String Equality

Here are some equal strings:

"abc"    equals  "abc"

"abc de" equals "abc de"

And here are some unequal strings:

"ab"     !equals   "abc"
"abC"    !equals   "abc"
"abc"    !equals   "aBc"

Here are the rules for string equality. The symbol x stands for a single character, as does y. The symbol X stands for a string of characters, as does Y. The symbol + stands for concatenation.

1. equals( "", "" )   = true

2. equals( "", X )    = false if X is not the empty string

3. equals( X, "" )    = false if X is not the empty string

4. equals( x+X, y+Y ) = false if x != y

5. equals( x+X, y+Y ) = true  if x == y and equals( X, Y )

Rule 4 means that if you see two strings that start with different characters, they the strings are not equal. For example,

equals( "bat", "radio" ) = false

In the above example, x is the character 'b', X is the string "at", y is the character 'r', Y is the string "adio".

Here is another example:

equals( "rat", "rat" ) = equals( "at", "at")   // rule 5
equals(  "at",  "at" ) = equals(  "t",  "t")   // rule 5
equals(   "t",   "t" ) = equals(   "",   "")   // rule 5
equals(    "",    "" ) = true                  // rule 1

For another example,

equals( "rat", "ra"  ) = equals( "at", "a")    // rule 5
equals(  "at",  "a"  ) = equals(  "t",  "")    // rule 5
equals(   "t",   ""  ) = false                 // rule 3

And yet another example,

equals( "rAt", "rat"  ) = equals( "At", "at")   // rule 5
equals(  "At",  "at"  ) = false                 // rule 4