Probabilistic Quantifiers in Softanza: Natural Proportions Meet Logical Precision

A continuous path leading toward a grand pyramid structure.

Basic Examples

Here’s how these quantifiers can be used in practice:

load "stzlib.ring"

? Some( NumbersIn( -5 : 5 ) )
#--> [ -1, -4, -5, 3 ]

? Most( PositiveNumbersIn( -5 : 5 ) )
#--> [ 1, 2, 4, 5 ]

Each probabilistic quantifier corresponds to a default proportion of items: - Few() → 10% - Some() → 30% - Most() → 90%

You can also customize these proportions using commands like SetFew(0.15) or SetMost(0.85).

The Probabiliistic Continuum

These quantifiers form a continuum:
No() → Few() → Some() → Half() → Many() → Most() → All()

They’re especially powerful when used in probabilistic and random contexts, like so:

SetSome(0.4)

? Some( RandomNumbersIn(1:10) )
#--> [ 5, 2, 7, 9 ]

? Few( RandomNumbersInU(1:10) ) # "U" for Unique items
#--> [ 1, 4 ]

For completeness, the All() and No() quantifiers are straightforward: - All() returns all items in a list. - No() returns an empty list.

Example:

? All([ "A", "B", "C" ])
#--> [ "A", "B", "C" ]

? No([ "A", "B", "C" ])
#--> []

A Sense of Semantic Beauty

For semantic convenience, alternative function names like AllOf(), NoOne(), and NoOneOf() are provided, making the expressions more natural:

Them = [ "Andy", "Bill", "Chris" ]

? AllOf(Them)
#--> [ "Andy", "Bill", "Chris" ]

? NoOneOf(Them)
#--> [ ]

Softanza also supports fluent forms of these functions, which can enhance code readability. By using the Q() suffix, we get more natural expressions:

MyExamNotes = [ 12, 17, 18, 16, 19 ]
Them = MyExamNotes # Semantic alias for clarity
Average = 10

? AllOfQQ(MyExamNotes).ArePositive()
#--> TRUE

? AllOfQQ(Them).AreGreaterThan(Average)
#--> TRUE

NOTE: The Q(aList) function promotes aList to a stzListObject, and QQ(aList) promotes it to a specific type of Softanza list, like QQ([1, 2, 3]), which returns a stzListOfNumbers object. This allows the use of specialized functions like ArePositive(), AreGreaterThan(), etc.

Logical Magic with Quantifiers

I'll show you the case of NothingIn() quantifier, which is an exact alternative of the No() quantifier we saw earlier.

I’ll prefix it with QQ() because I’m working with a list of email addresses and want to promote it to a stzListOfStrings object to check the emails against a regular expression pattern using the Macth() function.

Now, here’s where it gets even more exciting—I’ll add the magical X() suffix!

The X() suffix offers a powerful mechanism to express logical statements declaratively and verify them directly. In this case: - NothingInQQX() checks whether none of the elements in the list satisfy a condition. - EverythingInQQX() checks whether all of them do.

Here’s an example of how it works:

? NothingInQQX([ "aee@net", "@com.com", "--?mail@org" ]).MatchesX(rxp(:eMail))
#--> TRUE  # No element in the list matches the email pattern.

? NothingInQQX([ "aee@net", "@com.com", "--?mail@org", "info@mail.com" ]).MatchesX(rxp(:eMail))
#--> FALSE # At least one element matches the email pattern.

? EverythingInQQX([ "hello@mail.com", "info@mail.org" ]).MatchesX(rxp(:eMail))
#--> TRUE  # All elements match the email pattern.

? EverythingInQQX([ "hello@mail.com", "info@mail.org", "~;@com" ]).MatchesX(rxp(:eMail))
#--> FALSE # Not all elements match the email pattern.

This approach combines intuitive expression with precise logic, allowing for clear and concise condition validation.

NOTE: The rxp(:email) utility returns the regular expression pattern for a valid email: "^[a-zA-Z0-9._%+-]+@[a-zA-Z0-9.-]+\.[a-zA-Z]{2,}$".

Conclusion

Probabilistic quantifiers in Softanza enhance coding fluency, bridging the gap between natural language and precise logic. They enable expressive, easy-to-read code while still maintaining the power of rigorous validation.

See them in action in Haro Notepad hereafter:

Cite

Mansour Ayouni. "Probabilistic Quantifiers in Softanza: Natural Proportions Meet Logical Precision". Softanza narrations, 2025. https://mayouni.github.io/stzsite/en/narrations/stz-probabilistic-quantifiers-narration.html

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