Use Functorial more often.

14 files changed, 65 insertions, 87 deletions

diff --git a/src/algebra/Makefile.am b/src/algebra/Makefile.am
index 4df8f821..49756d95 100644
--- a/src/algebra/Makefile.am
+++ b/src/algebra/Makefile.am
@@ -271,11 +271,12 @@ strap-0/MATCAT.$(FASLEXT): strap-0/ARR2CAT.$(FASLEXT) \
 	strap-0/EUCDOM.$(FASLEXT) strap-0/INTDOM.$(FASLEXT) \
 	strap-0/FIELD.$(FASLEXT) strap-0/FINAGG.$(FASLEXT)
 
-strap-0/IDPC.$(FASLEXT): strap-0/SETCAT.$(FASLEXT)
+strap-0/IDPC.$(FASLEXT): strap-0/SETCAT.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT)
 
 strap-0/AMR.$(FASLEXT): strap-0/RING.$(FASLEXT) strap-0/BMODULE.$(FASLEXT) \
 	strap-0/ALGEBRA.$(FASLEXT) strap-0/FIELD.$(FASLEXT) \
-	strap-0/CHARZ.$(FASLEXT) strap-0/CHARNZ.$(FASLEXT)
+	strap-0/CHARZ.$(FASLEXT) strap-0/CHARNZ.$(FASLEXT) \
+	strap-0/FUNCTOR.$(FASLEXT)
 
 strap-0/FAMR.$(FASLEXT): strap-0/AMR.$(FASLEXT) \
 	strap-0/FRETRCT.$(FASLEXT)
@@ -372,7 +373,7 @@ strap-0/SUP.$(FASLEXT): strap-0/UPOLYC.$(FASLEXT) strap-0/PR.$(FASLEXT)
 
 strap-0/TABLE.$(FASLEXT): strap-0/TBAGG.$(FASLEXT)
 
-strap-0/EQ.$(FASLEXT): strap-0/TYPE.$(FASLEXT) \
+strap-0/EQ.$(FASLEXT): strap-0/TYPE.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT) \
 	strap-0/IEVALAB.$(FASLEXT) strap-0/KOERCE.$(FASLEXT) \
 	strap-0/BOOLEAN.$(FASLEXT) strap-0/EVALAB.$(FASLEXT) \
 	strap-0/ABELSG.$(FASLEXT) strap-0/ABELGRP.$(FASLEXT) \
@@ -393,7 +394,7 @@ strap-0/SYNTAX.$(FASLEXT): strap-0/UTYPE.$(FASLEXT) \
 	strap-0/IDENT.$(FASLEXT) strap-0/STRING.$(FASLEXT) \
 	strap-0/KOERCE.$(FASLEXT) strap-0/INFORM.$(FASLEXT)
 
-strap-0/FR.$(FASLEXT): strap-0/INTDOM.$(FASLEXT) \
+strap-0/FR.$(FASLEXT): strap-0/INTDOM.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT) \
 	strap-0/DIFEXT.$(FASLEXT) strap-0/FEVALAB.$(FASLEXT) \
 	strap-0/ALGEBRA.$(FASLEXT) strap-0/FRETRCT.$(FASLEXT)
 
@@ -570,11 +571,12 @@ strap-1/HYPCAT.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 strap-1/AHYP.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 strap-1/ELEMFUN.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 
-strap-1/IDPC.$(FASLEXT): strap-1/SETCAT.$(FASLEXT)
+strap-1/IDPC.$(FASLEXT): strap-1/SETCAT.$(FASLEXT) strap-1/FUNCTOR.$(FASLEXT)
 
 strap-1/AMR.$(FASLEXT): strap-1/RING.$(FASLEXT) strap-1/BMODULE.$(FASLEXT) \
 	strap-1/ALGEBRA.$(FASLEXT) strap-1/FIELD.$(FASLEXT) \
-	strap-1/CHARZ.$(FASLEXT) strap-1/CHARNZ.$(FASLEXT)
+	strap-1/CHARZ.$(FASLEXT) strap-1/CHARNZ.$(FASLEXT) \
+	strap-1/FUNCTOR.$(FASLEXT)
 
 strap-1/FAMR.$(FASLEXT): strap-1/AMR.$(FASLEXT) \
 	strap-1/FRETRCT.$(FASLEXT)
@@ -967,11 +969,12 @@ strap-2/AHYP.$(FASLEXT): strap-2/TYPE.$(FASLEXT)
 strap-2/ELEMFUN.$(FASLEXT): strap-2/TYPE.$(FASLEXT)
 
 
-strap-2/IDPC.$(FASLEXT): strap-2/SETCAT.$(FASLEXT)
+strap-2/IDPC.$(FASLEXT): strap-2/SETCAT.$(FASLEXT) strap-2/FUNCTOR.$(FASLEXT)
 
 strap-2/AMR.$(FASLEXT): strap-2/RING.$(FASLEXT) strap-2/BMODULE.$(FASLEXT) \
 	strap-2/ALGEBRA.$(FASLEXT) strap-2/FIELD.$(FASLEXT) \
-	strap-2/CHARZ.$(FASLEXT) strap-2/CHARNZ.$(FASLEXT)
+	strap-2/CHARZ.$(FASLEXT) strap-2/CHARNZ.$(FASLEXT) \
+	strap-2/FUNCTOR.$(FASLEXT)
 
 strap-2/FAMR.$(FASLEXT): strap-2/AMR.$(FASLEXT) \
 	strap-2/FRETRCT.$(FASLEXT)
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index ad03d585..974aa974 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -1761,11 +1761,12 @@ strap-0/MATCAT.$(FASLEXT): strap-0/ARR2CAT.$(FASLEXT) \
 	strap-0/EUCDOM.$(FASLEXT) strap-0/INTDOM.$(FASLEXT) \
 	strap-0/FIELD.$(FASLEXT) strap-0/FINAGG.$(FASLEXT)
 
-strap-0/IDPC.$(FASLEXT): strap-0/SETCAT.$(FASLEXT)
+strap-0/IDPC.$(FASLEXT): strap-0/SETCAT.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT)
 
 strap-0/AMR.$(FASLEXT): strap-0/RING.$(FASLEXT) strap-0/BMODULE.$(FASLEXT) \
 	strap-0/ALGEBRA.$(FASLEXT) strap-0/FIELD.$(FASLEXT) \
-	strap-0/CHARZ.$(FASLEXT) strap-0/CHARNZ.$(FASLEXT)
+	strap-0/CHARZ.$(FASLEXT) strap-0/CHARNZ.$(FASLEXT) \
+	strap-0/FUNCTOR.$(FASLEXT)
 
 strap-0/FAMR.$(FASLEXT): strap-0/AMR.$(FASLEXT) \
 	strap-0/FRETRCT.$(FASLEXT)
@@ -1862,7 +1863,7 @@ strap-0/SUP.$(FASLEXT): strap-0/UPOLYC.$(FASLEXT) strap-0/PR.$(FASLEXT)
 
 strap-0/TABLE.$(FASLEXT): strap-0/TBAGG.$(FASLEXT)
 
-strap-0/EQ.$(FASLEXT): strap-0/TYPE.$(FASLEXT) \
+strap-0/EQ.$(FASLEXT): strap-0/TYPE.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT) \
 	strap-0/IEVALAB.$(FASLEXT) strap-0/KOERCE.$(FASLEXT) \
 	strap-0/BOOLEAN.$(FASLEXT) strap-0/EVALAB.$(FASLEXT) \
 	strap-0/ABELSG.$(FASLEXT) strap-0/ABELGRP.$(FASLEXT) \
@@ -1883,7 +1884,7 @@ strap-0/SYNTAX.$(FASLEXT): strap-0/UTYPE.$(FASLEXT) \
 	strap-0/IDENT.$(FASLEXT) strap-0/STRING.$(FASLEXT) \
 	strap-0/KOERCE.$(FASLEXT) strap-0/INFORM.$(FASLEXT)
 
-strap-0/FR.$(FASLEXT): strap-0/INTDOM.$(FASLEXT) \
+strap-0/FR.$(FASLEXT): strap-0/INTDOM.$(FASLEXT) strap-0/FUNCTOR.$(FASLEXT) \
 	strap-0/DIFEXT.$(FASLEXT) strap-0/FEVALAB.$(FASLEXT) \
 	strap-0/ALGEBRA.$(FASLEXT) strap-0/FRETRCT.$(FASLEXT)
 
@@ -2060,11 +2061,12 @@ strap-1/HYPCAT.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 strap-1/AHYP.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 strap-1/ELEMFUN.$(FASLEXT): strap-1/TYPE.$(FASLEXT)
 
-strap-1/IDPC.$(FASLEXT): strap-1/SETCAT.$(FASLEXT)
+strap-1/IDPC.$(FASLEXT): strap-1/SETCAT.$(FASLEXT) strap-1/FUNCTOR.$(FASLEXT)
 
 strap-1/AMR.$(FASLEXT): strap-1/RING.$(FASLEXT) strap-1/BMODULE.$(FASLEXT) \
 	strap-1/ALGEBRA.$(FASLEXT) strap-1/FIELD.$(FASLEXT) \
-	strap-1/CHARZ.$(FASLEXT) strap-1/CHARNZ.$(FASLEXT)
+	strap-1/CHARZ.$(FASLEXT) strap-1/CHARNZ.$(FASLEXT) \
+	strap-1/FUNCTOR.$(FASLEXT)
 
 strap-1/FAMR.$(FASLEXT): strap-1/AMR.$(FASLEXT) \
 	strap-1/FRETRCT.$(FASLEXT)
@@ -2455,11 +2457,12 @@ strap-2/HYPCAT.$(FASLEXT): strap-2/TYPE.$(FASLEXT)
 strap-2/AHYP.$(FASLEXT): strap-2/TYPE.$(FASLEXT)
 strap-2/ELEMFUN.$(FASLEXT): strap-2/TYPE.$(FASLEXT)
 
-strap-2/IDPC.$(FASLEXT): strap-2/SETCAT.$(FASLEXT)
+strap-2/IDPC.$(FASLEXT): strap-2/SETCAT.$(FASLEXT) strap-2/FUNCTOR.$(FASLEXT)
 
 strap-2/AMR.$(FASLEXT): strap-2/RING.$(FASLEXT) strap-2/BMODULE.$(FASLEXT) \
 	strap-2/ALGEBRA.$(FASLEXT) strap-2/FIELD.$(FASLEXT) \
-	strap-2/CHARZ.$(FASLEXT) strap-2/CHARNZ.$(FASLEXT)
+	strap-2/CHARZ.$(FASLEXT) strap-2/CHARNZ.$(FASLEXT) \
+	strap-2/FUNCTOR.$(FASLEXT)
 
 strap-2/FAMR.$(FASLEXT): strap-2/AMR.$(FASLEXT) \
 	strap-2/FRETRCT.$(FASLEXT)
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet
index df09311f..ae602dc3 100644
--- a/src/algebra/aggcat.spad.pamphlet
+++ b/src/algebra/aggcat.spad.pamphlet
@@ -2709,7 +2709,7 @@ BitAggregate(): Category ==
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
---Copyright (C) 2007-2010, Gabriel Dos Reis.
+--Copyright (C) 2007-2013, Gabriel Dos Reis.
 --All rights reserved.
 --
 --Redistribution and use in source and binary forms, with or without
diff --git a/src/algebra/array2.spad.pamphlet b/src/algebra/array2.spad.pamphlet
index 6a7330dc..00450e5d 100644
--- a/src/algebra/array2.spad.pamphlet
+++ b/src/algebra/array2.spad.pamphlet
@@ -15,7 +15,7 @@
 ++ Two dimensional array categories and domains
 ++ Author:
 ++ Date Created: 27 October 1989
-++ Date Last Updated: May 16, 2013
+++ Date Last Updated: May 19, 2013
 ++ Keywords: array, data structure
 ++ Examples:
 ++ References:
@@ -85,10 +85,6 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where
     setColumn!: (%,Integer,Col) -> %
       ++ setColumn!(m,j,v) sets to jth column of m to v
 --% Map and Zip
-    map: (R -> R,%) -> %
-      ++ map(f,a) returns \spad{b}, where \spad{b(i,j) = f(a(i,j))} for all \spad{i, j}
-    map!: (R -> R,%) -> %
-      ++ map!(f,a)  assign \spad{a(i,j)} to \spad{f(a(i,j))} for all \spad{i, j}
     map:((R,R) -> R,%,%) -> %
       ++ map(f,a,b) returns \spad{c}, where \spad{c(i,j) = f(a(i,j),b(i,j))}
       ++ for all \spad{i, j}
diff --git a/src/algebra/derham.spad.pamphlet b/src/algebra/derham.spad.pamphlet
index 1ff71c4c..babf6987 100644
--- a/src/algebra/derham.spad.pamphlet
+++ b/src/algebra/derham.spad.pamphlet
@@ -112,7 +112,7 @@ ExtAlgBasis(): Export == Implement where
 )abbrev domain ANTISYM AntiSymm
 ++   Author: Larry A. Lambe
 ++   Date     : 01/26/91.
-++   Revised  : 30 Nov 94
+++   Revised  : May 19, 2013.
 ++
 ++   based on AntiSymmetric '89
 ++
@@ -134,7 +134,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where
   coef ==> c
   Term ==> Record(k:EAB,c:R)
  
-  Export == Join(LALG(R), RetractableTo(R)) with
+  Export == Join(LALG(R),RetractableTo(R),Functorial R) with
       leadingCoefficient : %           -> R
 	++ leadingCoefficient(p) returns the leading
 	++ coefficient of antisymmetric polynomial p.
@@ -164,10 +164,6 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where
 	++  i.e., if degree(p) = 0.
       degree             : %           -> NNI
 	++  degree(p) returns the homogeneous degree of p.
-      map                : (R -> R, %) -> %
-	++  map(f,p) changes each coefficient of p by the
-	++  application of f.
-
 
 --    1 corresponds to the empty monomial Nul = [0,...,0]
 --    from EAB.  In terms of the exterior algebra on X,
@@ -308,7 +304,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where
 )abbrev domain DERHAM DeRhamComplex
 ++ Author: Larry A. Lambe
 ++ Date    : 01/26/91.
-++ Revised : 12/01/91.
+++ Revised : May 19, 2013.
 ++
 ++ based on code from '89 (AntiSymmetric)
 ++
@@ -332,7 +328,7 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where
   O       ==> OutputForm
   R       ==> Expression(CoefRing)
  
-  Export == Join(LALG(R), RetractableTo(R)) with
+  Export == Join(LALG(R), RetractableTo(R),Functorial R) with
       leadingCoefficient : %           -> R
 	++ leadingCoefficient(df) returns the leading
 	++ coefficient of differential form df.
@@ -358,9 +354,6 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where
 	++  i.e., if degree(df) = 0.
       degree             : %           -> I
 	++  degree(df) returns the homogeneous degree of differential form df.
-      map                : (R -> R, %) -> %
-	++  map(f,df) replaces each coefficient x of differential 
-        ++  form df by \spad{f(x)}.
       totalDifferential    : R -> %
 	++  totalDifferential(x) returns the total differential 
 	++  (gradient) form for element x.
@@ -417,6 +410,8 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, Gabriel Dos Reis.
+--All rights reversed.
 --
 --Redistribution and use in source and binary forms, with or without
 --modification, are permitted provided that the following conditions are
diff --git a/src/algebra/equation2.spad.pamphlet b/src/algebra/equation2.spad.pamphlet
index 7b810399..3f6dc30c 100644
--- a/src/algebra/equation2.spad.pamphlet
+++ b/src/algebra/equation2.spad.pamphlet
@@ -32,7 +32,7 @@ import List
 --FOR THE BENEFIT  OF LIBAX0 GENERATION
 ++ Author: Stephen M. Watt, enhancements by Johannes Grabmeier
 ++ Date Created: April 1985
-++ Date Last Updated: June 3, 1991; September 2, 1992
+++ Date Last Updated: May 19, 2013.
 ++ Basic Operations: =
 ++ Related Domains:
 ++ Also See:
@@ -50,7 +50,7 @@ import List
 
 Equation(S: Type): public == private where
   Ex ==> OutputForm
-  public ==> Type with
+  public == Functorial S with
     =: (S, S) -> $
         ++ a=b creates an equation.
     equation: (S, S) -> $
@@ -61,9 +61,6 @@ Equation(S: Type): public == private where
         ++ lhs(eqn) returns the left hand side of equation eqn.
     rhs: $ -> S
         ++ rhs(eqn) returns the right hand side of equation eqn.
-    map: (S -> S, $) -> $
-        ++ map(f,eqn) constructs a new equation by applying f to both
-        ++ sides of eqn.
     if S has InnerEvalable(Symbol,S) then
              InnerEvalable(Symbol,S)
     if S has SetCategory then
@@ -273,7 +270,7 @@ import Equation
 )abbrev category FEVALAB FullyEvalableOver
 ++ Author:
 ++ Date Created:
-++ Date Last Updated: June 3, 1991
+++ Date Last Updated: May 19, 2013
 ++ Basic Operations:
 ++ Related Domains: Equation
 ++ Also See:
@@ -284,9 +281,7 @@ import Equation
 ++ Description:
 ++    This category provides a selection of evaluation operations
 ++    depending on what the argument type R provides.
-FullyEvalableOver(R:SetCategory): Category == with
-    map: (R -> R, $) -> $
-        ++ map(f, ex) evaluates ex, applying f to values of type R in ex.
+FullyEvalableOver(R:SetCategory): Category == Functorial R with
     if R has Eltable(R, R) then Eltable(R, $)
     if R has Evalable(R) then Evalable(R)
     if R has InnerEvalable(Symbol, R) then InnerEvalable(Symbol, R)
@@ -307,6 +302,8 @@ FullyEvalableOver(R:SetCategory): Category == with
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index c0228db0..983557ab 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -551,6 +551,7 @@
   (|FullyRetractableTo| . FRETRCT)
   (|FunctionFieldCategory| . FFCAT)
   (|FunctionSpace| . FS)
+  (|Functorial| . FUNCTOR)
   (|GcdDomain| . GCDDOM)
   (|GradedAlgebra| . GRALG)
   (|GradedModule| . GRMOD)
diff --git a/src/algebra/fr.spad.pamphlet b/src/algebra/fr.spad.pamphlet
index babaa801..fcdbf432 100644
--- a/src/algebra/fr.spad.pamphlet
+++ b/src/algebra/fr.spad.pamphlet
@@ -16,6 +16,7 @@
 )abbrev domain FR Factored
 ++ Author: Robert S. Sutor
 ++ Date Created: 1985
+++ Date Last Modified: May 19, 2013.
 ++ Change History:
 ++   21 Jan 1991  J Grabmeier     Corrected a bug in exquo.
 ++   16 Aug 1994  R S Sutor       Improved convert to InputForm
@@ -48,8 +49,8 @@ Factored(R: IntegralDomain): Exports == Implementation where
   FF     ==> Record(flg: fUnion, fctr: R, xpnt: Integer)
   SRFE   ==> Set(Record(factor:R, exponent:Integer))
 
-  Exports ==> Join(IntegralDomain, DifferentialExtension R, Algebra R,
-                   FullyEvalableOver R, FullyRetractableTo R) with
+  Exports == Join(IntegralDomain, DifferentialExtension R, Algebra R,
+               FullyEvalableOver R, FullyRetractableTo R,Functorial R) with
     expand: % -> R
       ++ expand(f) multiplies the unit and factors together, yielding an
       ++ "unfactored" object. Note: this is purposely not called \spadfun{coerce} which would
@@ -126,12 +127,6 @@ Factored(R: IntegralDomain): Exports == Implementation where
       ++ For example, when working with factored integers, this operation will
       ++ ensure that the bases are all positive integers.
 
-    map:     (R -> R, %) -> %
-      ++ map(fn,u) maps the function \userfun{fn} across the factors of
-      ++ \spadvar{u} and creates a new factored object. Note: this clears
-      ++ the information flags (sets them to "nil") because the effect of
-      ++ \userfun{fn} is clearly not known in general.
-
     -- the following operations are conditional on R
 
     if R has GcdDomain then GcdDomain
@@ -621,6 +616,8 @@ FactoredFunctions2(R, S): Exports == Implementation where
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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
diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet
index 1f3e6151..d97010d9 100644
--- a/src/algebra/indexedp.spad.pamphlet
+++ b/src/algebra/indexedp.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev category IDPC IndexedDirectProductCategory
 ++ Author: James Davenport, Gabriel Dos Reis
 ++ Date Created:
-++ Date Last Updated: June 28, 2010
+++ Date Last Updated: May 19, 2013.
 ++ Basic Functions:
 ++ Related Constructors:
 ++ Also See:
@@ -26,11 +26,8 @@
 ++ respect to an ordered indexing set.
 
 IndexedDirectProductCategory(A:BasicType,S:OrderedType): Category ==
-  Join(BasicType,ConvertibleFrom List IndexedProductTerm(A,S)) with
+  Join(BasicType,Functorial A,ConvertibleFrom List IndexedProductTerm(A,S)) with
     if A has SetCategory and S has SetCategory then SetCategory
-    map:           (A -> A, %) -> %
-       ++ map(f,z) returns the new element created by applying the
-       ++ function f to each component of the direct product element z.
     monomial:         (A, S) -> %
        ++ monomial(a,s) constructs a direct product element with the s
        ++ component set to \spad{a}
diff --git a/src/algebra/ituple.spad.pamphlet b/src/algebra/ituple.spad.pamphlet
index f441c9e8..0cf9c839 100644
--- a/src/algebra/ituple.spad.pamphlet
+++ b/src/algebra/ituple.spad.pamphlet
@@ -20,7 +20,7 @@ import Stream
 ++ Infinite tuples for the interpreter
 ++ Author: Clifton J. Williamson
 ++ Date Created: 16 February 1990
-++ Date Last Updated: February 5, 2011
+++ Date Last Updated: May 13, 2013.
 ++ Keywords:
 ++ Examples:
 ++ References:
@@ -28,10 +28,7 @@ import Stream
 ++   This package implements 'infinite tuples' for the interpreter.
 ++   The representation is a stream.
 InfiniteTuple(S:Type): Exports == Implementation where
-  Exports == CoercibleTo OutputForm with
-    map: (S -> S, %) -> %
-      ++ map(f,t) replaces the tuple t
-      ++ by \spad{[f(x) for x in t]}.
+  Exports == Join(Functorial S,CoercibleTo OutputForm) with
     filterWhile: (S -> Boolean, %) -> %
       ++ filterWhile(p,t) returns \spad{[x for x in t while p(x)]}.
     filterUntil: (S -> Boolean, %) -> %
@@ -113,6 +110,8 @@ InfiniteTupleFunctions3(A:Type, B:Type,C:Type): Exports
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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
diff --git a/src/algebra/matcat.spad.pamphlet b/src/algebra/matcat.spad.pamphlet
index 6b4a56d5..f183082a 100644
--- a/src/algebra/matcat.spad.pamphlet
+++ b/src/algebra/matcat.spad.pamphlet
@@ -550,7 +550,7 @@ MatrixCategory(R,Row,Col): Category == Definition where
 )abbrev category RMATCAT RectangularMatrixCategory
 ++ Authors: Grabmeier, Gschnitzer, Williamson
 ++ Date Created: 1987
-++ Date Last Updated: July 1990
+++ Date Last Updated: May 19, 2013.
 ++ Basic Operations:
 ++ Related Domains: RectangularMatrix(m,n,R)
 ++ Also See:
@@ -643,9 +643,6 @@ RectangularMatrixCategory(m,n,R,Row,Col): Category == Definition where
       ++ Error: if the index outside the proper range.
 
 --% Map and Zip
-
-    map: (R -> R,%) -> %
-      ++ \spad{map(f,a)} returns b, where \spad{b(i,j) = a(i,j)} for all i, j.
     map:((R,R) -> R,%,%) -> %
       ++ \spad{map(f,a,b)} returns c, where c is such that
       ++ \spad{c(i,j) = f(a(i,j),b(i,j))} for all \spad{i}, j.
diff --git a/src/algebra/mring.spad.pamphlet b/src/algebra/mring.spad.pamphlet
index 9521b586..8eafac0a 100644
--- a/src/algebra/mring.spad.pamphlet
+++ b/src/algebra/mring.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev domain MRING MonoidRing
 ++ Authors: Stephan M. Watt; revised by Johannes Grabmeier
 ++ Date Created: January 1986
-++ Date Last Updated: 14 December 1995, Mike Dewar
+++ Date Last Updated: May 13, 2013.
 ++ Basic Operations: *, +, monomials, coefficients
 ++ Related Constructors: Polynomial
 ++ Also See:
@@ -42,7 +42,7 @@
 MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where
     Term ==> Record(coef: R, monom: M)
 
-    MRcategory ==> Join(Ring, RetractableTo M, RetractableTo R) with
+    MRcategory == Join(Ring,RetractableTo M,RetractableTo R,Functorial R) with
         monomial         : (R, M) -> %
           ++ monomial(r,m) creates a scalar multiple of the basis element m.
         coefficient : (%, M) -> R
@@ -54,9 +54,6 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where
           ++ terms(f) gives the list of non-zero coefficients combined
           ++ with their corresponding basis element as records.
           ++ This is the internal representation.
-        map         : (R -> R, %) -> %
-          ++ map(fn,u) maps function fn onto the coefficients
-          ++ of the non-zero monomials of u.
         monomial?   : % -> Boolean
           ++ monomial?(f) tests if f is a single monomial.
         coefficients: % -> List R
@@ -361,6 +358,8 @@ MonoidRingFunctions2(R,S,M) : Exports == Implementation where
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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
diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet
index b56c9a97..b9780274 100644
--- a/src/algebra/polycat.spad.pamphlet
+++ b/src/algebra/polycat.spad.pamphlet
@@ -14,7 +14,7 @@
 )abbrev category AMR AbelianMonoidRing
 ++ Author:
 ++ Date Created:
-++ Date Last Updated:
+++ Date Last Updated: May 19, 2013.
 ++ Basic Functions:
 ++ Related Constructors:
 ++ Also See:
@@ -33,16 +33,13 @@
 ++ Conceptually at least, only the non-zero terms are ever operated on.
 
 AbelianMonoidRing(R:Ring, E:OrderedAbelianMonoid): Category ==
-        Join(Ring,BiModule(R,R)) with
+        Join(Ring,BiModule(R,R),Functorial R) with
     leadingCoefficient: % -> R
       ++ leadingCoefficient(p) returns the coefficient highest degree term of p.
     leadingMonomial: % -> %
       ++ leadingMonomial(p) returns the monomial of p with the highest degree.
     degree: % -> E
       ++ degree(p) returns the maximum of the exponents of the terms of p.
-    map: (R -> R, %) -> %
-      ++ map(fn,u) maps function fn onto the coefficients
-      ++ of the non-zero monomials of u.
     monomial?: % -> Boolean
       ++ monomial?(p) tests if p is a single monomial.
     monomial: (R,E) -> %
@@ -1100,6 +1097,8 @@ CommuteUnivariatePolynomialCategory(R, UP, UPUP): Exports == Impl where
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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
diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet
index 249a5e0e..b2021bf8 100644
--- a/src/algebra/xpoly.spad.pamphlet
+++ b/src/algebra/xpoly.spad.pamphlet
@@ -142,7 +142,7 @@ import RetractableTo
 )abbrev category FMCAT FreeModuleCat
 ++ Author: Michel Petitot petitot@lifl.fr
 ++ Date Created: 91
-++ Date Last Updated: 7 Juillet 92
+++ Date Last Updated: May 19, 2013.
 ++ Fix History: compilation v 2.1 le 13 dec 98
 ++ Basic Functions:
 ++ Related Constructors:
@@ -168,15 +168,12 @@ FreeModuleCat(R, Basis):Category == Exports where
    Basis: SetCategory
    TERM ==> Record(k: Basis, c: R)
    
-   Exports == Join(BiModule(R,R), RetractableTo Basis) with
+   Exports == Join(Functorial R,BiModule(R,R),RetractableTo Basis) with
         *                : (R, Basis) -> %
           ++ \spad{r*b} returns the product of \spad{r} by \spad{b}.
         coefficient        : (%, Basis) -> R
           ++ \spad{coefficient(x,b)} returns the coefficient 
           ++ of \spad{b} in \spad{x}.
-        map                : (R -> R, %) -> %
-          ++ \spad{map(fn,u)} maps function \spad{fn} onto the coefficients
-          ++  of the non-zero monomials of \spad{u}.
         monom              : (Basis, R) -> %
           ++ \spad{monom(b,r)} returns the element with the single monomial
           ++  \spad{b} and coefficient \spad{r}.
@@ -362,7 +359,7 @@ import RetractableTo
 )abbrev category XFALG XFreeAlgebra
 ++ Author: Michel Petitot petitot@lifl.fr
 ++ Date Created: 91
-++ Date Last Updated: 7 Juillet 92
+++ Date Last Updated: May 19, 2013.
 ++ Fix History: compilation v 2.1 le 13 dec 98
 ++ Basic Functions:
 ++ Related Constructors:
@@ -381,7 +378,7 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where
    I      ==> Integer
    TERM   ==> Record(k: WORD, c: R)
 
-   Catdef == Join(Ring, XAlgebra(R), RetractableTo WORD) 
+   Catdef == Join(Ring, XAlgebra(R), Functorial R,RetractableTo WORD) 
      with
        *: (vl,%) -> %
          ++ \spad{v * x} returns the product of a variable \spad{x} by \spad{x}.
@@ -432,8 +429,6 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where
              ++ This multiplication is associative and commutative.
           sh :(%,NNI) -> %
              ++ \spad{sh(x,n)} returns the shuffle power of \spad{x} to the \spad{n}.
-       map   : (R -> R, %) -> %
-         ++ \spad{map(fn,x)} returns \spad{Sum(fn(r_i) w_i)} if \spad{x} writes \spad{Sum(r_i w_i)}.
        varList: % -> List vl
          ++ \spad{varList(x)} returns the list of variables which appear in \spad{x}.
 
@@ -488,7 +483,7 @@ import FreeMonoidCat
 )abbrev domain XPR XPolynomialRing
 ++ Author: Michel Petitot petitot@lifl.fr
 ++ Date Created: 91
-++ Date Last Updated: 7 Juillet 92
+++ Date Last Updated: May 13, 2013.
 ++ Fix History: compilation v 2.1 le 13 dec 98
 ++ Basic Functions:
 ++ Related Constructors:
@@ -509,7 +504,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where
   EX     ==> OutputForm
   NNI    ==> NonNegativeInteger
 
-  T == Join(Ring, XAlgebra(R), FreeModuleCat(R,E),CoercibleFrom E) with
+  T == Join(Ring,XAlgebra(R),FreeModuleCat(R,E),CoercibleFrom E,Functorial R) with
     --operations
       *: (%,R) -> %
         ++ \spad{p*r} returns the product of \spad{p} by \spad{r}.
@@ -536,8 +531,6 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where
         ++ \spad{quasiRegular?(x)} return true if \spad{constant(p)} is zero.
       quasiRegular : % -> % 
         ++ \spad{quasiRegular(x)} return \spad{x} minus its constant term.
-      map   : (R -> R, %) -> %
-        ++ \spad{map(fn,x)} returns \spad{Sum(fn(r_i) w_i)} if \spad{x} writes \spad{Sum(r_i w_i)}.
       if R has Field then / : (%,R) -> %
         ++ \spad{p/r} returns \spad{p*(1/r)}.
 
@@ -1097,6 +1090,8 @@ XPolynomial(R:Ring) == XRecursivePolynomial(Symbol, R)
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
+--Copyright (C) 2007-2013, 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