请求明确fpip递归判定需求并提供Racket示例输入输出

Got it, let's break down the requirements clearly and provide concrete examples to make this recursive check procedure's purpose unambiguous.

Exact Requirements for the check(s, varlst) Recursive Procedure #

First, let's formalize the definition of the fully parenthesized infix +- expression (fpip) that you're validating, since it was cut off in your question:

var ::= a | b | c | d | e | f | g
fpip ::= var 
       | ( fpip '+' fpip ) 
       | ( fpip '-' fpip )

This means:

1. A single valid variable (from a to g) is a valid fpip.
2. Any two valid fpips combined with + or -, wrapped in parentheses, is also a valid fpip (no unparenthesized operations allowed).

Now, the check procedure must:

• Be recursive: Validate sub-expressions by calling itself instead of using iterative loops for core logic.
• Take two inputs:
  • s: An S-expression (either an atomic variable symbol or a nested list representing a compound expression).
  • varlst: A list of allowed identifier symbols (subset of {a,b,c,d,e,f,g}).
• Return a boolean (true if s is a valid fpip; false otherwise).
• Follow these validation rules:
  • Base Case: If s is an atom, return true only if s exists in varlst.
  • Recursive Case: If s is a list:
    1. The list must match a valid compound fpip structure (we'll cover two common S-expression representations below).
    2. The operator must be either '+' or '-'.
    3. Both left and right sub-expressions must be valid fpips (verified via recursive check calls).
    4. Parentheses must be properly matched (if part of the S-expression structure).

Example Inputs & Outputs #

Let's use two common S-expression representations for clarity:

Representation 1: Directly Parsed Fully Parenthesized Infix String

Here, each textual infix expression converts to a list where parentheses are explicit elements. For example, (a + b) becomes ( '(' a '+' b ')' ).

Using varlst = (a b c):

Representation 2: Abstract Syntax Tree (Prefix Form)

Here, compound expressions are 3-element lists with the operator first (common in Lisp-like languages). For example, (a + b) becomes ( '+' a b ).

Using varlst = (a b c):

Key Edge Cases to Validate #

Ensure your recursive procedure handles:

• Variables not present in varlst
• Mismatched/missing parentheses (for representation 1)
• Lists of incorrect length
• Invalid operators (anything other than + or -)
• Deeply nested expressions (to test recursion depth)

内容的提问来源于stack exchange，提问作者Will