* algebra/perman.spad.pamphlet (Permanent): Specify type of local

	variable j.
	* algebra/patmatch1.spad.pamphlet (PatternMatchTools): Tidy.
	* algebra/padic.spad.pamphlet: Restrict type of literal constants.
	* algebra/sttf.spad.pamphlet: Likewise.
	* algebra/puiseux.spad.pamphlet: Likewise.
	* algebra/odealg.spad.pamphlet (SystemODESolver) [applyLodo0]:
	Specify type of local variable ans.
	* algebra/numtheor.spad.pamphlet (IntegerNumberTheoryFunctions): Tidy.
	* algebra/naalgc.spad.pamphlet (MonadWithUnit) [rightPower]:
	Specify type of local variable res.
	[leftPower]: Likewise.
	* algebra/lodop.spad.pamphlet (NonCommutativeOperatorDivision)
	[leftLcm]: Specify type of local variable v.
	* algebra/intfact.spad.pamphlet (IntegerRoots) [approxSqrt]:
	Specify type of local variables old and new.
	* algebra/elfuts.spad.pamphlet
	(EllipticFunctionsUnivariateTaylorSeries):  Restrict types of
	literal constants.
	* algebra/ffnb.spad.pamphlet
	(FiniteFieldNormalBasisExtensionByPolynomial): Likewise.
	* algebra/fnla.spad.pamphlet (FreeNilpotentLie): Likewise.
	* algebra/intaux.spad.pamphlet (IntegrationResult): Likewise.
	* algebra/defintef.spad.pamphlet
	(ElementaryFunctionDefiniteIntegration) [checkSMP]:  Specify type
	in the 	definition of local variable n.
	* algebra/combinat.spad.pamphlet (IntegerCombinatoricFunctions):
	Tidy definition of local variables.
	* algebra/clifford.spad.pamphlet (CliffordAlgebra): Specify type in
	the definition of local variables k, exchanges, bz.
	* algebra/catdef.spad.pamphlet (CartesianTensor): Specify type in the
	definition of local varibles rx and offz.
	Remove useless variables zol, xol, oly, and zoly.

23 files changed, 153 insertions, 105 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index 3037cb37..b026d971 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,41 @@
 2011-10-24  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
+	* algebra/perman.spad.pamphlet (Permanent): Specify type of local
+	variable j.
+	* algebra/patmatch1.spad.pamphlet (PatternMatchTools): Tidy.
+	* algebra/padic.spad.pamphlet: Restrict type of literal constants.
+	* algebra/sttf.spad.pamphlet: Likewise.
+	* algebra/puiseux.spad.pamphlet: Likewise.
+	* algebra/odealg.spad.pamphlet (SystemODESolver) [applyLodo0]:
+	Specify type of local variable ans.
+	* algebra/numtheor.spad.pamphlet (IntegerNumberTheoryFunctions): Tidy.
+	* algebra/naalgc.spad.pamphlet (MonadWithUnit) [rightPower]:
+	Specify type of local variable res.
+	[leftPower]: Likewise.
+	* algebra/lodop.spad.pamphlet (NonCommutativeOperatorDivision)
+	[leftLcm]: Specify type of local variable v.
+	* algebra/intfact.spad.pamphlet (IntegerRoots) [approxSqrt]:
+	Specify type of local variables old and new.
+	* algebra/elfuts.spad.pamphlet
+	(EllipticFunctionsUnivariateTaylorSeries):  Restrict types of
+	literal constants.
+	* algebra/ffnb.spad.pamphlet
+	(FiniteFieldNormalBasisExtensionByPolynomial): Likewise.
+	* algebra/fnla.spad.pamphlet (FreeNilpotentLie): Likewise.
+	* algebra/intaux.spad.pamphlet (IntegrationResult): Likewise.
+	* algebra/defintef.spad.pamphlet
+	(ElementaryFunctionDefiniteIntegration) [checkSMP]:  Specify type
+	in the 	definition of local variable n.
+	* algebra/combinat.spad.pamphlet (IntegerCombinatoricFunctions):
+	Tidy definition of local variables.
+	* algebra/clifford.spad.pamphlet (CliffordAlgebra): Specify type in
+	the definition of local variables k, exchanges, bz.
+	* algebra/catdef.spad.pamphlet (CartesianTensor): Specify type in the
+	definition of local varibles rx and offz.
+	Remove useless variables zol, xol, oly, and zoly.
+
+2011-10-24  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
 	* interp/compiler.boot (compArgumentsAndTryAgain): Fail only if
 	elaboration of all arguments fails.
 
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index dcd03071..aad21917 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -1164,6 +1164,7 @@ axiom_algebra_layer_10_objects = \
 	$(addprefix $(OUT)/, \
 	   $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_10)))
 $(OUT)/ARRAY2.$(FASLEXT): $(OUT)/IFARRAY.$(FASLEXT)
+$(OUT)/ORESUP.$(FASLEXT): $(OUT)/PR.$(FASLEXT)
 
 axiom_algebra_layer_11 = \
   APPLYORE ARRAY1   ARRAY12  ARRAY2   \
diff --git a/src/algebra/carten.spad.pamphlet b/src/algebra/carten.spad.pamphlet
index a1fd01f6..7cc2fbbb 100644
--- a/src/algebra/carten.spad.pamphlet
+++ b/src/algebra/carten.spad.pamphlet
@@ -272,7 +272,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
             v = dim2 => 2
             v = dim3 => 3
             v = dim4 => 4
-            rx := 0
+            rx: NNI := 0
             while v ~= 0 repeat
                 qr := divide(v, dim)
                 v  := qr.quotient
@@ -431,7 +431,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
             z
         coerce(m: SM(dim,R)): % ==
             z := new(dim**2, 0)
-            offz := 0
+            offz: NNI := 0
             for i in 0..dim-1 repeat
                 for j in 0..dim-1 repeat
                     set!(z, offz + j, m(i+1,j+1))
@@ -500,7 +500,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
                 error "Improper index for contraction"
             if i > j then (i,j) := (j,i)
 
-            rl:= (rx- j) pretend NNI; nl:= dim**rl; zol:= 1;     xol:= zol
+            rl:= (rx- j) pretend NNI; nl:= dim**rl
             rm:= (j-i-1) pretend NNI; nm:= dim**rm; zom:= nl;    xom:= zom*dim
             rh:= (i - 1) pretend NNI; nh:= dim**rh; zoh:= nl*nm
             xoh:= zoh*dim**2
@@ -511,7 +511,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
                 for m in 1..nm _
                 for xm in xh.. by xom for zm in zh.. by zom repeat
                     for l in 1..nl _
-                    for xl in xm.. by xol for zl in zm.. by zol repeat
+                    for xl in xm.. for zl in zm.. repeat
                         set!(z, zl, 0)
                         for k in 1..dim for xk in xl.. by xok repeat
                             set!(z, zl, get(z,zl) + get(x,xk))
@@ -524,11 +524,11 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
             i < 1 or i > rx or j < 1 or j > ry =>
                 error "Improper index for contraction"
 
-            rly:= (ry-j) pretend NNI;  nly:= dim**rly;  oly:= 1;    zoly:= 1
+            rly:= (ry-j) pretend NNI;  nly:= dim**rly
             rhy:= (j -1) pretend NNI; nhy:= dim**rhy 
-            ohy:= nly*dim; zohy:= zoly*nly
+            ohy:= nly*dim; zohy:= nly
             rlx:= (rx-i) pretend NNI;  nlx:= dim**rlx  
-            olx:= 1;        zolx:= zohy*nhy
+            zolx:= zohy*nhy
             rhx:= (i -1) pretend NNI;  nhx:= dim**rhx
             ohx:= nlx*dim;  zohx:= zolx*nlx
 
@@ -537,11 +537,11 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
             for dxh in 1..nhx _
             for xh in 0.. by ohx for zhx in 0.. by zohx repeat
                 for dxl in 1..nlx _
-                for xl in xh.. by olx for zlx in zhx.. by zolx repeat
+                for xl in xh.. for zlx in zhx.. by zolx repeat
                     for dyh in 1..nhy _
                     for yh in 0.. by ohy for zhy in zlx.. by zohy repeat
                         for dyl in 1..nly _
-                        for yl in yh.. by oly for zly in zhy.. by zoly repeat
+                        for yl in yh.. for zly in zhy.. repeat
                             set!(z, zly, 0)
                             for k in 1..dim _
                             for xk in xl.. by nlx for yk in yl.. by nly repeat
@@ -556,13 +556,13 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
                 error "Improper indicies for transposition"
             if i > j then (i,j) := (j,i)
 
-            rl:= (rx- j) pretend NNI; nl:= dim**rl; zol:= 1;      zoi := zol*nl
+            rl:= (rx- j) pretend NNI; nl:= dim**rl; zoi := nl
             rm:= (j-i-1) pretend NNI; nm:= dim**rm; zom:= nl*dim; zoj := zom*nm
             rh:= (i - 1) pretend NNI; nh:= dim**rh; zoh:= nl*nm*dim**2
             z   := new(#x, 0)
             for h in 1..nh for zh in 0..  by zoh repeat _
             for m in 1..nm for zm in zh.. by zom repeat _
-            for l in 1..nl for zl in zm.. by zol repeat _
+            for l in 1..nl for zl in zm.. repeat _
                 for p in 1..dim _
                 for zp in zl.. by zoi for xp in zl.. by zoj repeat
                     for q in 1..dim _
diff --git a/src/algebra/clifford.spad.pamphlet b/src/algebra/clifford.spad.pamphlet
index 2ae3cffb..ab4c481e 100644
--- a/src/algebra/clifford.spad.pamphlet
+++ b/src/algebra/clifford.spad.pamphlet
@@ -316,7 +316,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
             bz := b2
             for i in 0..n-1 | bit?(b1,i) repeat
                 -- Apply rule  ei*ej = -ej*ei for i~=j
-                k := 0
+                k: NNI := 0
                 for j in i+1..n-1 | bit?(b1, j) repeat k := k+1
                 for j in 0..i-1   | bit?(bz, j) repeat k := k+1
                 if odd? k then c := -c
@@ -344,7 +344,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
             -- The Rep assumes n is small so bubble sort is ok.
             -- Using bubble sort keeps the exchange info obvious.
             wasordered   := false
-            exchanges := 0
+            exchanges: NNI := 0
             while not wasordered repeat
                 wasordered := true
                 for i in 1..#lb-1 repeat
@@ -356,7 +356,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
  
             -- 2. Prepare the basis element
             -- Apply identity ei*ei = Q(ei).
-            bz := 0
+            bz: NNI := 0
             for b in lb repeat
                 bn := (b-1)::NNI
                 if bit?(bz, bn) then
@@ -364,7 +364,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
                     bz:= ( bz - 2**bn )::NNI
                 else
                     bz:= bz + 2**bn
-            [c, bz::NNI]
+            [c, bz]
  
         monomial(c, lb) ==
             r := canonMonom(c, lb)
diff --git a/src/algebra/combinat.spad.pamphlet b/src/algebra/combinat.spad.pamphlet
index f597f98f..23b4a1eb 100644
--- a/src/algebra/combinat.spad.pamphlet
+++ b/src/algebra/combinat.spad.pamphlet
@@ -72,8 +72,8 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
       n < m::I => P(convert(n)@Z)
       concat!(P, new((convert(n+1)@Z - m)::N,0)$IndexedFlexibleArray(I,0))
       for i in m..convert(n)@Z repeat
-         s:I := 1
-         t:I := 0
+         s: I := 1
+         t: I := 0
          for k in 1.. repeat
             l := (3*k*k-k) quo 2
             l > i => leave
@@ -96,18 +96,23 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
       F.Fv := f
  
    binomial(n, m) ==
-      s,b:I
       negative? n or negative? m or m > n => 0
       m = 0 => 1
       n < 2*m => binomial(n, n-m)
-      (s,b) := (0,1)
+      s: I := 0
+      b: I := 1
       if B.Bn = n then
          B.Bm = m+1 =>
             b := (B.Bv * (m+1)) quo (n-m)
             B.Bn := n
             B.Bm := m
             return(B.Bv := b)
-         if m >= B.Bm then (s := B.Bm; b := B.Bv) else (s,b) := (0,1)
+         if m >= B.Bm then
+           s := B.Bm
+           b := B.Bv
+         else
+           s := 0
+           b := 1
       for k in convert(s+1)@Z .. convert(m)@Z repeat
         b := (b*(n-k::I+1)) quo k::I
       B.Bn := n
@@ -122,12 +127,13 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
       factorial n quo s
  
    permutation(n, m) ==
-      t:I
       negative? m or n < m => 0
       m := n-m
       p:I := 1
       for k in convert(m+1)@Z .. convert(n)@Z by 2 repeat
-         if k::I = n then t := n else t := (k*(k+1))::I
+         t: I :=
+           k::I = n => n
+           (k*(k+1))::I
          p := p * t
       p
  
diff --git a/src/algebra/defintef.spad.pamphlet b/src/algebra/defintef.spad.pamphlet
index 34eb5e03..fc604038 100644
--- a/src/algebra/defintef.spad.pamphlet
+++ b/src/algebra/defintef.spad.pamphlet
@@ -131,7 +131,7 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where
            ((w := checkSMP(t, x, k, a, b)) case "failed") or (w::B) => return w
          false
       (v := isPlus p) case List(P) =>
-         n := 0              -- number of summand having a pole
+         n: Z := 0              -- number of summand having a pole
          for t in v::List(P) repeat
            (w := checkSMP(t, x, k, a, b)) case "failed" => return w
            if w::B then n := n + 1
diff --git a/src/algebra/elfuts.spad.pamphlet b/src/algebra/elfuts.spad.pamphlet
index 89b64578..23b4f781 100644
--- a/src/algebra/elfuts.spad.pamphlet
+++ b/src/algebra/elfuts.spad.pamphlet
@@ -57,7 +57,7 @@ EllipticFunctionsUnivariateTaylorSeries(Coef,UTS):
              integrate(1,sign*k**2*$UPS scd.1*$UPS scd.2*$UPS dx)]
  
     sncndn(z,k) ==
-      empty? z => [0 :: ST,1 :: ST,1::ST]
+      empty? z => [0@Coef :: ST,1@Coef :: ST,1@Coef::ST]
       frst z = 0 => YS(sncndnre(k,#1,deriv z,-1),3)
       error "ELFUTS:sncndn: constant coefficient should be 0"
     sn(x,k)  == series sncndn.(coefficients x,k).1
diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet
index 673fd906..b0b42e01 100644
--- a/src/algebra/ffnb.spad.pamphlet
+++ b/src/algebra/ffnb.spad.pamphlet
@@ -590,7 +590,7 @@ FiniteFieldNormalBasisExtensionByPolynomial(GF,uni): Exports == _
             one? x.i => b
             ((x.i)::OUT) *$OUT b
           l:=cons(mon,l)$(List OUT)
-      null(l)$(List OUT) => (0::OUT)
+      null(l)$(List OUT) => (0@GF::OUT)
       r:=reduce("+",l)$(List OUT)
       r
 
diff --git a/src/algebra/fnla.spad.pamphlet b/src/algebra/fnla.spad.pamphlet
index 4feb3a97..b82a1288 100644
--- a/src/algebra/fnla.spad.pamphlet
+++ b/src/algebra/fnla.spad.pamphlet
@@ -283,12 +283,12 @@ FreeNilpotentLie(n:NNI,class:NNI,R: CommutativeRing): Export == Implement where
        r::O * mkcomm(mkcomm(coms(k).1)$Com,mkcomm(coms(k).3)$Com)$Com::O
 
      shallowExpand(f) ==
-       f = 0           => 0::O
+       f = 0           => 0@R::O
        reductum(f) = 0 => shallowE(lC f,lS f)
        shallowE(lC f,lS f) + shallowExpand(reductum f)
 
      deepExpand(f) ==
-       f = 0          => 0::O
+       f = 0          => 0@R::O
        reductum(f) = 0 =>
          lC(f)=1 => Fac(value(lS f))::O
          lC(f)::O * Fac(value(lS f))::O
diff --git a/src/algebra/intaux.spad.pamphlet b/src/algebra/intaux.spad.pamphlet
index d88eb62b..b5267540 100644
--- a/src/algebra/intaux.spad.pamphlet
+++ b/src/algebra/intaux.spad.pamphlet
@@ -171,7 +171,7 @@ IntegrationResult(F:Field): Exports == Implementation where
       l := reverse! [LOG2O f for f in logpart u]$List(O)
       if ratpart u ~= 0 then l := concat(ratpart(u)::O, l)
       if not elem? u then l := concat([NE2O f for f in notelem u], l)
-      null l => 0::O
+      null l => 0@F::O
       reduce("+", l)
 
     NE2O ne ==
diff --git a/src/algebra/intfact.spad.pamphlet b/src/algebra/intfact.spad.pamphlet
index f405476f..f24922c5 100644
--- a/src/algebra/intfact.spad.pamphlet
+++ b/src/algebra/intfact.spad.pamphlet
@@ -324,7 +324,8 @@ IntegerRoots(I:IntegerNumberSystem): Exports == Implementation where
          s := shift(s, n)
          return ((1 + s + a quo s) quo two)
       -- initial approximation for the root is within a factor of 2
-      (new, old) := (shift(1, n quo two), 1)
+      old: I := 1
+      new: I := shift(1, n quo two)
       while new ~= old repeat
          (new, old) := ((1 + new + a quo new) quo two, new)
       new
diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet
index 53a38c6c..758dcf12 100644
--- a/src/algebra/lodop.spad.pamphlet
+++ b/src/algebra/lodop.spad.pamphlet
@@ -186,7 +186,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef  where
             b = 0 =>a
             b0 := b
             u  := monomial(1,0)$P
-            v  := 0
+            v: P := 0
             while leadingCoefficient b ~= 0 repeat
                 qr     := leftDivide(a,b)
                 (a, b) := (b, qr.remainder)
diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet
index c256691a..ce4b81ef 100644
--- a/src/algebra/naalgc.spad.pamphlet
+++ b/src/algebra/naalgc.spad.pamphlet
@@ -119,12 +119,12 @@ MonadWithUnit(): Category == Monad with
          expt(x,n pretend PositiveInteger)
       rightPower(a: %,n: NonNegativeInteger) ==
         zero? n => 1
-        res := 1
+        res: % := 1
         for i in 1..n repeat res := res * a
         res
       leftPower(a: %,n: NonNegativeInteger) ==
         zero? n => 1
-        res := 1
+        res: % := 1
         for i in 1..n repeat res := a * res
         res
 
diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet
index f1251618..4a8101ea 100644
--- a/src/algebra/numtheor.spad.pamphlet
+++ b/src/algebra/numtheor.spad.pamphlet
@@ -335,8 +335,8 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where
   fibonacci n ==
     n = 0 => 0
     negative? n => (odd? n => 1; -1) * fibonacci(-n)
-    f1, f2 : I
-    (f1,f2) := (0,1)
+    f1: I := 0
+    f2: I := 1
     for k in length(n)-2 .. 0 by -1 repeat
       t := f2**2
       (f1,f2) := (t+f1**2,t+2*f1*f2)
diff --git a/src/algebra/odealg.spad.pamphlet b/src/algebra/odealg.spad.pamphlet
index 1a3d355d..b96ffa9d 100644
--- a/src/algebra/odealg.spad.pamphlet
+++ b/src/algebra/odealg.spad.pamphlet
@@ -205,7 +205,7 @@ SystemODESolver(F, LO): Exports == Implementation where
 
 -- computes +/[m(r, i) mm(i, c) for i ranging over the last n columns of m]
     applyLodo0(m, r, mm, c, n) ==
-      ans := 0
+      ans: F := 0
       rr := maxRowIndex mm
       cc := maxColIndex m
       for i in 1..n repeat
diff --git a/src/algebra/padic.spad.pamphlet b/src/algebra/padic.spad.pamphlet
index d7265998..260bb580 100644
--- a/src/algebra/padic.spad.pamphlet
+++ b/src/algebra/padic.spad.pamphlet
@@ -289,7 +289,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where
     showAll?() == true
 
     coerce(x:%):OUT ==
-      empty?(st := stream x) => 0 :: OUT
+      empty?(st := stream x) => 0@I :: OUT
       count : NNI := _$streamCount$Lisp
       l : L OUT := empty()
       n : NNI := 0
@@ -309,8 +309,8 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where
         explicitlyEmpty? st => l
         eq?(st,rst st) and frst st = 0 => l
         concat(prefix("O" :: OUT,[PEXPR ** (n :: OUT)]),l)
-      empty? l => 0 :: OUT
-      reduce("+",reverse! l)
+      empty? l => 0@I :: OUT
+      reduce(_+,reverse! l)
 
 @
 \section{domain PADIC PAdicInteger}
@@ -515,7 +515,7 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where
       m := getExpon x; zp := getZp x
       uu := digits zp
       l : L OUT := empty()
-      empty? uu => 0 :: OUT
+      empty? uu => 0@I :: OUT
       count : NNI := _$streamCount$Lisp
       n : NNI := 0
       while n <= count and not empty? uu repeat
@@ -535,7 +535,7 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where
         explicitlyEmpty? uu => l
         eq?(uu,rst uu) and frst uu = 0 => l
         concat(prefix("O" :: OUT,[PEXPR ** ((n :: I) + m) :: OUT]),l)
-      empty? l => 0 :: OUT
+      empty? l => 0@I :: OUT
       reduce("+",reverse! l)
 
 @
diff --git a/src/algebra/patmatch1.spad.pamphlet b/src/algebra/patmatch1.spad.pamphlet
index 2b7da476..e0812ea2 100644
--- a/src/algebra/patmatch1.spad.pamphlet
+++ b/src/algebra/patmatch1.spad.pamphlet
@@ -532,10 +532,10 @@ PatternMatchTools(S, R, P): Exports == Implementation where
       l1:PRS := failed()
       t : P
       for x in setDifference(ls, bad)
-        while (t := x; failed?(l1 := pmatch(x, p, l))) repeat 0
+        while (t := x; failed?(l1 := pmatch(x, p, l))) repeat nil
       failed? l1 =>
         for x in bad
-          while (t := x; failed?(l1 := pmatch(x, p, l))) repeat 0
+          while (t := x; failed?(l1 := pmatch(x, p, l))) repeat nil
         failed? l1 => [addMatchRestricted(p, ident, l, ident), ls]
         [l1, remove(t, ls)]
       [l1, remove(t, ls)]
diff --git a/src/algebra/perman.spad.pamphlet b/src/algebra/perman.spad.pamphlet
index b45620a4..73e20b31 100644
--- a/src/algebra/perman.spad.pamphlet
+++ b/src/algebra/perman.spad.pamphlet
@@ -164,7 +164,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
       vv : V V I := firstSubsetGray(n)$GRAY
         -- For the meaning of the elements of vv, see GRAY.
       w : V R := new(n,0$R)
-      j := 1   -- Will be the number of the element changed in subset
+      j: I := 1   -- Will be the number of the element changed in subset
       while j ~= (n+1) repeat  -- we sum over all subsets of (1,...,n)
         sgn := -sgn
         b := sgn
@@ -209,7 +209,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
       for i in 1..n repeat
         b := b * w.i
       a := a+b
-      j := 1   -- Will be the number of the element changed in subset
+      j: I := 1   -- Will be the number of the element changed in subset
       while j ~= n repeat  -- we sum over all subsets of (1,...,n-1)
         sgn := -sgn
         b := sgn
@@ -255,7 +255,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
       for i in 1..n repeat
         b := b *$R w.i
       a := a +$R b
-      j := 1   -- Will be the number of the element changed in subset
+      j: I := 1   -- Will be the number of the element changed in subset
       while j ~= n repeat  -- we sum over all subsets of (1,...,n-1)
         sgn := -sgn
         b := sgn
diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet
index b465790c..0abb2891 100644
--- a/src/algebra/puiseux.spad.pamphlet
+++ b/src/algebra/puiseux.spad.pamphlet
@@ -532,7 +532,7 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
     termsToOutputForm:(RN,RN,ST,OUT) -> OUT
     termsToOutputForm(m,rat,uu,xxx) ==
       l : L OUT := empty()
-      empty? uu => 0 :: OUT
+      empty? uu => 0@Coef :: OUT
       count : NNI := _$streamCount$Lisp
       n : NNI := 0
       while n <= count and not empty? uu repeat
@@ -552,7 +552,7 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
         explicitlyEmpty? uu => l
         eq?(uu,rst uu) and frst uu = 0 => l
         concat(prefix("O" :: OUT,[xxx ** (((n::I) * rat + m) :: OUT)]),l)
-      empty? l => 0 :: OUT
+      empty? l => 0@Coef :: OUT
       reduce("+",reverse! l)
 
     coerce(upxs:%):OUT ==
diff --git a/src/algebra/radix.spad.pamphlet b/src/algebra/radix.spad.pamphlet
index df8308ad..ae148819 100644
--- a/src/algebra/radix.spad.pamphlet
+++ b/src/algebra/radix.spad.pamphlet
@@ -113,7 +113,7 @@ RadixExpansion(bb): Exports == Implementation where
     coerce(a):RN == (wholePart a) :: RN + fractionPart a
     coerce(n):%  == n :: RN :: %
     coerce(q):%  ==
-      s := 1; if negative? q then (s := -1; q := -q)
+      s: I := 1; if negative? q then (s := -1; q := -q)
       qr      := divide(numer q,denom q)
       whole   := radixInt (qr.quotient,bb)
       fractn  := radixFrac(qr.remainder,denom q,bb)
@@ -130,11 +130,11 @@ RadixExpansion(bb): Exports == Implementation where
     floor a == floor(a::RN)
 
     wholePart a ==
-      n0 := 0
+      n0: I := 0
       for r in a.int repeat n0 := bb*n0 + r
       a.sgn*n0
     fractionPart(a: %): Fraction Integer ==
-      n0 := 0
+      n0: I := 0
       for r in a.pfx repeat n0 := bb*n0 + r
       null a.cyc =>
           a.sgn*n0/bb**((#a.pfx)::NNI)
@@ -188,7 +188,7 @@ RadixExpansion(bb): Exports == Implementation where
       if not null a.pfx then le := concat(intgroup a.pfx,le)
       if not null le    then le := concat("." :: OUT,le)
       if not null a.int then le := concat(intgroup a.int,le)
-      else le := concat(0 :: OUT,le)
+      else le := concat(0@I :: OUT,le)
       rex := exprgroup le
       if negative? a.sgn then -rex else rex
 
diff --git a/src/algebra/solvedio.spad.pamphlet b/src/algebra/solvedio.spad.pamphlet
index f83c9cb6..7b68eb4b 100644
--- a/src/algebra/solvedio.spad.pamphlet
+++ b/src/algebra/solvedio.spad.pamphlet
@@ -156,7 +156,7 @@ DiophantineSolutionPackage(): Cat == Capsule where
     verifyMinimality(sol, graph, flag) ==
       -- test whether sol contains a minimal homogeneous solution
       flag =>  -- sol is a homogeneous solution
-        i := 1
+        i: I := 1
         while sol.i = 0 repeat
           i := i + 1
         x := sol.i
diff --git a/src/algebra/special.spad.pamphlet b/src/algebra/special.spad.pamphlet
index 8a619f7b..b8c1c293 100644
--- a/src/algebra/special.spad.pamphlet
+++ b/src/algebra/special.spad.pamphlet
@@ -294,7 +294,8 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where
 
         laguerreL(n, x) ==
             n = 0 => 1
-            (p1, p0) := (-x + 1, 1)
+            p0: R := 1
+            p1: R := -x + 1
             for i in 1..n-1 repeat
                 (p1, p0) := ((2*i::R + 1 - x)*p1 - i**2*p0, p1)
             p1
@@ -312,19 +313,22 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where
             p1
         chebyshevT(n, x) ==
             n = 0 => 1
-            (p1, p0) := (x, 1)
+            p0: R := 1
+            p1: R := x
             for i in 1..n-1 repeat
                 (p1, p0) := (2*x*p1 - p0, p1)
             p1
         chebyshevU(n, x) ==
             n = 0 => 1
-            (p1, p0) := (2*x, 1)
+            p0: R := 1
+            p1: R := 2*x
             for i in 1..n-1 repeat
                 (p1, p0) := (2*x*p1 - p0, p1)
             p1
         hermiteH(n, x) ==
             n = 0 => 1
-            (p1, p0) := (2*x, 1)
+            p0: R := 1
+            p1: R := 2*x
             for i in 1..n-1 repeat
                 (p1, p0) := (2*x*p1 - 2*i*p0, p1)
             p1
diff --git a/src/algebra/sttf.spad.pamphlet b/src/algebra/sttf.spad.pamphlet
index f65e7bbc..682d3fb7 100644
--- a/src/algebra/sttf.spad.pamphlet
+++ b/src/algebra/sttf.spad.pamphlet
@@ -134,7 +134,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
     expre(r,e,dx) == lazyIntegrate(r,e*dx)
 
     exp z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (coef := frst z) = 0 => YS expre(1,#1,deriv z)
       TRANSFCN => YS expre(exp coef,#1,deriv z)
       error concat("exp: ",TRCONST)
@@ -165,7 +165,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       -- [lazyIntegrate(rs,st1),lazyIntegrate(rc,st2)]
 
     sincos z ==
-      empty? z => [0 :: ST,1 :: ST]
+      empty? z => [0@Coef :: ST,1@Coef :: ST]
       l :=
         (coef := frst z) = 0 => YS(sincosre(0,1,#1,deriv z,-1),2)
         TRANSFCN => YS(sincosre(sin coef,cos coef,#1,deriv z,-1),2)
@@ -176,7 +176,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
     cos z == sincos(z).cos
 
     tanre:(Coef,ST,ST,Coef) -> ST
-    tanre(r,t,dx,sign) == lazyIntegrate(r,((1 :: ST) + sign*t*t)*dx)
+    tanre(r,t,dx,sign) == lazyIntegrate(r,((1@Coef :: ST) + sign*t*t)*dx)
 
     -- When the compiler had difficulties with the above definition,
     -- I did the following to help it:
@@ -191,13 +191,13 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       -- lazyIntegrate(r,st1)
 
     tan z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (coef := frst z) = 0 => YS tanre(0,#1,deriv z,1)
       TRANSFCN => YS tanre(tan coef,#1,deriv z,1)
       error concat("tan: ",TRCONST)
 
     cotre:(Coef,ST,ST) -> ST
-    cotre(r,t,dx) == lazyIntegrate(r,-((1 :: ST) + t*t)*dx)
+    cotre(r,t,dx) == lazyIntegrate(r,-((1@Coef :: ST) + t*t)*dx)
 
     -- When the compiler had difficulties with the above definition,
     -- I did the following to help it:
@@ -218,7 +218,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       error concat("cot: ",TRCONST)
 
     sec z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       frst z = 0 => recip(cos z) :: ST
       TRANSFCN =>
         cosz := cos z
@@ -245,12 +245,12 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       "failed"
 
     asin z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (coef := frst z) = 0 =>
-        integrate(0,powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+        integrate(0,powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
       TRANSFCN =>
         coef = 1 or coef = -1 =>
-          x := (1 :: ST) - z*z
+          x := (1@Coef :: ST) - z*z
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("asin: ",MAYFPOW)
@@ -260,7 +260,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
           (quot := (deriv z) exquo squirt) case "failed" =>
              error concat("asin: ",NOTINV)
           integrate(asin coef,quot :: ST)
-        integrate(asin coef,powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+        integrate(asin coef,powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
       error concat("asin: ",TRCONST)
 
     acos z ==
@@ -270,7 +270,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       TRANSFCN =>
         coef := frst z
         coef = 1 or coef = -1 =>
-          x := (1 :: ST) - z*z
+          x := (1@Coef :: ST) - z*z
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("acos: ",MAYFPOW)
@@ -280,15 +280,15 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
           (quot := (-deriv z) exquo squirt) case "failed" =>
              error concat("acos: ",NOTINV)
           integrate(acos coef,quot :: ST)
-        integrate(acos coef,-powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+        integrate(acos coef,-powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
       error concat("acos: ",TRCONST)
 
     atan z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (coef := frst z) = 0 =>
-        integrate(0,(recip((1 :: ST) + z*z) :: ST) * (deriv z))
+        integrate(0,(recip((1@Coef :: ST) + z*z) :: ST) * (deriv z))
       TRANSFCN =>
-        (y := recip((1 :: ST) + z*z)) case "failed" =>
+        (y := recip((1@Coef :: ST) + z*z)) case "failed" =>
           error concat("atan: ",LOGS)
         integrate(atan coef,(y :: ST) * (deriv z))
       error concat("atan: ",TRCONST)
@@ -298,7 +298,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
         TRANSFCN => acot(0)$Coef :: ST
         error concat("acot: ",TRCONST)
       TRANSFCN =>
-        (y := recip((1 :: ST) + z*z)) case "failed" =>
+        (y := recip((1@Coef :: ST) + z*z)) case "failed" =>
           error concat("acot: ",LOGS)
         integrate(acot frst z,-(y :: ST) * (deriv z))
       error concat("acot: ",TRCONST)
@@ -309,7 +309,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
         (coef := frst z) = 0 =>
           error "asec: constant coefficient should not be 0"
         coef = 1 or coef = -1 =>
-          x := z*z - (1 :: ST)
+          x := z*z - (1@Coef :: ST)
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("asec: ",MAYFPOW)
@@ -321,7 +321,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
           (quot2 := (quot :: ST) exquo z) case "failed" =>
             error concat("asec: ",NOTINV)
           integrate(asec coef,quot2 :: ST)
-        integrate(asec coef,(powern(-1/2,z*z-(1::ST))*(deriv z)) / z)
+        integrate(asec coef,(powern(-1/2,z*z-(1@Coef::ST))*(deriv z)) / z)
       error concat("asec: ",TRCONST)
 
     acsc z ==
@@ -330,7 +330,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
         (coef := frst z) = 0 =>
           error "acsc: constant coefficient should not be zero"
         coef = 1 or coef = -1 =>
-          x := z*z - (1 :: ST)
+          x := z*z - (1@Coef :: ST)
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("acsc: ",MAYFPOW)
@@ -342,13 +342,13 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
           (quot2 := (quot :: ST) exquo z) case "failed" =>
             error concat("acsc: ",NOTINV)
           integrate(acsc coef,quot2 :: ST)
-        integrate(acsc coef,-(powern(-1/2,z*z-(1::ST))*(deriv z)) / z)
+        integrate(acsc coef,-(powern(-1/2,z*z-(1@Coef::ST))*(deriv z)) / z)
       error concat("acsc: ",TRCONST)
 
 --% Hyperbolic Trigonometric Functions
 
     sinhcosh z ==
-      empty? z => [0 :: ST,1 :: ST]
+      empty? z => [0@Coef :: ST,1@Coef :: ST]
       l :=
         (coef := frst z) = 0 => YS(sincosre(0,1,#1,deriv z,1),2)
         TRANSFCN => YS(sincosre(sinh coef,cosh coef,#1,deriv z,1),2)
@@ -359,7 +359,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
     cosh z == sinhcosh(z).cosh
 
     tanh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (coef := frst z) = 0 => YS tanre(0,#1,deriv z,-1)
       TRANSFCN => YS tanre(tanh coef,#1,deriv z,-1)
       error concat("tanh: ",TRCONST)
@@ -381,10 +381,10 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       recip(sinhz) :: ST
 
     asinh z ==
-      empty? z => 0 :: ST
-      (coef := frst z) = 0 => log(z + powern(1/2,(1 :: ST) + z*z))
+      empty? z => 0@Coef :: ST
+      (coef := frst z) = 0 => log(z + powern(1/2,(1@Coef :: ST) + z*z))
       TRANSFCN =>
-        x := (1 :: ST) + z*z
+        x := (1@Coef :: ST) + z*z
         -- compute order of 'x', in case coefficient(z,0) = +- %i
         (ord := orderOrFailed x) case "failed" =>
           error concat("asinh: ",MAYFPOW)
@@ -401,7 +401,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       TRANSFCN =>
         coef := frst z
         coef = 1 or coef = -1 =>
-          x := z*z - (1 :: ST)
+          x := z*z - (1@Coef :: ST)
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("acosh: ",MAYFPOW)
@@ -409,16 +409,16 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
           odd? order => error concat("acosh: ",FPOWERS)
           -- the argument to 'log' must have a non-zero constant term
           log(z + powern(1/2,x))
-        log(z + powern(1/2,z*z - (1 :: ST)))
+        log(z + powern(1/2,z*z - (1@Coef :: ST)))
       error concat("acosh: ",TRCONST)
 
     atanh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (coef := frst z) = 0 =>
-        (inv(2::RN)::Coef) * log(((1 :: ST) + z)/((1 :: ST) - z))
+        (inv(2::RN)::Coef) * log(((1@Coef :: ST) + z)/((1@Coef :: ST) - z))
       TRANSFCN =>
         coef = 1 or coef = -1 => error concat("atanh: ",LOGS)
-        (inv(2::RN)::Coef) * log(((1 :: ST) + z)/((1 :: ST) - z))
+        (inv(2::RN)::Coef) * log(((1@Coef :: ST) + z)/((1@Coef :: ST) - z))
       error concat("atanh: ",TRCONST)
 
     acoth z ==
@@ -427,7 +427,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
         error concat("acoth: ",TRCONST)
       TRANSFCN =>
         frst z = 1 or frst z = -1 => error concat("acoth: ",LOGS)
-        (inv(2::RN)::Coef) * log((z + (1 :: ST))/(z - (1 :: ST)))
+        (inv(2::RN)::Coef) * log((z + (1@Coef :: ST))/(z - (1@Coef :: ST)))
       error concat("acoth: ",TRCONST)
 
     asech z ==
@@ -435,27 +435,27 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
       TRANSFCN =>
         (coef := frst z) = 0 => error concat("asech: ",NPOWLOG)
         coef = 1 or coef = -1 =>
-          x := (1 :: ST) - z*z
+          x := (1@Coef :: ST) - z*z
           -- compute order of 'x'
           (ord := orderOrFailed x) case "failed" =>
             error concat("asech: ",MAYFPOW)
           (order := ord :: I) = -1 => return asech(coef) :: ST
           odd? order => error concat("asech: ",FPOWERS)
-          log(((1 :: ST) + powern(1/2,x))/z)
-        log(((1 :: ST) + powern(1/2,(1 :: ST) - z*z))/z)
+          log(((1@Coef :: ST) + powern(1/2,x))/z)
+        log(((1@Coef :: ST) + powern(1/2,(1@Coef :: ST) - z*z))/z)
       error concat("asech: ",TRCONST)
 
     acsch z ==
       empty? z => error "acsch: acsch(0) is undefined"
       TRANSFCN =>
         frst z = 0 => error concat("acsch: ",NPOWLOG)
-        x := z*z + (1 :: ST)
+        x := z*z + (1@Coef :: ST)
         -- compute order of 'x'
         (ord := orderOrFailed x) case "failed" =>
           error concat("acsc: ",MAYFPOW)
         (order := ord :: I) = -1 => return acsch(frst z) :: ST
         odd? order => error concat("acsch: ",FPOWERS)
-        log(((1 :: ST) + powern(1/2,x))/z)
+        log(((1@Coef :: ST) + powern(1/2,x))/z)
       error concat("acsch: ",TRCONST)
 
 @
@@ -563,7 +563,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
 --% Exponentials and Logarithms
 
     exp z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (frst z) = 0 =>
         expx := exp(monom(1,1))$STTF
         compose(expx,z)
@@ -581,21 +581,21 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
 --% Trigonometric Functions
 
     sin z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         sinx := sin(monom(1,1))$STTF
         compose(sinx,z)
       error concat("sin: ",ZERO)
 
     cos z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (frst z) = 0 =>
         cosx := cos(monom(1,1))$STTF
         compose(cosx,z)
       error concat("cos: ",ZERO)
 
     tan z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         tanx := tan(monom(1,1))$STTF
         compose(tanx,z)
@@ -607,7 +607,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
       error concat("cot: ",ZERO)
 
     sec z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (frst z) = 0 =>
         secx := sec(monom(1,1))$STTF
         compose(secx,z)
@@ -619,14 +619,14 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
       error concat("csc: ",ZERO)
 
     asin z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         asinx := asin(monom(1,1))$STTF
         compose(asinx,z)
       error concat("asin: ",ZERO)
 
     atan z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         atanx := atan(monom(1,1))$STTF
         compose(atanx,z)
@@ -640,21 +640,21 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
 --% Hyperbolic Trigonometric Functions
 
     sinh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         sinhx := sinh(monom(1,1))$STTF
         compose(sinhx,z)
       error concat("sinh: ",ZERO)
 
     cosh z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (frst z) = 0 =>
         coshx := cosh(monom(1,1))$STTF
         compose(coshx,z)
       error concat("cosh: ",ZERO)
 
     tanh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         tanhx := tanh(monom(1,1))$STTF
         compose(tanhx,z)
@@ -666,7 +666,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
       error concat("coth: ",ZERO)
 
     sech z ==
-      empty? z => 1 :: ST
+      empty? z => 1@Coef :: ST
       (frst z) = 0 =>
         sechx := sech(monom(1,1))$STTF
         compose(sechx,z)
@@ -678,14 +678,14 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
       error concat("csch: ",ZERO)
 
     asinh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         asinhx := asinh(monom(1,1))$STTF
         compose(asinhx,z)
       error concat("asinh: ",ZERO)
 
     atanh z ==
-      empty? z => 0 :: ST
+      empty? z => 0@Coef :: ST
       (frst z) = 0 =>
         atanhx := atanh(monom(1,1))$STTF
         compose(atanhx,z)