path: root/src/algebra/domain.spad.pamphlet

\documentclass{article}
\usepackage{axiom}

\author{Gabriel Dos~Reis}

\begin{document}

\begin{abstract}
\end{abstract}

\tableofcontents
\eject

\section{The Constructor domain}

<<domain CTORKIND ConstructorKinid>>=
)abbrev domain CTORKIND ConstructorKind
++ Author: Gabriel Dos Reis
++ Date Create: October 07, 2008.
++ Date Last Updated: October 07, 2008.
++ Related Constructors: 
++ Description:
++   This domain enumerates the three kinds of constructors
++   available in OpenAxiom: category constructors, domain
++   constructors, and package constructors.
ConstructorKind(): Public == Private where
  Public == SetCategory with
    category: % ++ `category' is the kind of category constructors
    domain: %   ++ `domain' is the kind of domain constructors
    package: %  ++ `package' is the kind of package constructors.
  Private == add
    category == 'category : %
    domain == 'domain : %
    package == 'package : %
    k1 = k2 == EQ(k1,k2)$Lisp
    coerce(k: %): OutputForm == k : OutputForm
@

<<category CTORCAT ConstructorCategory>>=
import ConstructorKind
)abbrev category CTORCAT ConstructorCategory
++ Author: Gabriel Dos Reis
++ Date Create: December 17, 2008.
++ Date Last Updated: December 21, 2008.
++ Basic Operations: name, kind, arity.
++ Description:
++   This category declares basic operations on all constructors.
ConstructorCategory(): Category == OperatorCategory Identifier with
     kind: % -> ConstructorKind
       ++ kind(ctor) returns the kind of the constructor `ctor'.
     dualSignature: % -> List Boolean
       ++ dualSignature(c) returns a list l of Boolean values with 
       ++ the following meaning: 
       ++   l.(i+1) holds when the constructor takes a domain object
       ++           as the `i'th argument.  Otherwise the argument
       ++           must be a non-domain object.
  add
    kind x == getConstructorKind(x)$Lisp
    arity x == getConstructorArity(x)$Lisp
    dualSignature x == getDualSignatureFromDB(x)$Lisp
@


<<domain CTOR Constructor>>=
)abbrev domain CTOR Constructor
++ Author: Gabriel Dos Reis
++ Date Create: October 07, 2008.
++ Date Last Updated: December 17, 2008.
++ Related Constructors: Domain, Category
++ Basic Operations: name, kind, arity.
++ Description:
++   This domain provides implementations for constructors.
Constructor(): ConstructorCategory with
     findConstructor: Symbol -> Maybe %
       ++ \spad{findConstructor(s)} attempts to find a constructor
       ++ named \spad{s}.  If successful, returns that constructor;
       ++ otherwise, returns \spad{nothing}.
  == add
    Rep == Identifier
    name x == rep x
    kind x == getConstructorKind(x)$Lisp
    arity x == getConstructorArity(x)$Lisp
    findConstructor s ==
      isConstructorName(s)$Lisp => just per(s pretend Identifier)
      nothing
@


\section{domain ConstructorCall}

<<domain CTORCALL ConstructorCall>>=
import SetCategory
import Symbol
import List Syntax
)abbrev domain CTORCALL ConstructorCall
++ Author: Gabriel Dos Reis
++ Date Created: January 19, 2008
++ Date Last Updated: July 03, 2008
++ Description: This domains represents a syntax object that
++ designates a category, domain, or a package.
++ See Also: Syntax, Domain
ConstructorCall(): Public == Private where
  Public == SetCategory with
    constructor: % -> Constructor
      ++ constructor(t) returns the name of the constructor used
      ++ to make the call.
    arguments: % -> List Syntax
      ++ arguments(t) returns the list of syntax objects for the
      ++ arguments used to invoke the constructor.

  Private == add
    constructor x ==
      CAR(x)$Lisp

    arguments x ==
      CDR(x)$Lisp

    x = y ==
      EQUAL(x,y)$Lisp

    coerce(x: %): OutputForm ==
      outputDomainConstructor(x)$Lisp
@


<<domain CATCTOR CategoryConstructor>>=
)abbrev domain CATCTOR CategoryConstructor
++ Author: Gabriel Dos Reis
++ Date Create: December 17, 2008.
++ Date Last Updated: December 20, 2008.
++ Related Constructors: Domain, Category
++ Description:
++   This domain provides representations for category constructors.
CategoryConstructor(): Public == Private where
  Public == Join(ConstructorCategory, CoercibleTo Constructor)
  Private == Constructor add
    coerce(x: %): Constructor == rep x

@

<<domain DOMCTOR DomainConstructor>>=
)abbrev domain DOMCTOR DomainConstructor
++ Author: Gabriel Dos Reis
++ Date Create: December 17, 2008.
++ Date Last Updated: December 20, 2008.
++ Related Constructors: Domain, Category
++ Description:
++   This domain provides representations for domains constructors.
DomainConstructor(): Public == Private where
  Public == Join(ConstructorCategory, CoercibleTo Constructor)
  Private == Constructor add
    coerce(x: %): Constructor == rep x

@

\section{The Signature domain}

<<domain SIG Signature>>=
import List
import Syntax
)abbrev domain SIG Signature
++ Author: Gabriel Dos Reis
++ Date Created: January 10, 2008
++ Date Last Updated: December 20, 2008
++ Description: This is the datatype for operation signatures as
++   used by the compiler and the interpreter.  Note that this domain
++   differs from SignatureAst.
++ See also: ConstructorCall, Domain.
Signature(): Public == Private where
  Public == SetCategory with
    signature: (List Syntax,Syntax) -> %
      ++ signature(s,t) constructs a Signature object with parameter
      ++ types indicaded by `s', and return type indicated by `t'.
    target: % -> Syntax
      ++ target(s) returns the target type of the signature `s'.
    source: % -> List Syntax
      ++ source(s) returns the list of parameter types of `s'.
  Private == add
    Rep == List Syntax
    signature(s,t) == per cons(t,s)
    target x == first rep x
    source x == rest rep x
    x = y == rep x = rep y
    printType(x: Syntax): OutputForm ==
      x::InputForm::OutputForm
    coerce(x: %): OutputForm ==
      #source x = 1 =>
        rarrow(printType first source x, printType target x)
      rarrow(paren [printType s for s in source x],
         printType target x)$OutputForm
@

\section{A domain for operator signatures}

<<domain OPSIG OperatorSignature>>=
)abbrev domain OPSIG OperatorSignature
++ Author: Gabriel Dos Reis
++ Date Created: December 20, 2008
++ Date Last Modified: December 20, 2008
++ Description:
++   This the datatype for an operator-signature pair.
OperatorSignature(): Public == Private where
  Public == OperatorCategory Identifier with
    signature: % -> Signature
      ++ signature(x) returns the signature of `x'.
    construct: (Identifier,Signature) -> %
      ++ construct(op,sig) construct a signature-operator with
      ++ operator name `op', and signature `sig'.
  Private == add
    construct(o,s) == LIST(o,s)$Lisp
    name x == CAR(x)$Lisp
    signature x == CADR(x)$Lisp
    x = y == EQUAL(x,y)$Lisp
    arity x == (#source signature x)::Arity
    coerce(x: %): OutputForm ==
      infix('_:::OutputForm, name(x)::OutputForm, 
              signature(x)::OutputForm)

@

\section{The SystemPredicate domain}

<<domain SYSPRED SystemPredicate>>=
)abbrev domain SYSPRED SystemPredicate
SystemPredicate(): Public == Private where
  Public == SetCategory
  Private == add
    x = y == EQUAL(x,y)$Lisp
    coerce(x: %): OutputForm ==
      NOT(x)$Lisp => '_false::OutputForm
      EQ(x,'T)$Lisp => '_true::OutputForm
      EQCAR(x,'NOT)$Lisp => not(CADR(x)$Lisp : % :: OutputForm)
@


\section{domain Category}
<<domain CATEGORY Category>>=
import CoercibleTo OutputForm
import CategoryConstructor
)abbrev domain CATEGORY Category
++ Author: Gabriel Dos Reis
++ Date Create: December 20, 2008.
++ Date Last Updated: February 16, 2008.
++ Basic Operations: coerce
++ Related Constructors: 
++ Also See: Type
Category(): Public == Private where
  Public == CoercibleTo OutputForm with
    constructor: % -> CategoryConstructor
      ++ constructor(c) returns the category constructor used to 
      ++ instantiate the category object `c'.
    exportedOperators: % -> List OperatorSignature
      ++ exportedOperators(c) returns the list of all operator signatures
      ++ exported by the category `c', along with their predicates.
    principalAncestors: % -> List ConstructorCall
      ++ principalAncestors(c) returns the list of all category
      ++ forms that are principal ancestors of the the category `c'.
    parents: % -> List ConstructorCall
      ++ parents(c) returns the list of all category forms directly
      ++ extended by the category `c'.
  Private == add
    constructor x ==
      CAR(devaluate(x)$Lisp)$Lisp

    exportedOperators c ==
      [CAR(x)$Lisp@OperatorSignature 
         for x in getCategoryExports(c)$Lisp@List(Syntax)]
    
    principalAncestors c == 
      getCategoryPrincipalAncestors(c)$Lisp

    parents c ==
      [CAR(x)$Lisp@ConstructorCall
         for x in getCategoryParents(c)$Lisp@List(Syntax)]

    coerce x ==
      outputDomainConstructor(x)$Lisp
@

\section{domain Domain}
<<domain DOMAIN Domain>>=
import Void
import ConstructorCall
import DomainConstructor
)abbrev domain DOMAIN Domain
++ Author: Gabriel Dos Reis
++ Date Create: October 18, 2007.
++ Date Last Updated: December 20, 2008.
++ Basic Operations: coerce, reify
++ Related Constructors: Type, Syntax, OutputForm
++ Also See: Type, ConstructorCall
Domain(): Public == Private where
  Public == SetCategory with
    constructor: % -> DomainConstructor
      ++ constructor(d) returns the domain constructor that is
      ++ instantiated to the domain object `d'.
    reify: % -> ConstructorCall
      ++ reify(d) returns the abstract syntax for the domain `x'.

    reflect: ConstructorCall -> %
      ++ reflect cc returns the domain object designated by the
      ++ ConstructorCall syntax `cc'.  The constructor implied 
      ++ by `cc' must be known to the system since it is instantiated.
   
    showSummary: % -> Void
      ++ showSummary(d) prints out implementation detail information
      ++ of domain `d'.

  Private == add
    constructor x ==
      CAR(devaluate(x)$Lisp)$Lisp

    coerce x ==
      outputDomainConstructor(x)$Lisp

    reify x ==
      devaluate(x)$Lisp @ ConstructorCall

    reflect cc ==
      evalDomain(cc)$Lisp @ %

    x = y ==
      reify x = reify y

    showSummary x ==
      showSummary(x)$Lisp

@


\section{License}
<<license>>=
--Copyright (C) 2007-2008, 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>>

<<domain CTORKIND ConstructorKinid>>
<<category CTORCAT ConstructorCategory>>
<<domain CTOR Constructor>>
<<domain CTORCALL ConstructorCall>>
<<domain CATCTOR CategoryConstructor>>
<<domain DOMCTOR DomainConstructor>>

<<domain SIG Signature>>
<<domain OPSIG OperatorSignature>>

<<domain CATEGORY Category>>
<<domain DOMAIN Domain>>
@