Abstract Syntax

The (optional) abstract syntax of a language may be specified by a simpler grammar than that for the concrete syntax. For example,
 
<Exp> ::= <Exp> + <Exp>  |  <Exp> - <Exp>  |  <Exp> * <Exp>  |  <Exp> / <Exp>  |  <id>  |  - <Exp>

A grammar for the abstract syntax of simple arithmetic expressions

Compared to the concrete syntax, the abstract syntax is ambiguous and is unsuitable for direct use in building a parser. However it is simpler than the concrete syntax and is very suitable to build the data-structure for the parse-tree returned by a parser, e.g.,
 
datatype Exp = binexp of Exp * Bopr * Exp | unexp of Uopr * Exp | varid of Ide | ...   in [exp.sml].
 
For example, given the input x+y*z either of the following trees is possible according to the abstract syntax above
 
Parse trees for x + y * z
+
*
x y z

correct bindings

  
*
+
x y z

incorrect bindings

 
but only the left tree is correct according to the conventional concrete syntax.
However the right tree would be the correct one given the input (x+y)*z. Note that there are no parentheses in the abstract syntax above nor in the parse trees. Parentheses are only needed to direct the parser to a certain parse and are not required in a parse tree which shows the binding of operators to operands by its very structure.