* interp/c-util.boot (displayAmbiguousSignatures): New.

	(ambiguousSignatureError): Likewise.
	* interp/define.boot (hasSigInTargetCategory): Use it to reject
	ambiguous lhs of a definition.
	* interp/lisplib.boot (leaveIfErrors): Fix typo.
	* algebra/aggcat.spad.pamphlet: Disambiguate definitions.
	* algebra/card.spad.pamphlet: Likewise.
	* algebra/dhmatrix.spad.pamphlet: Likewise.
	* algebra/divisor.spad.pamphlet: Likewise.
	* algebra/expexpan.spad.pamphlet: Likewise.
	* algebra/ffcat.spad.pamphlet: Likewise.
	* algebra/ffcg.spad.pamphlet: Likewise.
	* algebra/ffnb.spad.pamphlet: Likewise.
	* algebra/ffp.spad.pamphlet: Likewise.
	* algebra/generic.spad.pamphlet: Likewise.
	* algebra/groebf.spad.pamphlet: Likewise.
	* algebra/modring.spad.pamphlet: Likewise.
	* algebra/moebius.spad.pamphlet: Likewise.
	* algebra/mts.spad.pamphlet: Likewise.
	* algebra/naalgc.spad.pamphlet: Likewise.
	* algebra/ore.spad.pamphlet: Likewise.
	* algebra/outform.spad.pamphlet: Likewise.
	* algebra/pf.spad.pamphlet: Likewise.
	* algebra/poly.spad.pamphlet: Likewise.
	* algebra/polycat.spad.pamphlet: Likewise.
	* algebra/prtition.spad.pamphlet: Likewise.
	* algebra/radix.spad.pamphlet: Likewise.
	* algebra/rep2.spad.pamphlet: Likewise.
	* algebra/stream.spad.pamphlet: Likewise.
	* algebra/string.spad.pamphlet: Likewise.
	* algebra/tree.spad.pamphlet: Likewise.
	* algebra/triset.spad.pamphlet: Likewise.
	* algebra/view2D.spad.pamphlet: Likewise.
	* algebra/sf.spad.pamphlet: Remove signature for hash.
	* algebra/si.spad.pamphlet: Likewise.

34 files changed, 213 insertions, 53 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index 43f5e6c1..73022569 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,41 @@
+2008-09-18  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
+	* interp/c-util.boot (displayAmbiguousSignatures): New.
+	(ambiguousSignatureError): Likewise.
+	* interp/define.boot (hasSigInTargetCategory): Use it to reject
+	ambiguous lhs of a definition.
+	* interp/lisplib.boot (leaveIfErrors): Fix typo.
+	* algebra/aggcat.spad.pamphlet: Disambiguate definitions.
+	* algebra/card.spad.pamphlet: Likewise.
+	* algebra/dhmatrix.spad.pamphlet: Likewise.
+	* algebra/divisor.spad.pamphlet: Likewise.
+	* algebra/expexpan.spad.pamphlet: Likewise.
+	* algebra/ffcat.spad.pamphlet: Likewise.
+	* algebra/ffcg.spad.pamphlet: Likewise.
+	* algebra/ffnb.spad.pamphlet: Likewise.
+	* algebra/ffp.spad.pamphlet: Likewise.
+	* algebra/generic.spad.pamphlet: Likewise.
+	* algebra/groebf.spad.pamphlet: Likewise.
+	* algebra/modring.spad.pamphlet: Likewise.
+	* algebra/moebius.spad.pamphlet: Likewise.
+	* algebra/mts.spad.pamphlet: Likewise.
+	* algebra/naalgc.spad.pamphlet: Likewise.
+	* algebra/ore.spad.pamphlet: Likewise.
+	* algebra/outform.spad.pamphlet: Likewise.
+	* algebra/pf.spad.pamphlet: Likewise.
+	* algebra/poly.spad.pamphlet: Likewise.
+	* algebra/polycat.spad.pamphlet: Likewise.
+	* algebra/prtition.spad.pamphlet: Likewise.
+	* algebra/radix.spad.pamphlet: Likewise.
+	* algebra/rep2.spad.pamphlet: Likewise.
+	* algebra/stream.spad.pamphlet: Likewise.
+	* algebra/string.spad.pamphlet: Likewise.
+	* algebra/tree.spad.pamphlet: Likewise.
+	* algebra/triset.spad.pamphlet: Likewise.
+	* algebra/view2D.spad.pamphlet: Likewise.
+	* algebra/sf.spad.pamphlet: Remove signature for hash.
+	* algebra/si.spad.pamphlet: Likewise.
+
 2008-09-18  Bill Page  <bill.page@newsynthesis.org>
 	    Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet
index 42a4f3fd..86d91cba 100644
--- a/src/algebra/aggcat.spad.pamphlet
+++ b/src/algebra/aggcat.spad.pamphlet
@@ -1050,6 +1050,9 @@ IndexedAggregate(Index: SetCategory, Entry: Type): Category ==
 import SetCategory
 import KeyedDictionary
 import IndexedAggregate
+import Boolean
+import OutputForm
+import List
 )abbrev category TBAGG TableAggregate
 ++ Author: Michael Monagan, Stephen Watt; revised by Manuel Bronstein and Richard Jenks
 ++ Date Created: August 87 through August 88
@@ -1098,7 +1101,7 @@ TableAggregate(Key:SetCategory, Entry:SetCategory): Category ==
       (r := search(k, t)) case Entry => r::Entry
       e
 
-   map_!(f, t) ==
+   map_!(f: Entry->Entry, t: %) ==
       for k in keys t repeat t.k := f t.k
       t
 
diff --git a/src/algebra/card.spad.pamphlet b/src/algebra/card.spad.pamphlet
index ce908e9c..e6ffb393 100644
--- a/src/algebra/card.spad.pamphlet
+++ b/src/algebra/card.spad.pamphlet
@@ -11,6 +11,8 @@
 \eject
 \section{domain CARD CardinalNumber}
 <<domain CARD CardinalNumber>>=
+import Boolean
+import NonNegativeInteger
 )abbrev domain CARD CardinalNumber
 ++ Author: S.M. Watt
 ++ Date Created: June 1986
@@ -133,7 +135,7 @@ CardinalNumber: Join(OrderedSet, AbelianMonoid, Monoid,
             finite? x => [FINord, n*x.ival]
             n = 0     => 0
             x
-        x**y ==
+        (x: %) ** (y: %) ==
             y = 0 =>
                 x ~= 0 => 1
                 error "0**0 not defined for cardinal numbers."
diff --git a/src/algebra/dhmatrix.spad.pamphlet b/src/algebra/dhmatrix.spad.pamphlet
index 5c075992..c6a968a3 100644
--- a/src/algebra/dhmatrix.spad.pamphlet
+++ b/src/algebra/dhmatrix.spad.pamphlet
@@ -1675,7 +1675,7 @@ DenavitHartenbergMatrix(R): Exports == Implementation where
 --         [ax,ay,az,-(px*ax+py*ay+pz*az)],_
 --         [ 0, 0, 0, 1]])
 
-    d * p ==
+    d:% * p: Point(R) ==
        v := p pretend Vector R
        v := concat(v, 1$R)
        v := d * v
diff --git a/src/algebra/divisor.spad.pamphlet b/src/algebra/divisor.spad.pamphlet
index 05a201cc..adc98c0f 100644
--- a/src/algebra/divisor.spad.pamphlet
+++ b/src/algebra/divisor.spad.pamphlet
@@ -788,8 +788,11 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where
       reduce makeDivisor(a, bb, 1)
 
 @
+
 \section{domain FDIV FiniteDivisor}
+
 <<domain FDIV FiniteDivisor>>=
+import Vector
 )abbrev domain FDIV FiniteDivisor
 ++ Finite rational divisors on a curve
 ++ Author: Manuel Bronstein
@@ -825,7 +828,7 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where
       0                       == 0$Rep
       coerce(d:$):OutputForm  == coerce(d)$Rep
       d1 = d2                 == d1 =$Rep d2
-      n * d                   == n *$Rep d
+      n:Integer * d:%         == n *$Rep d
       d1 + d2                 == d1 +$Rep d2
       - d                     == -$Rep d
       ideal d                 == ideal(d)$Rep
@@ -856,7 +859,7 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where
       ideal d                 == d.id
       decompose d             == [ideal d, 1]
       d1 = d2                 == basis(ideal d1) = basis(ideal d2)
-      n * d                   == divisor(ideal(d) ** n)
+      n: Integer * d:%        == divisor(ideal(d) ** n)
       d1 + d2                 == divisor(ideal d1 * ideal d2)
       - d                     == divisor inv ideal d
       divisor(h, d, dp, g, r) == makeDivisor(d, lift h - (r * dp)::RF::UPUP, g)
diff --git a/src/algebra/expexpan.spad.pamphlet b/src/algebra/expexpan.spad.pamphlet
index 30e4877b..5dbc4c57 100644
--- a/src/algebra/expexpan.spad.pamphlet
+++ b/src/algebra/expexpan.spad.pamphlet
@@ -160,7 +160,7 @@ UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen):_
     dominantTermOnList : (L Term,RN,I) -> Union(Term,"failed")
     iDominantTerm : L Term -> Union(Record(%term:Term,%type:String),"failed")
 
-    retractIfCan f ==
+    retractIfCan(f: %): Union(UPXS,"failed") ==
       (numberOfMonomials f = 1) and (zero? degree f) => leadingCoefficient f
       "failed"
 
diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet
index c87c4c12..b69923d4 100644
--- a/src/algebra/ffcat.spad.pamphlet
+++ b/src/algebra/ffcat.spad.pamphlet
@@ -117,8 +117,18 @@ ExtensionField(F:Field) : Category  == Join(Field,RetractableTo F,VectorSpace F)
       Frobenius(a,s) == a ** (size()$F ** s)
 
 @
+
 \section{category FAXF FiniteAlgebraicExtensionField}
+
 <<category FAXF FiniteAlgebraicExtensionField>>=
+import Boolean
+import NonNegativeInteger
+import PositiveInteger
+import Vector
+import Matrix
+import SparseUnivariatePolynomial
+import OnePointCompletion
+import CardinalNumber
 )abbrev category FAXF FiniteAlgebraicExtensionField
 ++ Author: J. Grabmeier, A. Scheerhorn
 ++ Date Created: 11 March 1991
@@ -283,7 +293,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _
       m
     algebraic? a == true
     transcendent? a == false
-    extensionDegree() == (#basis()) :: PositiveInteger
+    extensionDegree(): PositiveInteger == (#basis()) :: PositiveInteger
     -- degree a == degree(minimalPolynomial a)$SUP(F) :: PI
     trace a ==
       b := basis()
@@ -384,7 +394,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _
                    for i in 0..extensionDegree()-1]
         gcd(p,f) = 1 => true
         false
-      degree a ==
+      degree(a: %): PositiveInteger ==
         y:$:=Frobenius a
         deg:PI:=1
         while y~=a repeat
@@ -475,8 +485,19 @@ DiscreteLogarithmPackage(M): public == private where
       disclog pretend NonNegativeInteger
 
 @
+
 \section{category FFIELDC FiniteFieldCategory}
+
 <<category FFIELDC FiniteFieldCategory>>=
+import Boolean
+import Integer
+import NonNegativeInteger
+import PositiveInteger
+import Matrix
+import List
+import Table
+import OnePointCompletion
+import SparseUnivariatePolynomial
 )abbrev category FFIELDC FiniteFieldCategory
 ++ Author: J. Grabmeier, A. Scheerhorn
 ++ Date Created: 11 March 1991
@@ -600,7 +621,7 @@ FiniteFieldCategory() : Category ==_
 --        equalone := one?(a**(q quo exp.factor))
         equalone := ((a**(q quo exp.factor)) = 1)
       not equalone
-    order e ==
+    order(e: %): PositiveInteger ==
       e = 0 => error "order(0) is not defined "
       ord:Integer:= size()-1 -- order e divides ord
       a:Integer:= 0
diff --git a/src/algebra/ffcg.spad.pamphlet b/src/algebra/ffcg.spad.pamphlet
index 212bc91b..941c34d6 100644
--- a/src/algebra/ffcg.spad.pamphlet
+++ b/src/algebra/ffcg.spad.pamphlet
@@ -25,8 +25,12 @@
 -- finite field represented by it's cyclic group and 'zero' as an
 -- extra element
 \end{verbatim}
+
 \section{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
+
 <<domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial>>=
+import SingleInteger
+import PrimitiveArray
 )abbrev domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial
 ++ Authors: J.Grabmeier, A.Scheerhorn
 ++ Date Created: 26.03.1991
@@ -282,7 +286,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_
       initelt?:=false
       void()$Void
 
-    extensionDegree() == extdeg pretend PI
+    extensionDegree(): PositiveInteger == extdeg pretend PI
 
     characteristic() == characteristic()$GF
 
diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet
index b342f19e..c283b9ff 100644
--- a/src/algebra/ffnb.spad.pamphlet
+++ b/src/algebra/ffnb.spad.pamphlet
@@ -379,8 +379,12 @@ InnerNormalBasisFieldFunctions(GF): Exports == Implementation where
       +/[monomial(x.i,(i-1)::NNI)$(SUP GF) for i in 1..(#x)::I]
 
 @
+
 \section{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
+
 <<domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial>>=
+import NonNegativeInteger
+import Matrix
 )abbrev domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial
 ++ Authors: J.Grabmeier, A.Scheerhorn
 ++ Date Created: 26.03.1991
@@ -514,7 +518,7 @@ FiniteFieldNormalBasisExtensionByPolynomial(GF,uni): Exports == _
     coerce(v:GF):$  == new(extdeg,v /$GF traceAlpha)$Rep
     represents(v)   ==  v::$
 
-    degree(a) ==
+    degree(a: %): PositiveInteger ==
       d:PI:=1
       b:= qPot(a::Rep,1)$INBFF
       while (b~=a) repeat
@@ -652,7 +656,7 @@ divisor of the order of the multiplicative group"
       if empty? facOfGroupSize then initializeElt()
       facOfGroupSize
 
-    extensionDegree() == extdeg
+    extensionDegree(): PositiveInteger == extdeg
 
     sizeOfGroundField() == size()$GF pretend NNI
 
diff --git a/src/algebra/ffp.spad.pamphlet b/src/algebra/ffp.spad.pamphlet
index 9b38f959..67b32b90 100644
--- a/src/algebra/ffp.spad.pamphlet
+++ b/src/algebra/ffp.spad.pamphlet
@@ -28,7 +28,9 @@
 -- 04.04.91 JG: comment of FFP was changed
 
 \end{verbatim}
+
 \section{domain FFP FiniteFieldExtensionByPolynomial}
+
 <<domain FFP FiniteFieldExtensionByPolynomial>>=
 )abbrev domain FFP FiniteFieldExtensionByPolynomial
 ++ Authors: R.Sutor, J. Grabmeier, O. Gschnitzer, A. Scheerhorn
@@ -130,7 +132,7 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_
       a:$:=norm(primitiveElement(),n)
       vector [a**i for i in 0..n-1]
 
-    degree(x) ==
+    degree(x: %): PositiveInteger ==
       y:$:=1
       m:=zero(extdeg,extdeg+1)$(Matrix GF)
       for i in 1..extdeg+1 repeat
@@ -249,7 +251,7 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_
 
     coerce(e:$):OutputForm == outputForm(lift(e),alpha)
 
-    extensionDegree() == extdeg
+    extensionDegree(): PositiveInteger == extdeg
 
     size() == (sizeCG + 1) pretend NNI
 
diff --git a/src/algebra/generic.spad.pamphlet b/src/algebra/generic.spad.pamphlet
index 611284be..01c7e3fc 100644
--- a/src/algebra/generic.spad.pamphlet
+++ b/src/algebra/generic.spad.pamphlet
@@ -9,8 +9,13 @@
 \eject
 \tableofcontents
 \eject
+
 \section{domain GCNAALG GenericNonAssociativeAlgebra}
+
 <<domain GCNAALG GenericNonAssociativeAlgebra>>=
+import Fraction
+import Polynomial
+import SparseUnivariatePolynomial
 )abbrev domain GCNAALG GenericNonAssociativeAlgebra
 ++ Authors: J. Grabmeier, R. Wisbauer
 ++ Date Created: 26 June 1991
@@ -209,11 +214,11 @@ GenericNonAssociativeAlgebra(R : CommutativeRing, n : PositiveInteger,_
         rightRankPoly := rightMinimalPolynomial genericElement
         void()$Void
 
-      leftRankPolynomial() ==
+      leftRankPolynomial(): SparseUnivariatePolynomial FPR ==
         if initLeft? then initializeLeft()
         leftRankPoly
 
-      rightRankPolynomial() ==
+      rightRankPolynomial(): SparseUnivariatePolynomial FPR ==
         if initRight? then initializeRight()
         rightRankPoly
 
diff --git a/src/algebra/groebf.spad.pamphlet b/src/algebra/groebf.spad.pamphlet
index 47225404..fe1a43e4 100644
--- a/src/algebra/groebf.spad.pamphlet
+++ b/src/algebra/groebf.spad.pamphlet
@@ -9,8 +9,12 @@
 \eject
 \tableofcontents
 \eject
+
 \section{package GBF GroebnerFactorizationPackage}
+
 <<package GBF GroebnerFactorizationPackage>>=
+import Boolean
+import List
 )abbrev package GBF GroebnerFactorizationPackage
 ++ Author: H. Michael Moeller, Johannes Grabmeier
 ++ Date Created: 24 August 1989
@@ -323,7 +327,7 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where
         we found reducible polynomials and continue splitting")$OUT
      createGroebnerBases([],[],[],basis,[],[],info)
 
-   groebnerFactorize(basis, nonZeroRestrictions) ==
+   groebnerFactorize(basis: List Dpol, nonZeroRestrictions: List Dpol) ==
      groebnerFactorize(basis, nonZeroRestrictions, false)
 
    groebnerFactorize(basis, nonZeroRestrictions, info) ==
@@ -337,7 +341,8 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where
      createGroebnerBases([],[],nonZeroRestrictions,basis,[],[],info)
 
    groebnerFactorize(basis) == groebnerFactorize(basis, [], false)
-   groebnerFactorize(basis,info) == groebnerFactorize(basis, [], info)
+   groebnerFactorize(basis: List Dpol,info: Boolean) == 
+     groebnerFactorize(basis, [], info)
 
 @
 \section{License}
diff --git a/src/algebra/modring.spad.pamphlet b/src/algebra/modring.spad.pamphlet
index bfd9912a..3ee11ff6 100644
--- a/src/algebra/modring.spad.pamphlet
+++ b/src/algebra/modring.spad.pamphlet
@@ -56,7 +56,7 @@ ModularRing(R,Mod,reduction:(R,Mod) -> R,
 
     --define
       modulus(x)   == x.modulo
-      coerce(x)    == x.val
+      coerce(x: %): R == x.val
       coerce(i:Integer):% == [i::R,0]$Rep
       i:Integer * x:% == (i::%)*x
       coerce(x):OutputForm == (x.val)::OutputForm
diff --git a/src/algebra/moebius.spad.pamphlet b/src/algebra/moebius.spad.pamphlet
index a6b10b66..d0681a82 100644
--- a/src/algebra/moebius.spad.pamphlet
+++ b/src/algebra/moebius.spad.pamphlet
@@ -1,16 +1,20 @@
 \documentclass{article}
 \usepackage{axiom}
 \begin{document}
-\title{\$SPAD/src/algebra moebius.spad}
+
+\title{src/algebra moebius.spad}
 \author{Stephen M. Watt}
 \maketitle
+
 \begin{abstract}
 \end{abstract}
-\eject
+
 \tableofcontents
 \eject
+
 \section{domain MOEBIUS MoebiusTransform}
 <<domain MOEBIUS MoebiusTransform>>=
+import OnePointCompletion
 )abbrev domain MOEBIUS MoebiusTransform
 ++ 2-by-2 matrices acting on P1(F).
 ++ Author: Stephen "Say" Watt
@@ -79,7 +83,7 @@ MoebiusTransform(F): Exports == Implementation where
  
     shift(t,f) == moebius(a(t) + f*c(t), b(t) + f*d(t), c(t), d(t))
     scale(t,f) == moebius(f*a(t),f*b(t),c(t),d(t))
-    recip t    == moebius(c(t),d(t),a(t),b(t))
+    recip(t: %): % == moebius(c(t),d(t),a(t),b(t))
  
     eval(t:%,f:F) == (a(t)*f + b(t))/(c(t)*f + d(t))
     eval(t:%,f:P1F) ==
diff --git a/src/algebra/mts.spad.pamphlet b/src/algebra/mts.spad.pamphlet
index 1d26d0a1..35399ac6 100644
--- a/src/algebra/mts.spad.pamphlet
+++ b/src/algebra/mts.spad.pamphlet
@@ -9,8 +9,13 @@
 \eject
 \tableofcontents
 \eject
+
 \section{domain SMTS SparseMultivariateTaylorSeries}
+
 <<domain SMTS SparseMultivariateTaylorSeries>>=
+import NonNegativeInteger
+import List
+import Stream
 )abbrev domain SMTS SparseMultivariateTaylorSeries
 ++ This domain provides multivariate Taylor series
 ++ Authors: William Burge, Stephen Watt, Clifton Williamson
@@ -84,7 +89,8 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_
       ints := integers(0)$STT pretend ST NNI
       map(monomial(#2 :: SMP,v,#1)$SMP,ints,s pretend ST Coef)$ST3(NNI,Coef,SMP)
  
-    coefficient(s,n) == elt(s,n + 1)$Rep  -- 1-based indexing for streams
+    coefficient(s:%,n: NNI) == 
+      elt(s,n + 1)$Rep  -- 1-based indexing for streams
  
 --% creation of series
  
diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet
index 2eee8450..37f1babe 100644
--- a/src/algebra/naalgc.spad.pamphlet
+++ b/src/algebra/naalgc.spad.pamphlet
@@ -119,12 +119,12 @@ MonadWithUnit(): Category == Monad with
       x:% ** n:NonNegativeInteger ==
          zero? n => 1
          expt(x,n pretend PositiveInteger)
-      rightPower(a,n) ==
+      rightPower(a: %,n: NonNegativeInteger) ==
         zero? n => 1
         res := 1
         for i in 1..n repeat res := res * a
         res
-      leftPower(a,n) ==
+      leftPower(a: %,n: NonNegativeInteger) ==
         zero? n => 1
         res := 1
         for i in 1..n repeat res := a * res
diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet
index 9617f107..3e2f769c 100644
--- a/src/algebra/ore.spad.pamphlet
+++ b/src/algebra/ore.spad.pamphlet
@@ -275,6 +275,8 @@ ApplyUnivariateSkewPolynomial(R:Ring, M: LeftModule R,
 @
 \section{domain AUTOMOR Automorphism}
 <<domain AUTOMOR Automorphism>>=
+import Integer
+import NonNegativeInteger
 )abbrev domain AUTOMOR Automorphism
 ++ Author: Manuel Bronstein
 ++ Date Created: 31 January 1994
@@ -308,7 +310,7 @@ Automorphism(R:Ring): Join(Group, Eltable(R, R)) with
       f = g                           == EQ(f, g)$Lisp
       elt(f, r)                       == apply(f, r, 1)
       inv f                           == apply(f, #1, - #2)
-      f ** n                          == apply(f, #1, n * #2)
+      (f: %) ** (n: Integer)          == apply(f, #1, n * #2)
       coerce(f:%):OutputForm          == message("R -> R")
       morphism(f:(R, Integer) -> R):% == f
       morphism(f:R -> R):%            == morphism(f, err)
diff --git a/src/algebra/outform.spad.pamphlet b/src/algebra/outform.spad.pamphlet
index 3f5c2aaf..00ca7d81 100644
--- a/src/algebra/outform.spad.pamphlet
+++ b/src/algebra/outform.spad.pamphlet
@@ -202,8 +202,18 @@ NumberFormats(): NFexports == NFimplementation where
             tot::PI
 
 @
+
 \section{domain OUTFORM OutputForm}
+
 <<domain OUTFORM OutputForm>>=
+import Void
+import Boolean
+import Integer
+import NonNegativeInteger
+import DoubleFloat
+import Symbol
+import String
+import List
 )abbrev domain OUTFORM OutputForm
 ++ Keywords: output, I/O, expression
 ++ SMW March/88
@@ -571,7 +581,7 @@ OutputForm(): SetCategory with
         vconcat(a,b)  == [eform VCONCAT, a, b]
         vconcat l     == cons(eform VCONCAT, l)
 
-        a ~= b      == [sform "~=",    a, b]
+        (a:% ~= b:%): % == [sform "~=",    a, b]
         a < b       == [sform "<",     a, b]
         a > b       == [sform ">",     a, b]
         a <= b      == [sform "<=",    a, b]
diff --git a/src/algebra/pf.spad.pamphlet b/src/algebra/pf.spad.pamphlet
index 338b56c2..4eaf3fbf 100644
--- a/src/algebra/pf.spad.pamphlet
+++ b/src/algebra/pf.spad.pamphlet
@@ -169,7 +169,7 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where
 
     inGroundField?(x)  == true
 
-    coordinates(x) == new(1,x)$(Vector $)
+    coordinates(x: %) == new(1,x)$(Vector $)
 
     represents(v)  == v.1
 
@@ -189,7 +189,7 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where
     minimalPolynomial(x) ==
       monomial(1,1)$(SUP $) - monomial(x,0)$(SUP $)
 
-    charthRoot x == x
+    charthRoot(x: %): % == x
 
 @
 \section{domain PF PrimeField}
diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet
index ec3a2f79..9cdc6ad8 100644
--- a/src/algebra/poly.spad.pamphlet
+++ b/src/algebra/poly.spad.pamphlet
@@ -383,8 +383,12 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C
           x/r == inv(r)*x
 
 @
+
 \section{domain SUP SparseUnivariatePolynomial}
+
 <<domain SUP SparseUnivariatePolynomial>>=
+import NonNegativeInteger
+import OutputForm
 )abbrev domain SUP SparseUnivariatePolynomial
 ++ Author: Dave Barton, Barry Trager
 ++ Date Created:
@@ -555,7 +559,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with
 
    if R has IntegralDomain then
     if R has approximate then
-     p1 exquo p2  ==
+     p1:% exquo p2:%  ==
         null p2 => error "Division by 0"
         p2 = 1 => p1
         p1=p2 => 1
@@ -571,7 +575,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with
         null p1 => reverse(rout)::%    -- nreverse?
         "failed"
     else -- R not approximate
-     p1 exquo p2  ==
+     p1:% exquo p2:%  ==
         null p2 => error "Division by 0"
         p2 = 1 => p1
       --(p1.lastElt.c exquo p2.lastElt.c) case "failed" => "failed"
diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet
index 4cdd3572..9f86558a 100644
--- a/src/algebra/polycat.spad.pamphlet
+++ b/src/algebra/polycat.spad.pamphlet
@@ -78,6 +78,9 @@ AbelianMonoidRing(R:Ring, E:OrderedAbelianMonoid): Category ==
 @
 \section{category FAMR FiniteAbelianMonoidRing}
 <<category FAMR FiniteAbelianMonoidRing>>=
+import Boolean
+import NonNegativeInteger
+import List
 )abbrev category FAMR FiniteAbelianMonoidRing
 ++ Author:
 ++ Date Created:
@@ -162,7 +165,7 @@ FiniteAbelianMonoidRing(R:Ring, E:OrderedAbelianMonoid): Category ==
     if R has Field then
        x/r == map(#1/r,x)
     if R has IntegralDomain then
-       x exquo r ==
+       (x: %) exquo (r: R) ==
           -- probably not a very good definition in most special cases
           zero? x => 0
           ans:% :=0
diff --git a/src/algebra/prtition.spad.pamphlet b/src/algebra/prtition.spad.pamphlet
index 0148ff2d..45466b9c 100644
--- a/src/algebra/prtition.spad.pamphlet
+++ b/src/algebra/prtition.spad.pamphlet
@@ -1,16 +1,21 @@
 \documentclass{article}
 \usepackage{axiom}
 \begin{document}
-\title{\$SPAD/src/algebra prtition.spad}
+
+\title{src/algebra prtition.spad}
 \author{William H. Burge}
 \maketitle
+
 \begin{abstract}
 \end{abstract}
-\eject
 \tableofcontents
 \eject
+
 \section{domain PRTITION Partition}
+
 <<domain PRTITION Partition>>=
+import Integer
+import List
 )abbrev domain PRTITION Partition
 ++ Domain for partitions of positive integers
 ++ Author: William H. Burge
@@ -56,7 +61,7 @@ Partition: Exports == Implementation where
     Rep := List Integer
     0 == nil()
  
-    coerce (s:%) == s pretend List Integer
+    coerce (s:%): List Integer == s pretend List Integer
     convert x == copy(x pretend L I)
  
     partition list == sort(#2 < #1,list)
diff --git a/src/algebra/radix.spad.pamphlet b/src/algebra/radix.spad.pamphlet
index 02fd8169..7cee785e 100644
--- a/src/algebra/radix.spad.pamphlet
+++ b/src/algebra/radix.spad.pamphlet
@@ -9,8 +9,14 @@
 \eject
 \tableofcontents
 \eject
+
 \section{domain RADIX RadixExpansion}
+
 <<domain RADIX RadixExpansion>>=
+import Integer
+import Fraction
+import List
+import Stream
 )abbrev domain RADIX RadixExpansion
 ++ Author: Stephen M. Watt
 ++ Date Created: October 1986
@@ -128,7 +134,7 @@ RadixExpansion(bb): Exports == Implementation where
       n0 := 0
       for r in a.int repeat n0 := bb*n0 + r
       a.sgn*n0
-    fractionPart a ==
+    fractionPart(a: %): Fraction Integer ==
       n0 := 0
       for r in a.pfx repeat n0 := bb*n0 + r
       null a.cyc =>
diff --git a/src/algebra/rep2.spad.pamphlet b/src/algebra/rep2.spad.pamphlet
index 45fddeb4..b1bc74ad 100644
--- a/src/algebra/rep2.spad.pamphlet
+++ b/src/algebra/rep2.spad.pamphlet
@@ -9,8 +9,17 @@
 \eject
 \tableofcontents
 \eject
+
 \section{package REP2 RepresentationPackage2}
+
 <<package REP2 RepresentationPackage2>>=
+import Boolean
+import Integer
+import PositiveInteger
+import List
+import Vector
+import Matrix
+
 )abbrev package REP2 RepresentationPackage2
 ++ Authors: Holger Gollan, Johannes Grabmeier
 ++ Date Created: 10 September 1987
@@ -745,7 +754,7 @@ RepresentationPackage2(R): public == private where
           meatAxe(algebraGenerators, false, 25, 7)
  
  
-        meatAxe (algebraGenerators, randomElements?) ==
+        meatAxe (algebraGenerators: L M R, randomElements?: Boolean) ==
           randomElements? => meatAxe (algebraGenerators, true, 25, 7)
           meatAxe(algebraGenerators, false, 6, 7)
  
diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet
index ddbedb5b..5a28b642 100644
--- a/src/algebra/sf.spad.pamphlet
+++ b/src/algebra/sf.spad.pamphlet
@@ -399,8 +399,6 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath,
         ++ x ** y returns the yth power of x (equal to \spad{exp(y log x)}).
       exp1 : () -> %
         ++ exp1() returns the natural log base \spad{2.718281828...}.
-      hash : % -> Integer
-        ++ hash(x) returns the hash key for x
       log2 :  % -> %
         ++ log2(x) computes the logarithm with base 2 for x.
       log10: % -> %
diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet
index 48bf6ac4..0a9f7095 100644
--- a/src/algebra/si.spad.pamphlet
+++ b/src/algebra/si.spad.pamphlet
@@ -59,8 +59,6 @@ IntegerNumberSystem(): Category ==
       ++ random() creates a random element.
    random   : % -> %
       ++ random(a) creates a random element from 0 to \spad{n-1}.
-   hash     : % -> %
-      ++ hash(n) returns the hash code of n.
    copy     : % -> %
       ++ copy(n) gives a copy of n.
    inc      : % -> %
diff --git a/src/algebra/stream.spad.pamphlet b/src/algebra/stream.spad.pamphlet
index 0879aad5..0241548c 100644
--- a/src/algebra/stream.spad.pamphlet
+++ b/src/algebra/stream.spad.pamphlet
@@ -551,11 +551,13 @@ CyclicStreamTools(S,ST): Exports == Implementation where
 \section{domain STREAM Stream}
 <<domain STREAM Stream>>=
 import Type
+import Void
 import Boolean
 import Integer
 import NonNegativeInteger
 import UniversalSegment
 import List
+import OutputForm
 )abbrev domain STREAM Stream
 ++ Implementation of streams via lazy evaluation
 ++ Authors: Burge, Watt; updated by Clifton J. Williamson
@@ -823,7 +825,7 @@ Stream(S): Exports == Implementation where
       p(frst x) => remove(p,rst x)
       concat(frst x,remove(p,rst x))
 
-    remove(p,x) ==
+    remove(p: S -> Boolean,x:%) ==
       explicitlyEmpty? x => empty()
       eq?(x,rst x) =>
         p(frst x) => empty()
diff --git a/src/algebra/string.spad.pamphlet b/src/algebra/string.spad.pamphlet
index 0b155aae..7a370732 100644
--- a/src/algebra/string.spad.pamphlet
+++ b/src/algebra/string.spad.pamphlet
@@ -117,6 +117,9 @@ Character: OrderedFinite() with
 
 \section{domain CCLASS CharacterClass}
 <<domain CCLASS CharacterClass>>=
+import Character
+import String
+import List
 )abbrev domain CCLASS CharacterClass
 ++ Author: Stephen M. Watt
 ++ Date Created: July 1986
@@ -204,7 +207,7 @@ CharacterClass: Join(SetCategory, ConvertibleTo String,
 	brace():%	== charClass []
 
 	insert_!(c, a)	== (a(ord c) := true; a)
-	remove_!(c, a)	== (a(ord c) := false; a)
+	remove_!(c: Character, a:%) == (a(ord c) := false; a)
 
 	inspect(a) ==
 	    for i in 0..N-1 | a.i repeat
diff --git a/src/algebra/tree.spad.pamphlet b/src/algebra/tree.spad.pamphlet
index a174308e..c574d9a4 100644
--- a/src/algebra/tree.spad.pamphlet
+++ b/src/algebra/tree.spad.pamphlet
@@ -9,8 +9,12 @@
 \eject
 \tableofcontents
 \eject
+
 \section{domain TREE Tree}
+
 <<domain TREE Tree>>=
+import Boolean
+import List
 )abbrev domain TREE Tree
 ++ Author:W. H. Burge
 ++ Date Created:17 Feb 1992
@@ -66,7 +70,7 @@ Tree(S: SetCategory): T==C where
     setvalue_!(t,s) == 
       t case empty => error "cannot set value of an empty tree"
       (t.node.value:=s;s)
-    count(n, t) == 
+    count(n: S, t: %) == 
       t case empty => 0
       i := +/[count(n, c) for c in children t]
       value t = n => i + 1
diff --git a/src/algebra/triset.spad.pamphlet b/src/algebra/triset.spad.pamphlet
index 2fa126c0..1057bf7b 100644
--- a/src/algebra/triset.spad.pamphlet
+++ b/src/algebra/triset.spad.pamphlet
@@ -9,8 +9,14 @@
 \eject
 \tableofcontents
 \eject
+
 \section{category TSETCAT TriangularSetCategory}
+
 <<category TSETCAT TriangularSetCategory>>=
+import Boolean
+import NonNegativeInteger
+import OutputForm
+import List
 )abbrev category TSETCAT TriangularSetCategory
 ++ Author: Marc Moreno Maza (marc@nag.co.uk)
 ++ Date Created: 04/26/1994
@@ -317,7 +323,7 @@ TriangularSetCategory(R:IntegralDomain,E:OrderedAbelianMonoidSup,_
                  p := init(p)
        red
 
-     reduce(p,ts,redOp,redOp?) ==
+     reduce(p: P,ts: S,redOp: (P,P)->P,redOp?: (P,P)->Boolean) ==
        (empty? ts) or (ground? p) => p
        ts0 := ts
        while (not empty? ts) and (not ground? p) repeat
@@ -428,7 +434,7 @@ TriangularSetCategory(R:IntegralDomain,E:OrderedAbelianMonoidSup,_
      algebraic? (v,ts) ==
        member?(v,algebraicVariables(ts))
 
-     select  (ts,v) ==
+     select(ts: %,v: V): Union(P,"failed") ==
        lp : List (P) := sort(supRittWu?,members(ts))$(List P)
        while (not empty? lp) and (not (v = mvar(first lp))) repeat
          lp := rest lp
diff --git a/src/algebra/view2D.spad.pamphlet b/src/algebra/view2D.spad.pamphlet
index 8d2b67e4..fc770f12 100644
--- a/src/algebra/view2D.spad.pamphlet
+++ b/src/algebra/view2D.spad.pamphlet
@@ -6,10 +6,11 @@
 \maketitle
 \begin{abstract}
 \end{abstract}
-\eject
 \tableofcontents
 \eject
+
 \section{domain GRIMAGE GraphImage}
+
 <<domain GRIMAGE GraphImage>>=
 )abbrev domain GRIMAGE GraphImage
 ++ Author: Jim Wen
@@ -365,7 +366,7 @@ GraphImage (): Exports == Implementation where
       unitsToBe
     graphImage                == graph []
 
-    makeGraphImage(llp) ==
+    makeGraphImage(llp: L L P) ==
       l := #llp
       makeGraphImage(llp,
         [pointColorDefault() for i in 1..l],
diff --git a/src/interp/c-util.boot b/src/interp/c-util.boot
index c45159a7..3735a815 100644
--- a/src/interp/c-util.boot
+++ b/src/interp/c-util.boot
@@ -794,3 +794,17 @@ displayModemaps E ==
  
 GCOPY ob == COPY ob  -- for now
  
+--%
+++ format the set of candidate operations.
+displayAmbiguousSignatures(op,sigs) ==
+  [:showCandidate(op, sig) for sig in sigs] where
+     showCandidate(op,sig) ==
+       ["%l", "        ", op, '": ", 
+         :bright formatUnabbreviated ["Mapping",:sig]]
+
+++ Display diagnostic message about ambiguous operation `op', with
+++ possible resolutions given by the list `sigs'.
+ambiguousSignatureError(op, sigs) ==
+  stackSemanticError(['"signature of lhs not unique.  Candidates are:",
+    :displayAmbiguousSignatures($op,sigs)],nil)
+
diff --git a/src/interp/define.boot b/src/interp/define.boot
index 2e096be4..2d1a94e4 100644
--- a/src/interp/define.boot
+++ b/src/interp/define.boot
@@ -996,10 +996,8 @@ hasSigInTargetCategory(argl,form,opsig,e) ==
     --accept only those signatures op right length which match declared modes
   0=c => (#(sig:= getSignatureFromMode(form,e))=#form => sig; nil)
   1<c =>
-    sig:= first potentialSigList
-    stackWarning('"signature of lhs not unique: %1bp chosen",
-      [["Mapping",:sig]])
-    sig
+    ambiguousSignatureError($op,potentialSigList)
+    first potentialSigList
   nil --this branch will force all arguments to be declared
  
 compareMode2Arg(x,m) == null x or modeEqual(x,m)
diff --git a/src/interp/lisplib.boot b/src/interp/lisplib.boot
index 7296b447..641b2799 100644
--- a/src/interp/lisplib.boot
+++ b/src/interp/lisplib.boot
@@ -425,7 +425,7 @@ initializeLisplib libName ==
 ++ return to toplevel reader.
 leaveIfErrors libName ==
   errorCount() ^=0 =>
-    sayMSG ['"   Errors in processing ",$liplibkind,'" ",:bright libName,'":"]
+    sayMSG ['"   Errors in processing ",$lisplibKind,'" ",:bright libName,'":"]
     sayMSG ['"     not replacing ",$spadLibFT,'" for",:bright libName]
     spadThrow()