Enumeration Type for Operator Associativity

The parser for formulas (Module parse) is fairly general. It allows that for each logical operator, the priority and the associativity can be defined.

The priority means binding strength or precedence. For instance, AND (&) usually binds stronger than OR (|), so "a & b | c" means "(a & b) | c" and "a | b & c" means "a | (b & c)".

The associativity refers to sequences of the same operator, e.g. "a & b & c". There are three possibilities:

• If "&" is left associative, this means "(a & b) & c".
• If "&" is right associative, this means "a & (b & c)".
• If "&" is not associative, this is an error.

This module defines a type assoc_t with the three values ASSOC_LEFT, ASSOC_RIGHT, and ASSOC_NONE.

Not that monadic (prefix) operators can never be left associative, only right associative (in which case e.g. "~ ~ p" (not not p) is legal, or not associative (in which case it is not legal).

In Prolog, the operator type "yfx" is left associative, the operator type "xfy" is right associative, and "xfx" is not associative. There are special types for unary operators ("fx" and "fy" for prefix operators).

The meaning of the different associativities is implemented in the parser:

• Left associativity means that if e.g. "&" is on the top of the operator stack, and you want to push another "&", you first pop the first one.
• Right associativity means that you can push an operator on top of an operator of the same priority.
• No associativity means that it is an error if the next input operator has the same priority as the top operator on the stack.

• Header File (assoc.h)