXCAT SExpressionCategory
++ Category for Lisp values
++ Author: S.M.Watt
++ Date Created: July 1987
++ Date Last Modified: 23 May 1991
++ Description:
++ This category allows the manipulation of Lisp values while keeping
++ the grunge fairly localized.
-- The coerce to expression lets the
-- values be displayed in the usual parenthesized way (displaying
-- them as type Expression can cause the formatter to die, since
-- certain magic cookies are in unexpected places).
-- SMW July 87
SExpressionCategory(Str, Sym, Int, Flt, Expr): Category == Decl where
Str, Sym, Int, Flt, Expr: SetCategory
Decl ==> SetCategory with
eq: (%,%) -> Boolean
++ eq(s, t) is true if EQ(s,t) is true in Lisp.
null?: % -> Boolean
++ null?(s) is true if s is the S-expression ().
atom?: % -> Boolean
++ atom?(s) is true if s is a Lisp atom.
pair?: % -> Boolean
++ pair?(s) is true if s has is a non-null Lisp list.
list?: % -> Boolean
++ list?(s) is true if s is a Lisp list, possibly ().
string?: % -> Boolean
++ string?(s) is true if s is an atom and belong to Str.
symbol?: % -> Boolean
++ symbol?(s) is true if s is an atom and belong to Sym.
integer?: % -> Boolean
++ integer?(s) is true if s is an atom and belong to Int.
float?: % -> Boolean
++ float?(s) is true if s is an atom and belong to Flt.
destruct: % -> List %
++ destruct((a1,...,an)) returns the list [a1,...,an].
string: % -> Str
++ string(s) returns s as an element of Str.
++ Error: if s is not an atom that also belongs to Str.
symbol: % -> Sym
++ symbol(s) returns s as an element of Sym.
++ Error: if s is not an atom that also belongs to Sym.
integer: % -> Int
++ integer(s) returns s as an element of Int.
++ Error: if s is not an atom that also belongs to Int.
float: % -> Flt
++ float(s) returns s as an element of Flt;
++ Error: if s is not an atom that also belongs to Flt.
expr: % -> Expr
++ expr(s) returns s as an element of Expr;
++ Error: if s is not an atom that also belongs to Expr.
convert: List % -> %
++ convert([a1,...,an]) returns the S-expression \spad{(a1,...,an)}.
convert: Str -> %
++ convert(x) returns the Lisp atom x;
convert: Sym -> %
++ convert(x) returns the Lisp atom x.
convert: Int -> %
++ convert(x) returns the Lisp atom x.
convert: Flt -> %
++ convert(x) returns the Lisp atom x.
convert: Expr -> %
++ convert(x) returns the Lisp atom x.
car: % -> %
++ car((a1,...,an)) returns a1.
cdr: % -> %
++ cdr((a1,...,an)) returns \spad{(a2,...,an)}.
"#": % -> Integer
++ #((a1,...,an)) returns n.
elt: (%, Integer) -> %
++ elt((a1,...,an), i) returns \spad{ai}.
elt: (%, List Integer) -> %
++ elt((a1,...,an), [i1,...,im]) returns \spad{(a_i1,...,a_im)}.
@
\section{domain SEXOF SExpressionOf}
<<domain SEXOF SExpressionOf>>=
)abbrev domain SEXOF SExpressionOf
++ Domain for Lisp values over arbitrary atomic types
++ Author: S.M.Watt
++ Date Created: July 1987
++ Date Last Modified: 23 May 1991
++ Description:
++ This domain allows the manipulation of Lisp values over
++ arbitrary atomic types.
-- Allows the names of the atomic types to be chosen.
-- *** Warning *** Although the parameters are declared only to be Sets,
-- *** Warning *** they must have the appropriate representations.
SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where
Str, Sym, Int, Flt, Expr: SetCategory
Decl ==> SExpressionCategory(Str, Sym, Int, Flt, Expr)
Body ==> add
Rep := Expr
dotex:OutputForm := INTERN(".")$Lisp
coerce(b:%):OutputForm ==
null? b => paren empty()
string? b => string(b)::OutputForm
atom? b => coerce(b)$Rep
r := b
while not atom? r repeat r := cdr r
l : List %
l1 := [b1::OutputForm for b1 in (l := destruct b)]
not null? r =>
paren blankSeparate concat_!(l1, [dotex, r::OutputForm])
#l = 2 and (first(l1) = QUOTE)@Boolean => quote first rest l1
paren blankSeparate l1
b1 = b2 == EQUAL(b1,b2)$Lisp
eq(b1, b2) == EQ(b1,b2)$Lisp
null? b == NULL(b)$Lisp
atom? b == ATOM(b)$Lisp
pair? b == PAIRP(b)$Lisp
list? b == PAIRP(b)$Lisp or NULL(b)$Lisp
string? b == STRINGP(b)$Lisp
symbol? b == IDENTP(b)$Lisp
integer? b == INTP(b)$Lisp
float? b == RNUMP(b)$Lisp
destruct b == (list? b => b pretend List %; error "Non-list")
string b == (STRINGP(b)$Lisp=> b pretend Str;error "Non-string")
symbol b == (IDENTP(b)$Lisp => b pretend Sym;error "Non-symbol")
float b == (RNUMP(b)$Lisp => b pretend Flt;error "Non-float")
integer b == (INTP(b)$Lisp => b pretend Int;error "Non-integer")
expr b == b pretend Expr
convert(l: List %) == l pretend %
convert(st: Str) == st pretend %
convert(sy: Sym) == sy pretend %
convert(n: Int) == n pretend %
convert(f: Flt) == f pretend %
convert(e: Expr) == e pretend %
car b == CAR(b)$Lisp
cdr b == CDR(b)$Lisp
# b == LENGTH(b)$Lisp
elt(b:%, i:Integer) == destruct(b).i
elt(b:%, li:List Integer) ==
for i in li repeat b := destruct(b).i
b
@
\section{domain SEX SExpression}
<<domain SEX SExpression>>=
)abbrev domain SEX SExpression
++ Domain for the standard Lisp values
++ Author: S.M.Watt
++ Date Created: July 1987
++ Date Last Modified: 23 May 1991
++ Description:
++ This domain allows the manipulation of the usual Lisp values;
SExpression()
== SExpressionOf(String, Symbol, Integer, DoubleFloat, OutputForm)
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--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>>
<<category SEXCAT SExpressionCategory>>
<<domain SEXOF SExpressionOf>>
<<domain SEX SExpression>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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