Sets II

Predefined sets

Wall has several predefined sets. Some of them resemble types in other languages, like int, string, symbol and complex. In Wall, int is the set of all integers, string is the set of all strings, symbol is the set of all symbols and complex is the set of all complex numbers.

w> // the set of all integers is equal to the
w> // set of all integers plus 0
w> int .== (s+e int 0)
true
w> // the set of all strings is equal to the
w> // set of all strings plus 0
w> string .== (s+e string 0)
false
w> foo =
w> // is foo a symbol?
w> symbol foo
true
w> // are the ints a subset of complex numbers?
w> subs? int complex
true

everything

There is one special set called everything that contains everything that Wall does or will ever contain, including itself.

w> // are the ints a subset of everything?
w> int.subs? everything
true
w> // the disjoint union of everything and everything
w> everything.s- everything
:[]
w> // does everything contain everything?
w> everything.subs? everything
true

The symbol _ is an alias for everything.

w> == _ everything
true

Sets are like guards

If you're coming from a language like Erlang or Clojure, you may be familiar with guards. In these language, a guard accepts any value and returns true or false depending on what the value is. In Wall, guards no different than sets. They are functions that contain every possible Wall value in their domain mapped to true or false in their range. Below, let's define a set (or guard) that checks if an integer is greater than 5.

w> gt5? = (filt-s int (> 5))
w> // is 6 greater than 5?
w> gt5? 6
true
w> // is 5 greater than 5?
w> gt5? 5
false
w> // is 'foo greater than 5?
w> gt5? 'foo
false