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

\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{src/algebra any.spad}
\author{Robert S. Sutor \and Gabriel Dos~Reis}
\maketitle

\begin{abstract}
\end{abstract}

\tableofcontents
\eject

\section{domain NONE None}

<<domain NONE None>>=
import SetCategory
import OutputForm
)abbrev domain NONE None
++ Author:
++ Date Created:
++ Change History:
++ Basic Functions: coerce
++ Related Constructors: NoneFunctions1
++ Also See: Any
++ AMS Classification:
++ Keywords: none, empty
++ Description:
++    \spadtype{None} implements a type with no objects. It is mainly
++    used in technical situations where such a thing is needed (e.g.
++    the interpreter and some of the internal \spadtype{Expression}
++    code).

None():SetCategory == add
    coerce(none:%):OutputForm == "NONE" :: OutputForm
    x:% = y:% == EQ(x,y)$Lisp

@


\section{The Maybe domain}

<<domain MAYBE Maybe>>=
import UnionType
import CoercibleTo OutputForm
import Boolean
)abbrev domain MAYBE Maybe
++ Author: Gabriel Dos Reis
++ Date Created: August 20, 2008
++ Also See: Union(T,"failed")
++ Description:
++   This domain implements the notion of optional vallue, where
++   a computation may fail to produce expected value.
++ Note: Ideally, this domain definition should be a one-liner.
++       That is currently impossible because of mismatch between
++       the `old representation' and `new representation' for domains.
Maybe(T: CoercibleTo OutputForm): Public == Private where
  Public == Join(UnionType,CoercibleTo OutputForm) with
    _case: (%,[| T |]) -> Boolean
      ++ x case T returns true if x is actually a data of type T.
    _case: (%,[| nothing |]) -> Boolean
      ++ x case nothing evaluates true if the value for x is missing.
    coerce: T -> % 
      ++ x::T injects the value x into %.
    coerce: % -> T
      ++ x::T tries to extract the value of T from the computation x.
      ++ Produces a runtime error when the computation fails.
    autoCoerce: % -> T
      ++ same as above but implicitly called by the compiler.
    nothing: %
      ++ represents failure.
  Private == add
    Rep == Union(T,"nothing")
    nothing == per("nothing"::Rep)
    coerce(x: T): % == per(x::Rep)
    coerce(x: %): T == rep(x)::T
    autoCoerce x == rep(x)::T
    x case T == rep x case T
    x case nothing == rep x case "nothing"
    coerce(x: %): OutputForm == 
      x case T => x::T::OutputForm
      paren(empty()$OutputForm)$OutputForm
@



\section{package NONE1 NoneFunctions1}

<<package NONE1 NoneFunctions1>>=
import None
)abbrev package NONE1 NoneFunctions1
++ Author:
++ Date Created:
++ Change History:
++ Basic Functions: coerce
++ Related Constructors: None
++ Also See:
++ AMS Classification:
++ Keywords:
++ Description:
++   \spadtype{NoneFunctions1} implements functions on \spadtype{None}.
++   It particular it includes a particulary dangerous coercion from
++   any other type to \spadtype{None}.

NoneFunctions1(S:Type): Exports == Implementation where
  Exports ==> with
    coerce: S -> None
      ++ coerce(x) changes \spad{x} into an object of type
      ++ \spadtype{None}.

  Implementation ==> add
    coerce(s:S):None == s pretend None

@

\section{domain ANY Any}

<<domain ANY Any>>=
import SetCategory
import Boolean
import String
import OutputForm
import SExpression
import None
)abbrev domain ANY Any
++ Author: Robert S. Sutor
++ Date Created:
++ Change History:
++ Basic Functions: any, domainOf, objectOf, dom, obj, showTypeInOutput
++ Related Constructors: AnyFunctions1
++ Also See: None
++ AMS Classification:
++ Keywords:
++ Description:
++   \spadtype{Any} implements a type that packages up objects and their
++   types in objects of \spadtype{Any}. Roughly speaking that means
++   that if \spad{s : S} then when converted to \spadtype{Any}, the new
++   object will include both the original object and its type. This is
++   a way of converting arbitrary objects into a single type without
++   losing any of the original information. Any object can be converted
++   to one of \spadtype{Any}.

Any(): SetCategory with
        any             : (SExpression, None) -> %
          ++ any(type,object) is a technical function for creating
          ++ an object of \spadtype{Any}. Arugment \spad{type} is a \spadgloss{LISP} form
          ++ for the type of \spad{object}.
        domainOf        : % -> OutputForm
          ++ domainOf(a) returns a printable form of the type of the
          ++ original object that was converted to \spadtype{Any}.
        objectOf        : % -> OutputForm
          ++ objectOf(a) returns a printable form of the
          ++ original object that was converted to \spadtype{Any}.
        dom             : % -> SExpression
          ++ dom(a) returns a \spadgloss{LISP} form of the type of the
          ++ original object that was converted to \spadtype{Any}.
        obj             : % -> None
          ++ obj(a) essentially returns the original object that was
          ++ converted to \spadtype{Any} except that the type is forced
          ++ to be \spadtype{None}.
        showTypeInOutput: Boolean -> String
          ++ showTypeInOutput(bool) affects the way objects of
          ++ \spadtype{Any} are displayed. If \spad{bool} is true
          ++ then the type of the original object that was converted
          ++ to \spadtype{Any} will be printed. If \spad{bool} is
          ++ false, it will not be printed.

 == add
     Rep := Record(dm: SExpression, ob: None)

     printTypeInOutputP:Reference(Boolean) := ref false

     obj x      == x.ob
     dom x      == x.dm
     domainOf x == x.dm pretend OutputForm
     x = y      == (x.dm = y.dm) and EQ(x.ob, y.ob)$Lisp

     objectOf(x : %) : OutputForm ==
       spad2BootCoerce(x.ob, x.dm,
          list("OutputForm"::Symbol)$List(Symbol))$Lisp

     showTypeInOutput(b : Boolean) : String ==
      printTypeInOutputP := ref b
      b=> "Type of object will be displayed in output of a member of Any"
      "Type of object will not be displayed in output of a member of Any"

     coerce(x):OutputForm ==
       obj1 : OutputForm := objectOf x
       not deref printTypeInOutputP => obj1
       dom1 :=
         p:Symbol := prefix2String(devaluate(x.dm)$Lisp)$Lisp
         atom?(p pretend SExpression) => list(p)$List(Symbol)
         list(p)$Symbol
       hconcat cons(obj1,
         cons(":"::OutputForm, [a::OutputForm for a in dom1]))

     any(domain, object) ==
       (isValidType(domain)$Lisp)@Boolean => [domain, object]
       domain := devaluate(domain)$Lisp
       (isValidType(domain)$Lisp)@Boolean => [domain, object]
       error "function any must have a domain as first argument"

@

\section{package ANY1 AnyFunctions1}

<<package ANY1 AnyFunctions1>>=
import Type
import Boolean
import Any
)abbrev package ANY1 AnyFunctions1
++ Author:
++ Date Created:
++ Change History:
++ Basic Functions:  coerce, retractIfCan, retractable?, retract
++ Related Constructors: Any
++ Also See:
++ AMS Classification:
++ Keywords:
++ Description:
++   \spadtype{AnyFunctions1} implements several utility functions for
++   working with \spadtype{Any}. These functions are used to go back
++   and forth between objects of \spadtype{Any} and objects of other
++   types.

AnyFunctions1(S:Type): with
        coerce      : S -> Any
          ++ coerce(s) creates an object of \spadtype{Any} from the
          ++ object \spad{s} of type \spad{S}.
        retractIfCan: Any -> Union(S, "failed")
          ++ retractIfCan(a) tries change \spad{a} into an object
          ++ of type \spad{S}. If it can, then such an object is
          ++ returned. Otherwise, "failed" is returned.
        retractable?: Any -> Boolean
          ++ retractable?(a) tests if \spad{a} can be converted
          ++ into an object of type \spad{S}.
        retract     : Any -> S
          ++ retract(a) tries to convert \spad{a} into an object of
          ++ type \spad{S}. If possible, it returns the object.
          ++ Error: if no such retraction is possible.

    == add
        import NoneFunctions1(S)

        Sexpr:SExpression := devaluate(S)$Lisp

        retractable? a  == dom(a) = Sexpr
        coerce(s:S):Any == any(Sexpr, s::None)

        retractIfCan a ==
            retractable? a => obj(a) pretend S
            "failed"

        retract a ==
            retractable? a => obj(a) pretend S
            error "Cannot retract value."

@

\section{domain PROPERTY Property}

<<domain PROPERTY Property>>=
import CoercibleTo OutputForm
import Symbol
import SExpression
)abbrev domain PROPERTY Property
++ Author: Gabriel Dos Reis
++ Date Created: October 24, 2007
++ Date Last Modified: January 18, 2008.
++ An `Property' is a pair of name and value.  
Property(): Public == Private where
  Public ==> CoercibleTo(OutputForm) with
    name: % -> Symbol         
      ++ name(p) returns the name of property p
    value: % -> SExpression   
      ++ value(p) returns value of property p
    property: (Symbol, SExpression) -> %
      ++ property(n,val) constructs a property with name `n' and
      ++ value `val'.
  
  Private ==> add
    rep(x: %): SExpression ==
      x pretend SExpression

    per(x: SExpression): % ==
      x pretend %

    name x == 
      -- Note: It is always well defined to take the `car' here
      -- because there is no way we could have type safely 
      -- constructed a null property.
      symbol car rep x

    value x ==
      cdr rep x

    property(n,val) ==
      per CONS(n,val)$Lisp
 
    coerce x ==
      v := value x
      val: OutputForm
      if null? v then val := false::OutputForm
      else if EQ(v, true)$Lisp : Boolean
           then val := true::OutputForm
           else val := v::OutputForm
      
      bracket(infix(outputForm '_=_>, outputForm name x, 
                val)$OutputForm)$OutputForm

@

\section{domain BINDING Binding}

<<domain BINDING Binding>>=
import CoercibleTo OutputForm
import Symbol
import List Property
)abbrev domain BINDING Binding
++ Author: Gabriel Dos Reis
++ Date Created: October 24, 2007
++ Date Last Modified: January 18, 2008.
++ A `Binding' is a name asosciated with a collection of properties.
Binding(): Public == Private where
  Public ==> CoercibleTo(OutputForm) with
    name: % -> Symbol               
      ++ name(b) returns the name of binding b
    properties: % -> List Property  
      ++ properties(b) returns the properties associated with binding b.
    binding: (Symbol, List Property) -> %
      ++ binding(n,props) constructs a binding with name `n' and 
      ++ property list `props'.

  Private ==> add
    rep(x: %): SExpression ==
      x pretend SExpression

    per(x: SExpression): % ==
      x pretend %

    name b ==
      -- this is well defined because there is no way one could
      -- type safely ask the name of an inexisting binding.
      symbol car rep b

    properties b ==
      (cdr rep b) pretend List(Property)

    binding(n,props) ==
      per CONS(n,props)$Lisp

    coerce b ==
      null? rep b => empty()$OutputForm
      rarrow(outputForm name b, (properties b)::OutputForm)$OutputForm
@

\section{domain CONTOUR Contour}

<<domain CONTOUR Contour>>=
import CoercibleTo OutputForm
import Symbol
import Binding
import List Binding
)abbrev domain CONTOUR Contour
++ Author: Gabriel Dos Reis
++ Date Created: October 24, 2007
++ Date Last Modified: January 18, 2008.
++ A `Contour' a list of bindings making up a `virtual scope'.
Contour(): Public == Private where
  Public ==> CoercibleTo(OutputForm) with
    bindings: % -> List Binding     
      ++ bindings(c) returns the list of bindings in countour c.
    push: (Binding,%) -> %
      ++ push(c,b) augments the contour with binding `b'.
    findBinding: (Symbol,%) -> Union(Binding, "failed")
      ++ findBinding(c,n) returns the first binding associated with `n'.
      ++ Otherwise `failed'.

  Private ==> add
    bindings c ==
      c pretend List(Binding)

    findBinding(n,c) ==
      for b in bindings c repeat
        EQ(n, name b)$Lisp => return b
      "failed"

    push(b,c) ==
      CONS(b,c)$Lisp pretend %

    coerce c ==
      (bindings c)::OutputForm
@

\section{domain SCOPE Scope}

<<domain SCOPE Scope>>=
import CoercibleTo OutputForm
import Binding
import List Contour
)abbrev domain SCOPE Scope
++ Author: Gabriel Dos Reis
++ Date Created: October 24, 2007
++ Date Last Modified: January 18, 2008.
++ A `Scope' is a sequence of contours.
Scope(): Public == Private where
  Public ==> CoercibleTo(OutputForm) with
    empty: () -> %
      ++ empty() returns an empty scope.
    contours: % -> List Contour     
      ++ contours(s) returns the list of contours in scope s.
    findBinding: (Symbol,%) -> Union(Binding, "failed")
      ++ findBinding(n,s) returns the first binding of `n' in `s'; 
      ++ otherwise `failed'.
    pushNewContour: (Binding,%) -> %
      ++ pushNewContour(b,s) pushs a new contour with sole binding `b'.
    currentScope: () -> %
      ++ currentScope() returns the scope currently in effect
    currentCategoryFrame: () -> %
      ++ currentCategoryFrame() returns the category frame currently
      ++ in effect.

  Private ==> add
    import Contour
    Rep == List Contour
    empty() ==
      per NIL$Lisp

    contours s ==
      rep s

    findBinding(n,s) ==
      for c in contours s repeat
        b := findBinding(n,c)$Contour
        not b case "failed" => return b
      "failed"

    pushNewContour(b,s) ==
      c := LIST(b)$Lisp
      CONS(c,s)$Lisp @ %

    currentScope() ==
      CAR(_$e$Lisp)$Lisp @ %

    currentCategoryFrame() ==
      CAR(_$CategoryFrame$Lisp)$Lisp @ %

    coerce s ==
      (contours s)::OutputForm
@

\section{domain ENV Environment}

<<domain ENV Environment>>=
import CoercibleTo OutputForm
import Symbol
import List Scope
import List Property
)abbrev domain ENV Environment
++ Author: Gabriel Dos Reis
++ Date Created: October 24, 2007
++ Date Last Modified: January 19, 2008.
++ An `Environment' is a stack of scope.
Environment(): Public == Private where
  Public ==> CoercibleTo(OutputForm) with
    empty: () -> %
      ++ empty() constructs an empty environment
    scopes: % -> List Scope     
      ++ scopes(e) returns the stack of scopes in environment e.
    getProperty: (Symbol, Symbol, %) -> Union(SExpression, "failed")
      ++ getProperty(n,p,e) returns the value of property with name `p'
      ++ for the symbol `n' in environment `e'. Otherwise, `failed'.
    setProperty!: (Symbol, Symbol, SExpression, %) -> %
      ++ setProperty!(n,p,v,e) binds the property `(p,v)' to `n'
      ++ in the topmost scope of `e'.
    getProperties: (Symbol, %) -> Union(List Property, "failed")
      ++ getBinding(n,e) returns the list of properties of `n' in
      ++ e; otherwise `failed'.
    setProperties!: (Symbol, List Property, %) -> %
      ++ setBinding!(n,props,e) set the list of properties of `n' 
      ++ to `props' in `e'.
    currentEnv: () -> %        
      ++ the current normal environment in effect.
    categoryFrame: () -> %  
       ++ the current category environment in the interpreter.

  Private ==> add
    Rep == List Scope
    empty() ==
      per NIL$Lisp

    scopes e ==
      rep e

    getProperty(n,p,e) ==
      v := get(n,p,e)$Lisp
      null? v => "failed"
      v 

    setProperty!(n,p,v,e) ==
      put(n,p,v,e)$Lisp @ %

    getProperties(n,e) ==
      b: SExpression := getProplist(n,e)$Lisp
      null? b => "failed"
      b pretend List(Property)

    setProperties!(n,b,e) ==
      addBinding(n,b,e)$Lisp @ %

    currentEnv() ==
      _$e$Lisp @ %

    categoryFrame() ==
      _$CategoryFrame$Lisp @ %

    coerce e ==
      (scopes e)::OutputForm
@


\section{License}

<<license>>=
--Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd.
--All rights reserved.
--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>>

-- Any and None complete the type lattice. They are also used in the
-- interpreter in various situations. For example, it is always possible
-- to resolve two types in the interpreter because at worst the answer
-- may be Any.

<<domain NONE None>>
<<domain MAYBE Maybe>>
<<package NONE1 NoneFunctions1>>
<<domain ANY Any>>
<<package ANY1 AnyFunctions1>>

<<domain PROPERTY Property>>
<<domain BINDING Binding>>
<<domain CONTOUR Contour>>
<<domain SCOPE Scope>>
<<domain ENV Environment>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}