Language Definition Question

Can someone please help me understand exactly what this means?

<stmt> := var <ident> = <expr>
    | <ident> = <expr>
    | for <ident> = <expr> to <expr> do <stmt> end
    | read_int <ident>
    | print <expr>
    | <stmt> ; <stmt>

<expr> := <string>
    | <int>
    | <arith_expr>
    | <ident>

<bin_expr> := <expr> <bin_op> <expr>
<bin_op> := + | - | * | /

<ident> := <char> <ident_rest>*
<ident_rest> := <char> | <digit>

<int> := <digit>+
<digit> := 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

<string> := " <string_elem>* "
<string_elem> := <any char other than ">

In the first part, I'm assuming <ident> means "Identifier", and <expr> means "Expression" and <arith_expr> means "Arithmatic Expression". But the rest is a little confusing to me.

Thank you

Solution

<stmt> := var <ident> = <expr>
    | <ident> = <expr>
    | for <ident> = <expr> to <expr> do <stmt> end
    | read_int <ident>
    | print <expr>
    | <stmt> ; <stmt>

Translation: A statement can be either

a variable declaration (with an expression)
a variable assignment (with an expression)
a for() loop (with two expressions and a statement)
read_int (with an identifier)
print (with an expression)
two statements separated by a semicolon

<expr> := <string>
    | <int>
    | <arith_expr>
    | <ident>

Translation: An expression can be either

a string literal
and integer
an arithmetic expression
an identifier

<bin_expr> := <expr> <bin_op> <expr>
<bin_op> := + | - | * | /

A binary expression consists of two expressions and a binary operator inbetween. Binary operators are:

+ - * /

<ident> := <char> <ident_rest>*
<ident_rest> := <char> | <digit>

An identifier always starts with a character, but the rest of the identifier can consist of characters and digits

<int> := <digit>+
<digit> := 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

definition of a digit

<string> := " <string_elem>* "
<string_elem> := <any char other than ">

definition of a string literal