How can I check that the value is String or Integer or Date?

In MUMPS, not everything is so simple, so specify technical task ;)

Example:

1. USER>set v1=1,v2="1" zzdump v1,v2
    
   0000: 31                                                      1
   0000: 31                                                      1

2. what to do with dates:
   30000 is a number or date 20.02.1923?
   or
   "20.02.1923" - is it a date or a string?
3. what about numbers: 0 is %TinyInt, %SmallInt, or %Integer?
4. what about boolean: 1 is %Boolean or %Integer?

In addition, you mix MUMPS (variable) and InterSystems ObjectScript (%Library.XXX): see Variable Types

Extending the reply of  @Vitaliy.Serdtsev 
Basically whatever your variable holds could be a %String  (also including binary values)
COS has a few check functions to interpret the content 

• $ISOBJECT
• $ISVALIDDOUBLE
• $ISVALIDNUM
• $INUMBER
• $LISTVALID
• the whole block of $ZD,$ZDH,$ZDT,$ZDTH,$ZT,$ZTH
• $MATCH

Further on the Pattern Match operator ?  let you sort out pure text and binary, .....

All you have is just content. It is left up to you to decide what type it is.
You can find out by those functions what is NOT.

Only the data type classes decide to some limit what type it should be.

There are actually two (maybe more) levels of ObjectScript.  There is basic ObjectScript, which is an very extended version of the ANSI M language.  [ footnote [ANSI M is the successor of the ANSI MUMPS language and that language, without the large number of extensions supported by basic ObjectScript, could be considered to be a third language level although no modern programmer would restrict their code to this much older language definition.] ]  And there is the Class Language ObjectScript, which includes things like type-name classes:  %Library.String (can be abbreviated %String), %Library.Integer (can be abbreviated %Integer), etc.  It also includes Class Methods (with syntax like ##class(Class.Name).ClassMethodName(arg1,arg2)) and there are Object Methods (which look like oref.ObjectMethodName(arg1,arg2), where oref must contains an extended ObjectScript object reference) and there are Object Properties (which look like oref.PropName, where oref must contain an extended ObjectScript object reference.)

An example of a basic ObjectScript statement is SET var1=42,var2="42"  Almost every operation in basic ObjectScript thinks var1 and var2 contain identical values.  So the string equality operation var1=var2 returns 1 because var1 is converted to a string and "42" equals "42".  The numeric comparison operations var1<var2 and var1'<var2 return 0 and 1 because var2 is converted to a numeric and 42<42 is false while 42'<42 is true.  We could also evaluate var1+var2 and the result will be 84 (or is that result "84"--who can tell?).

In Class Language ObjectScript you can declare
          property LimitedInt : %Integer(MAXVAL=10);
and if you (directly or indirectly) call the %ValidateObject() method on a class object containing the property LimitedInt then the contents of LimitedInt may be checked to make sure they look like an integer with a value not greater than 10.  However, only Class Language methods like %SerializeObject, %ValidatObject, %Save, etc. make these checks on the value of LimitedInt.  If someone executes
          SET oref.LimitedInt=20.95
in basic ObjectScript, the basic ObjectScript execution will not signal an error despite the fact that 20.95 is larger than the MAXVAL and despite the fact that 20.95 is NOT a %Integer.  Only executing an appropriate Class Language method will detect that oref.LimitedInt does not contain a valid value.  The purpose of %Library.DataType subclasses is to make it possible that a %Save() method does not save invalid property values into a data base.

Certain ObjectScript conversions may change an ObjectScript value.  This can happen when changing a well-formed numeric string to be a decimal number because the decimal arithmetic implemented in ObjectScript mathematics supports no more than 19 decimal digits of precision.  Consider,

USER>set a="12345678901234567890123",b="12345678901234567890124",c="123456789012345678901230"
USER>write b>a," ",a>b," ",+a," ",+b
0 0 12345678901234567890000 12345678901234567890000

Because the > and < operators are arithmetic-comparison operators the string operands are converted to a numeric value with only 19 significant digits of precision and the resulting numeric values for a and b end up being equal so neither b>a nor a>b are true.  However, the sorts-after operator, ]], orders the canonical numeric strings before any non-empty string that does not have canonical numeric syntax.  The canonical numeric strings are sorted in numeric order while strings that do not have canonical numeric syntax are sorted in textual string order.  This is also the default rule for ordering subscript values in ObjectScript.  Operands of ]] are converted to strings before doing  this subscript ordering.  The values a, b and c are all canonical numeric strings and ObjectScript is perfectly capable of doing the sorts-after string comparisons on very long canonical numeric strings.  Consider,

USER>write a]]b," ",b]]a," ",b]]c," ",c]]b
0 1 0 1

Now a and b are both canonical numeric strings with 23 digits and their first 22 digits are equal but the b has a 23rd digit larger than the 23rd digit of a, so b sorts-after a.  But b does not sorts-after c because c has more significant digits so the canonical numeric value of c is greater than the canonical numeric value of b.

The basic ObjectScript language has a very small class of built-in types.

(1) There are the ObjectScript string values, which include the subclass of canonical numeric strings.

(2) There are the default decimal floating-point values which do not have more 19 digits of decimal precision (and may sometimes have less than 19 digits of precision because the implemented accuracy of ObjectScript decimal arithmetic operations is approximately 18.96 decimal digits.)  Every decimal floating-point value can be converted exactly to a canonical numeric string (but canonical numeric string values with more than 18 digit characters cannot always be converted exactly to a decimal floating-point numeric result but must instead be a decimal numeric value that is an approximation.

(3) Basic ObjectScript supports a third set of "$DOUBLE values" which contains the *binary* floating-point values specified by the IEEE 64-bit binary floating-type type.  The 64-bit binary floating-point arithmetic specified by the IEEE standard has approximately 15.95 decimal digits of precision but since the representation is binary, and not decimal, an exact conversion of a 64-bit IEEE binary floating-point value to a decimal string can have over 1000 digits.  Now every $DOUBLE binary floating-point value could be exactly converted to a canonical numeric string but it is not reasonable to have such a conversion produce such long strings.  The default conversion of a $DOUBLE value to a canonical numeric string will have no more than 20 significant digits, and the approximated 20th significant digit will never be a 5 or 0 (unless that 20th digit results in an exact conversion.)  Using a default canonical numeric string with 20 significant digits for $DOUBLE conversions means the ]], sorts-after, operator will correctly order a $DOUBLE binary floating-point value in-between the adjacent 19-digit decimal floating-point values of the ObjetScript default decimal numeric type.

(4) There are also the oref values which are the basic ObjectScript values created by Class Language ObjectScript.  Basic ObjectScript can do property evaluation, property assignment and method calls using the basic ObjectScript oref type.  Basic ObjectScript can convert oref values to the ObjectScript string type and the ObjectScript decimal arithmetic type but neither of these conversions is particularly useful unless you are debugging.

The first part is easy... string, integer,... that's not the problem.

The second part, is it a date or not depends on the date format(s) you expect (or allow).

But for the first part, you can use this approach:

/// Return values
/// 0=empty, 1=string, 2=integer, 3=float/radix-10, 4=float/radix-2, 5=object
ClassMethod ValType(var) 
{
  if var="" quit 0
  if $isobject(var) quit 5
  quit $select($length(var)>254:1, 1:$translate($ascii($listbuild(var),2),1245678,1122334))
}

Of course, hardcore people would use just one line

ClassMethod ValType(var) { q $s(var="":0, $isobject(var):5, $l(var)>254:1, 1:$tr($a($lb(var),2),1245678,1122334)) }