* algebra/wtpol.spad.pamphlet (WeightedPolynomials): No

	HomotopicTo P.
	(OrdinaryWeightedPolynomials): Likewise.
	* algebra/modmonom.spad.pamphlet (ModuleMonomial): Now
	HomotopicTo MM.
	* algebra/matrix.spad.pamphlet (coerce$RectangularMatrix): Remove
	redundant signature.
	* algebra/lodop.spad.pamphlet (OrdinaryDifferentialRing): Now
	HomotopicTo HomotopicTo R.
	* algebra/alql.spad.pamphlet (DataList): Now HomotopicTo List S.
	* algebra/array1.spad.pamphlet (Tuple): Now HomotopicTo
	PrimitiveArray S.
	* algebra/kl.spad.pamphlet (CachableSet): Now HomotopicTo S.
	* algebra/java.spad.pamphlet (JavaBytecode): Now HomotopicTo Byte.
	* algebra/fname.spad.pamphlet (FileNameCategory): Extends
	HomotopicTo String.
	* algebra/data.spad.pamphlet (Byte): Now HomotopicTo Character.

16 files changed, 56 insertions, 78 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index 75128c99..72b59787 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,25 @@
 2008-11-20  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
+	* algebra/wtpol.spad.pamphlet (WeightedPolynomials): No
+	HomotopicTo P.
+	(OrdinaryWeightedPolynomials): Likewise.
+	* algebra/modmonom.spad.pamphlet (ModuleMonomial): Now
+	HomotopicTo MM.
+	* algebra/matrix.spad.pamphlet (coerce$RectangularMatrix): Remove
+	redundant signature.
+	* algebra/lodop.spad.pamphlet (OrdinaryDifferentialRing): Now
+	HomotopicTo HomotopicTo R.
+	* algebra/alql.spad.pamphlet (DataList): Now HomotopicTo List S.
+	* algebra/array1.spad.pamphlet (Tuple): Now HomotopicTo
+	PrimitiveArray S.
+	* algebra/kl.spad.pamphlet (CachableSet): Now HomotopicTo S.
+	* algebra/java.spad.pamphlet (JavaBytecode): Now HomotopicTo Byte.
+	* algebra/fname.spad.pamphlet (FileNameCategory): Extends
+	HomotopicTo String.
+	* algebra/data.spad.pamphlet (Byte): Now HomotopicTo Character.
+
+2008-11-20  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
 	* algebra/coerce.spad.pamphlet (HomotopicTo): New.
 	* algebra/exposed.lsp.pamphlet: Expose it.
 	* algebra/Makefile.pamphlet (axiom_algebra_layer_1): Include HOMOTOP.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 9b0d0643..21ffaeee 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -361,7 +361,7 @@ axiom_algebra_layer_0 = \
   PRIMCAT  PRINT    PTRANFN  SPFCAT   TYPE     UTYPE    \
            PROPERTY BASTYPE  BASTYPE- CATEGORY LMODULE  \
   RMODULE  FINITE   STEP     SGROUP   SGROUP-  ABELSG   \
-  ABELSG-  ORDSET   ORDSET-  FNCAT    FILECAT  SEXCAT   \
+  ABELSG-  ORDSET   ORDSET-           FILECAT  SEXCAT   \
   MKBCFUNC MKRECORD MKUCFUNC DROPT1   PLOT1    ITFUN2   \
   ITFUN3   STREAM1  STREAM2  STREAM3  ANY1     SEGBIND2 \
   COMBOPC  EQ2      NONE1    CONDUIT  IOMODE   CTORKIND
@@ -376,7 +376,7 @@ axiom_algebra_layer_1 = \
   AGG      AGG-     IEVALAB  IEVALAB- FORTCAT   ITUPLE   \
   PATAB    PPCURVE  PSCURVE  REAL     RESLATC   RETRACT  \
   RETRACT- SEGCAT   BINDING           BMODULE   LOGIC    \
-  LOGIC-   EVALAB   EVALAB-  FEVALAB  FEVALAB-  BYTE     \
+  LOGIC-   EVALAB   EVALAB-  FEVALAB  FEVALAB-           \
   OSGROUP  MAYBE    DATAARY  PROPLOG  HOMOTOP
 
 axiom_algebra_layer_1_nrlibs = \
@@ -388,7 +388,8 @@ axiom_algebra_layer_1_objects = \
 axiom_algebra_layer_2 = \
   ELTAGG   ELTAGG- FMC      FMFUN   FORTFN   FVC     \
   SYNTAX   FVFUN   INTRET   IXAGG   IXAGG-   SEGXCAT \
-  CONTOUR  LIST3   MKFUNC   OASGP   KTVLOGIC
+  CONTOUR  LIST3   MKFUNC   OASGP   KTVLOGIC FNCAT   \
+  BYTE
 
 axiom_algebra_layer_2_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_2))
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 00b3080d..cc6071bc 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -190,7 +190,7 @@ axiom_algebra_layer_0 = \
   PRIMCAT  PRINT    PTRANFN  SPFCAT   TYPE     UTYPE    \
            PROPERTY BASTYPE  BASTYPE- CATEGORY LMODULE  \
   RMODULE  FINITE   STEP     SGROUP   SGROUP-  ABELSG   \
-  ABELSG-  ORDSET   ORDSET-  FNCAT    FILECAT  SEXCAT   \
+  ABELSG-  ORDSET   ORDSET-           FILECAT  SEXCAT   \
   MKBCFUNC MKRECORD MKUCFUNC DROPT1   PLOT1    ITFUN2   \
   ITFUN3   STREAM1  STREAM2  STREAM3  ANY1     SEGBIND2 \
   COMBOPC  EQ2      NONE1    CONDUIT  IOMODE   CTORKIND
@@ -219,7 +219,7 @@ axiom_algebra_layer_1 = \
   AGG      AGG-     IEVALAB  IEVALAB- FORTCAT   ITUPLE   \
   PATAB    PPCURVE  PSCURVE  REAL     RESLATC   RETRACT  \
   RETRACT- SEGCAT   BINDING           BMODULE   LOGIC    \
-  LOGIC-   EVALAB   EVALAB-  FEVALAB  FEVALAB-  BYTE     \
+  LOGIC-   EVALAB   EVALAB-  FEVALAB  FEVALAB-           \
   OSGROUP  MAYBE    DATAARY  PROPLOG  HOMOTOP
 
 axiom_algebra_layer_1_nrlibs = \
@@ -238,7 +238,8 @@ axiom_algebra_layer_1_objects = \
 axiom_algebra_layer_2 = \
   ELTAGG   ELTAGG- FMC      FMFUN   FORTFN   FVC     \
   SYNTAX   FVFUN   INTRET   IXAGG   IXAGG-   SEGXCAT \
-  CONTOUR  LIST3   MKFUNC   OASGP   KTVLOGIC
+  CONTOUR  LIST3   MKFUNC   OASGP   KTVLOGIC FNCAT   \
+  BYTE
 
 axiom_algebra_layer_2_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_2))
diff --git a/src/algebra/alql.spad.pamphlet b/src/algebra/alql.spad.pamphlet
index 514f6288..4e568141 100644
--- a/src/algebra/alql.spad.pamphlet
+++ b/src/algebra/alql.spad.pamphlet
@@ -14,11 +14,7 @@
 )abbrev domain DLIST DataList
 ++ This domain provides some nice functions on lists
 DataList(S:OrderedSet) : Exports == Implementation where
-  Exports == ListAggregate(S) with
-    coerce: List S -> %
-      ++ coerce(l) creates a datalist from l  	
-    coerce: % -> List S
-      ++ coerce(x) returns the list of elements in x
+  Exports == Join(ListAggregate(S), HomotopicTo List S) with
     datalist: List S -> %
       ++ datalist(l) creates a datalist from l 
     elt: (%,"unique") -> %
diff --git a/src/algebra/array1.spad.pamphlet b/src/algebra/array1.spad.pamphlet
index 2d1d3a27..85368781 100644
--- a/src/algebra/array1.spad.pamphlet
+++ b/src/algebra/array1.spad.pamphlet
@@ -92,9 +92,7 @@ PrimitiveArrayFunctions2(A, B): Exports == Implementation where
 )abbrev domain TUPLE Tuple
 ++ This domain is used to interface with the interpreter's notion
 ++ of comma-delimited sequences of values.
-Tuple(S:Type): CoercibleTo(PrimitiveArray S) with
-  coerce: PrimitiveArray S -> %
-	++ coerce(a) makes a tuple from primitive array a
+Tuple(S:Type): HomotopicTo (PrimitiveArray S) with
   select: (%, NonNegativeInteger) -> S
 	++ select(x,n) returns the n-th element of tuple x.
 	++ tuples are 0-based
diff --git a/src/algebra/data.spad.pamphlet b/src/algebra/data.spad.pamphlet
index 10fb2431..0e2a8863 100644
--- a/src/algebra/data.spad.pamphlet
+++ b/src/algebra/data.spad.pamphlet
@@ -26,15 +26,12 @@ import OutputForm
 ++   Byte is the datatype of 8-bit sized unsigned integer values.
 Byte(): Public == Private where
   Public == Join(OrderedSet, CoercibleTo NonNegativeInteger,
-              CoercibleTo Character) with
+              HomotopicTo Character) with
     byte: NonNegativeInteger -> %
       ++ byte(x) injects the unsigned integer value `v' into
       ++ the Byte algebra.  `v' must be non-negative and less than 256.
     coerce: NonNegativeInteger -> %
       ++ coerce(x) has the same effect as byte(x).
-    coerce: Character -> %
-      ++ coerce(c) views `c' a a byte.  In particular `c' is supposed
-      ++ to have a numerical value less than 256.
     bitand: (%,%) -> %
       ++ bitand(x,y) returns the bitwise `and' of `x' and `y'.
     bitior: (%,%) -> %
diff --git a/src/algebra/fname.spad.pamphlet b/src/algebra/fname.spad.pamphlet
index e9c558fb..22c7e45a 100644
--- a/src/algebra/fname.spad.pamphlet
+++ b/src/algebra/fname.spad.pamphlet
@@ -28,15 +28,7 @@
 ++ Description:
 ++   This category provides an interface to names in the file system.
  
-FileNameCategory(): Category == SetCategory with
- 
-        coerce: String -> %
-            ++ coerce(s) converts a string to a file name
-            ++ according to operating system-dependent conventions.
-        coerce: % -> String
-            ++ coerce(fn) produces a string for a file name
-            ++ according to operating system-dependent conventions.
-
+FileNameCategory(): Category == Join(SetCategory, HomotopicTo String) with
         filename: (String, String, String) -> %
             ++ filename(d,n,e) creates a file name with
             ++ d as its directory, n as its name and e as its extension.
diff --git a/src/algebra/java.spad.pamphlet b/src/algebra/java.spad.pamphlet
index c0624228..c5a6667b 100644
--- a/src/algebra/java.spad.pamphlet
+++ b/src/algebra/java.spad.pamphlet
@@ -19,11 +19,8 @@
 ++ Description:  This domain defines the datatype for the Java
 ++ Virtual Machine byte codes.
 JavaBytecode(): Public == Private where
-  Public ==> Join(CoercibleTo OutputForm, CoercibleTo Byte) with
-    coerce: Byte -> %
-      ++ coerce(x) the numerical byte value into a JVM bytecode.
-
-  Private ==> add
+  Public == Join(CoercibleTo OutputForm, HomotopicTo Byte)
+  Private == add
     -- mnemonics equivalent of bytecodes.
     mnemonics : PrimitiveArray Symbol := 
       [['nop, 'aconst__null, 'iconst__m1, 'iconst__0, 'iconst__1,  _
diff --git a/src/algebra/kl.spad.pamphlet b/src/algebra/kl.spad.pamphlet
index 26a8b374..e4091c90 100644
--- a/src/algebra/kl.spad.pamphlet
+++ b/src/algebra/kl.spad.pamphlet
@@ -116,11 +116,8 @@ SortedCache(S:CachableSet): Exports == Implementation where
 ++ Description:
 ++   MakeCachableSet(S) returns a cachable set which is equal to S as a set.
 MakeCachableSet(S:SetCategory): Exports == Implementation where
-  Exports ==> Join(CachableSet, CoercibleTo S) with
-    coerce: S -> %
-      ++ coerce(s) returns s viewed as an element of %.
-
-  Implementation ==> add
+  Exports == Join(CachableSet, HomotopicTo S)
+  Implementation == add
     import SortedCache(%)
 
     Rep := Record(setpart: S, pos: NonNegativeInteger)
diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet
index 680ed017..c126e54d 100644
--- a/src/algebra/lodop.spad.pamphlet
+++ b/src/algebra/lodop.spad.pamphlet
@@ -217,12 +217,8 @@ OrdinaryDifferentialRing(Kernels,R,var): DRcategory == DRcapsule where
     Kernels:SetCategory
     R: PartialDifferentialRing(Kernels)
     var : Kernels
-    DRcategory == Join(BiModule($,$), DifferentialRing) with
+    DRcategory == Join(BiModule($,$), DifferentialRing, HomotopicTo R) with
         if R has Field then Field
-        coerce: R -> $
-            ++ coerce(r) views r as a value in the ordinary differential ring.
-        coerce: $ -> R
-            ++ coerce(p) views p as a valie in the partial differential ring.
     DRcapsule == R add
         n: Integer
         Rep := R
diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet
index 9e4318b6..660a5de4 100644
--- a/src/algebra/matrix.spad.pamphlet
+++ b/src/algebra/matrix.spad.pamphlet
@@ -284,9 +284,6 @@ RectangularMatrix(m,n,R): Exports == Implementation where
     rectangularMatrix: Matrix R -> $
       ++ \spad{rectangularMatrix(m)} converts a matrix of type \spadtype{Matrix}
       ++ to a matrix of type \spad{RectangularMatrix}.
-    coerce: $ -> Matrix R
-      ++ \spad{coerce(m)} converts a matrix of type \spadtype{RectangularMatrix}
-      ++ to a matrix of type \spad{Matrix}.
  
   Implementation ==> Matrix R add
     minr ==> minRowIndex
diff --git a/src/algebra/modmonom.spad.pamphlet b/src/algebra/modmonom.spad.pamphlet
index 593d5aa8..b91555eb 100644
--- a/src/algebra/modmonom.spad.pamphlet
+++ b/src/algebra/modmonom.spad.pamphlet
@@ -20,15 +20,11 @@ ModuleMonomial(IS: OrderedSet,
 
    MM ==> Record(index:IS, exponent:E)
 
-   T == OrderedSet  with
+   T == Join(OrderedSet, HomotopicTo MM)  with
         exponent: $ -> E
 		++ exponent(x) \undocumented
         index: $ -> IS
 		++ index(x) \undocumented
-        coerce: MM -> $
-		++ coerce(x) \undocumented
-        coerce: $ -> MM
-		++ coerce(x) \undocumented
         construct: (IS, E) -> $
 		++ construct(i,e) \undocumented
    C == MM  add
diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp
index 57f96e29..06bc62b3 100644
--- a/src/algebra/strap/DFLOAT.lsp
+++ b/src/algebra/strap/DFLOAT.lsp
@@ -1031,14 +1031,15 @@
                          |AbelianGroup&| NIL NIL NIL |AbelianMonoid&|
                          |Monoid&| NIL |OrderedSet&|
                          |AbelianSemiGroup&| |SemiGroup&|
-                         |TranscendentalFunctionCategory&| NIL
+                         |TranscendentalFunctionCategory&|
+                         |RetractableTo&| |RetractableTo&| NIL
                          |SetCategory&| NIL
                          |ElementaryFunctionCategory&| NIL
                          |HyperbolicFunctionCategory&|
                          |ArcTrigonometricFunctionCategory&|
                          |TrigonometricFunctionCategory&| NIL NIL
-                         |RadicalCategory&| |RetractableTo&| NIL
-                         |RetractableTo&| NIL NIL NIL |BasicType&| NIL)
+                         |RadicalCategory&| NIL NIL NIL NIL
+                         |BasicType&| NIL)
                       (CONS '#((|FloatingPointSystem|)
                                (|RealNumberSystem|) (|Field|)
                                (|EuclideanDomain|)
@@ -1064,8 +1065,9 @@
                                (|PatternMatchable| 101) (|OrderedSet|)
                                (|AbelianSemiGroup|) (|SemiGroup|)
                                (|TranscendentalFunctionCategory|)
-                               (|RealConstant|) (|SetCategory|)
-                               (|ConvertibleTo| 41)
+                               (|RetractableTo| 104)
+                               (|RetractableTo| 24) (|RealConstant|)
+                               (|SetCategory|) (|ConvertibleTo| 41)
                                (|ElementaryFunctionCategory|)
                                (|ArcHyperbolicFunctionCategory|)
                                (|HyperbolicFunctionCategory|)
@@ -1073,9 +1075,7 @@
                                (|TrigonometricFunctionCategory|)
                                (|OpenMath|) (|ConvertibleTo| 129)
                                (|RadicalCategory|)
-                               (|RetractableTo| 104)
                                (|CoercibleFrom| 104)
-                               (|RetractableTo| 24)
                                (|CoercibleFrom| 24)
                                (|ConvertibleTo| 101)
                                (|ConvertibleTo| 13) (|BasicType|)
diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp
index 0e57fde8..72601092 100644
--- a/src/algebra/strap/INT.lsp
+++ b/src/algebra/strap/INT.lsp
@@ -637,8 +637,8 @@
                          |AbelianGroup&| NIL NIL NIL |AbelianMonoid&|
                          |Monoid&| NIL NIL |OrderedSet&|
                          |AbelianSemiGroup&| |SemiGroup&| NIL
-                         |SetCategory&| NIL NIL NIL NIL NIL NIL NIL
-                         |RetractableTo&| NIL NIL |BasicType&| NIL)
+                         |RetractableTo&| |SetCategory&| NIL NIL NIL
+                         NIL NIL NIL NIL NIL NIL |BasicType&| NIL)
                       (CONS '#((|IntegerNumberSystem|)
                                (|EuclideanDomain|)
                                (|UniqueFactorizationDomain|)
@@ -662,13 +662,13 @@
                                (|StepThrough|) (|PatternMatchable| 11)
                                (|OrderedSet|) (|AbelianSemiGroup|)
                                (|SemiGroup|) (|RealConstant|)
-                               (|SetCategory|) (|OpenMath|)
-                               (|ConvertibleTo| 9) (|ConvertibleTo| 45)
+                               (|RetractableTo| 11) (|SetCategory|)
+                               (|OpenMath|) (|ConvertibleTo| 9)
+                               (|ConvertibleTo| 45)
                                (|ConvertibleTo| 48)
                                (|CombinatorialFunctionCategory|)
                                (|ConvertibleTo| 123)
                                (|ConvertibleTo| 50)
-                               (|RetractableTo| 11)
                                (|CoercibleFrom| 11)
                                (|ConvertibleTo| 11) (|BasicType|)
                                (|CoercibleTo| 36))
diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp
index 2da14713..d98748ea 100644
--- a/src/algebra/strap/SINT.lsp
+++ b/src/algebra/strap/SINT.lsp
@@ -581,8 +581,8 @@
                          |AbelianGroup&| NIL NIL NIL |AbelianMonoid&|
                          |Monoid&| NIL NIL |OrderedSet&|
                          |AbelianSemiGroup&| |SemiGroup&| |Logic&| NIL
-                         |SetCategory&| NIL NIL NIL NIL NIL NIL
-                         |RetractableTo&| NIL NIL |BasicType&| NIL)
+                         |RetractableTo&| |SetCategory&| NIL NIL NIL
+                         NIL NIL NIL NIL NIL |BasicType&| NIL)
                       (CONS '#((|IntegerNumberSystem|)
                                (|EuclideanDomain|)
                                (|UniqueFactorizationDomain|)
@@ -606,13 +606,12 @@
                                (|StepThrough|) (|PatternMatchable| 12)
                                (|OrderedSet|) (|AbelianSemiGroup|)
                                (|SemiGroup|) (|Logic|) (|RealConstant|)
-                               (|SetCategory|) (|OpenMath|)
-                               (|ConvertibleTo| 90)
+                               (|RetractableTo| 12) (|SetCategory|)
+                               (|OpenMath|) (|ConvertibleTo| 90)
                                (|ConvertibleTo| 91)
                                (|CombinatorialFunctionCategory|)
                                (|ConvertibleTo| 92)
                                (|ConvertibleTo| 94)
-                               (|RetractableTo| 12)
                                (|CoercibleFrom| 12)
                                (|ConvertibleTo| 12) (|BasicType|)
                                (|CoercibleTo| 29))
diff --git a/src/algebra/wtpol.spad.pamphlet b/src/algebra/wtpol.spad.pamphlet
index 12129139..bd7f9805 100644
--- a/src/algebra/wtpol.spad.pamphlet
+++ b/src/algebra/wtpol.spad.pamphlet
@@ -40,15 +40,11 @@ WeightedPolynomials(R:Ring,VarSet: OrderedSet, E:OrderedAbelianMonoidSup,
                            P:PolynomialCategory(R,E,VarSet),
                              vl:List VarSet, wl:List NonNegativeInteger,
                               wtlevel:NonNegativeInteger):
-       Ring with
+       Join(Ring, HomotopicTo P) with
          if R has CommutativeRing then Algebra(R)
-         coerce: $ -> P
-	         ++ convert back into a "P", ignoring weights
          if R has Field then "/": ($,$) -> Union($,"failed")
 	         ++ x/y division (only works if minimum weight
 	         ++ of divisor is zero, and if R is a Field)
-         coerce: P -> $
-	         ++ coerce(p) coerces p into Weighted form, applying weights and ignoring terms
          changeWeightLevel: NonNegativeInteger -> Void
         	 ++ changeWeightLevel(n) changes the weight level to the new value given:
 	         ++ NB: previously calculated terms are not affected
@@ -153,13 +149,8 @@ import NonNegativeInteger
 OrdinaryWeightedPolynomials(R:Ring,
                              vl:List Symbol, wl:List NonNegativeInteger,
                               wtlevel:NonNegativeInteger):
-       Ring with
+       Join(Ring, HomotopicTo Polynomial R) with
          if R has CommutativeRing then Algebra(R)
-         coerce: $ -> Polynomial(R)
-	         ++ coerce(p) converts back into a Polynomial(R), ignoring weights
-         coerce: Polynomial(R) -> $
-      	 	++ coerce(p) coerces a Polynomial(R) into Weighted form,
-         	++ applying weights and ignoring terms
          if R has Field then "/": ($,$) -> Union($,"failed")
 	         ++ x/y division (only works if minimum weight
        		 ++ of divisor is zero, and if R is a Field)