Edit detail for string conversions revision 1 of 1

Here is a package that converts strings to numbers. It is only to be considered as a starting point. There is no error checking, it is probably slow and certainly buggy...

)abbrev package STRCNV StringConversions
StringConversions(): Exports == Implementation where
    Exports == with

      coerce: String -> Integer

      coerce: String -> Fraction Integer

      coerce: String -> List Fraction Integer

      coerce: String -> List Integer

      coerce: String -> Set Integer

    Implementation == add

      sexfloat:SExpression:=convert(coerce("Float")@Symbol)$SExpression

      coerce(s: String): Fraction Integer ==
        if not NUMBERP(READ_-FROM_-STRING(s)$Lisp)$Lisp
        then error "coerce: String -> Fraction Integer: not a number"
        else
          sex := interpret(packageTran(ncParseFromString(s)$Lisp)$Lisp)$Lisp
          if (car car sex = sexfloat) then
             retract((cdr cdr sex) pretend Float)@Fraction(Integer)
          else
            if integer?(cdr sex) then
              ((cdr sex) pretend Integer)::Fraction Integer
            else
              (cdr cdr sex) pretend Fraction Integer

      coerce(s: String): Integer ==
        PARSE_-INTEGER(s)$Lisp

      coerce(r: String): List Fraction Integer ==
        map(coerce #1, split(r, char(" "))$String)_
          $FiniteLinearAggregateFunctions2(String, List String, Fraction Integer, _
                                           List Fraction Integer)

      coerce(r: String): List Integer ==
        map(coerce(#1), split(r, char(" "))$String)_
          $FiniteLinearAggregateFunctions2(String, List String, Integer, _
                                           List Integer)

      coerce(r: String): Set Integer ==
        s: String := delete(delete(r, #r), 1)
        brace(map(PARSE_-INTEGER(#1)$Lisp, split(s, char(" "))$String)_
          $FiniteLinearAggregateFunctions2(String, List String, Integer, _
                                           List Integer))$Set(Integer)

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1862277760152673546-25px.001.spad
      using old system compiler.
   STRCNV abbreviates package StringConversions 
------------------------------------------------------------------------
   initializing NRLIB STRCNV for StringConversions 
   compiling into NRLIB STRCNV 
   compiling exported coerce : String -> Fraction Integer
****** comp fails at level 5 with expression: ******
error in function coerce 

(SEQ
 (LET (|:| #1=#:G671 (|Boolean|))
   ((|Sel| |Lisp| NUMBERP) ((|Sel| |Lisp| READ-FROM-STRING) |s|)))
 (|exit| 1
  (IF #1#
      (SEQ | << |
           (LET |sex|
             ((|Sel| |Lisp| |interpret|)
              ((|Sel| |Lisp| |packageTran|)
               ((|Sel| |Lisp| |ncParseFromString|) |s|))))
           | >> |
           (LET (|:| #2=#:G673 (|Boolean|))
             (= (|car| (|car| |sex|)) |sexfloat|))
           (|exit| 1
            (IF #2#
                (@ (|retract| (|pretend| (|cdr| (|cdr| |sex|)) (|Float|)))
                 (|Fraction| (|Integer|)))
                (SEQ
                 (LET (|:| #3=#:G672 (|Boolean|))
                   (|integer?| (|cdr| |sex|)))
                 (|exit| 1
                  (IF #3#
                      (|::| (|pretend| (|cdr| |sex|) (|Integer|))
                       (|Fraction| (|Integer|)))
                      (|pretend| (|cdr| (|cdr| |sex|))
                       (|Fraction| (|Integer|)))))))))
      (|error| "coerce: String -> Fraction Integer: not a number"))))
****** level 5  ******
$x:= (LET sex ((Sel Lisp interpret) ((Sel Lisp packageTran) ((Sel Lisp ncParseFromString) s))))
$m:= NoValueMode
$f:=
((((#:G671 # #) (|s| # #) (|sexfloat| # #) (|#| #) ...)))

   >> Apparent user error:
   No mode in assignment to: 
   sex

Let's try it:

coerce("123.12")@FRAC INT

   An expression involving @ Fraction(Integer) actually evaluated to 
      one of type None . Perhaps you should use :: Fraction(Integer) .