如何编写符合要求的BNF：支持无限元素列表且append仅接受多列表

Hey there! Let's break down your original BNF and adjust it to fully meet your requirements.

Issues in the Original Grammar #

1. Undefined Non-Terminal: <SNS> isn't defined—we need to explicitly distinguish atomic elements (symbols/numbers) from compound lists to enforce the append rule.
2. Invalid Recursion: The mutual recursion between <LIST> and <APPEND> allows append to accept atomic symbols (since <LIST> includes <SNS>), which violates your requirement that append can't take single symbols directly.
3. Redundant Productions: Your <LIST> rules for (list <SNS>), (list <LIST>), etc., can be simplified into a single production that handles any number of elements.
4. Misaligned <APPEND> Definition: Including <LIST> as an alternative for <APPEND> implies an atomic symbol is a valid append expression, which doesn't fit with append being a function call.

Corrected BNF #

This grammar clearly separates atomic elements from compound lists, enforces append's parameter rules, and supports lists with any combination of symbols, numbers, or other lists:

# Terminal symbols (adjust regex patterns to match your syntax needs)
<SYMBOL> ::= [a-zA-Z_][a-zA-Z0-9_]*
<NUMBER> ::= [0-9]+(\.[0-9]+)?

# Atomic elements (symbols/numbers—these are not considered lists themselves)
<ATOM> ::= <SYMBOL> | <NUMBER>

# Elements allowed inside a list: atoms or other lists
<LIST_ELEMENT> ::= <ATOM> | <LIST>

# Literal list: empty list or list with 1+ elements
<LITERAL_LIST> ::= (list) | (list <LIST_ELEMENT> <LIST_ELEMENT>*)

# Append function: accepts 1+ lists as arguments (no atoms allowed)
<APPEND_CALL> ::= (append <LIST> <LIST>*)

# A List is either a literal list or the result of an append call
<LIST> ::= <LITERAL_LIST> | <APPEND_CALL>

How This Meets Your Requirements #

1. List Content:
   • <LITERAL_LIST> can contain any number of symbols, numbers, or other lists (literal or append-derived). Examples of valid lists:
     • (list apple 42 (list banana cherry))
     • (append (list x) (list y z))
     • (list (append (list 10) (list 20)) orange)
2. Append Function Rules:
   • <APPEND_CALL> only accepts <LIST> arguments (literal lists or other append calls), so atomic symbols/numbers can't be passed directly.
     • Valid append calls: (append (list a) (list b)), (append (list 1) (append (list 2) (list 3)))
     • Invalid append calls (rejected by the grammar): (append a), (append 5 (list b))

Optional Variant: Atoms as Singleton Lists #

If you intended atoms to be treated as single-element lists (common in some functional languages), we can adjust the grammar to allow that while still blocking atoms in append arguments:

<SYMBOL> ::= [a-zA-Z_][a-zA-Z0-9_]*
<NUMBER> ::= [0-9]+(\.[0-9]+)?

<ATOM> ::= <SYMBOL> | <NUMBER>

# A "list value" can be an atom (singleton) or a compound list
<LIST_VALUE> ::= <ATOM> | <COMPOUND_LIST>

# Elements inside compound lists can be any list value
<LIST_ELEMENT> ::= <LIST_VALUE>

<LITERAL_LIST> ::= (list) | (list <LIST_ELEMENT> <LIST_ELEMENT>*)

# Append only accepts compound lists (no atoms directly)
<APPEND_CALL> ::= (append <COMPOUND_LIST> <COMPOUND_LIST>*)

# Compound lists are literal lists or append calls
<COMPOUND_LIST> ::= <LITERAL_LIST> | <APPEND_CALL>

In this variant:

• apple or 42 count as valid <LIST_VALUE>s (singleton lists)
• But (append apple) is invalid, while (append (list apple)) is allowed—preserving your rule that append can't take single symbols directly.

内容的提问来源于stack exchange，提问作者Tomer