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Built-in relations

On their own, built-in numbers and strings act no different than other uninterpreted constants, but they can be manipulated with special relations added by #builtin declarations.

A #builtin declarations connects a certain identifiers to a certain built-in relation. If you write

#builtin INT_PLUS plus
#builtin NAT_SUCC s

then the identifiers plus and s will be treated, throughout the program, as a built-in definition instead of as a regular identifier.

  • The NAT_ZERO builtin takes no arguments and represents the natural number zero.
  • The NAT_SUCC builtin takes one natural number argument, and adds one to it. If NAT_SUCC is s, then the premise s X == 0 will always fail, since X would have to be negative for that solution to work.
  • The INT_PLUS builtin takes two or more integer arguments and adds them all.
  • The INT_MINUS builtin takes two integer arguments and returns an integer, subtracting the second from the first.
  • The STRING_CONCAT builtin takes two or more string arguments and concatenates them.

How built-in relations work

All built-in relations