Slrj.chat.md

(based on a conversation I had with Jacob Prinz)

SYSTEM

You are a knowledgeable programming languages assistant. You help the user analyze a new programming language.

USER

Slrj is a new programming language. The grammar of Slrj expressions is defined as follows, where "x" is any Slrj expression, and "A", "B", and "C" are atomic values.

x ::= A | B | C | (x x)

The small-step semantics of Slrj are defined by the following rewrite rules, where "x -> y" is the relation that "x" steps to "y", for some Slrj expressions "x" and "y".

(A B) -> A
((B x) y) -> (y x)
(C x) -> x

A Slrj expression is evaluated by applying rewrite rules from Slrj's semantics until no more rewrite rules can be applied. The following are some examples of evaluations of Slrj expressions.

• "(A ((B A) A))" evaluates to "A"
• "(C (A B))" evaluates to "A"
• "(B (B (C C)))" evaluates to "C"

Show the steps for evaluating the Slrj expression "(C ((B A) B))".

ASSISTANT (GPT-4 Chat)

To evaluate the Slrj expression "(C ((B A) B))", we will apply the rewrite rules step by step until no more rules can be applied. Here's the evaluation process:

1. Start with the given expression: (C ((B A) B))

2. Apply the rewrite rule for (A B) -> A: (C (A B))

3. Apply the rewrite rule for (C x) -> x: (A B)

4. Apply the rewrite rule for (A B) -> A: A

So, the evaluation of the Slrj expression "(C ((B A) B))" is "A".

COMMENT

It always gets confused about at least one of the rules, even with varying temperatures. My guess is that it's trying to pattern match on existing examples of evaluation, which look similar from the point of view of textual pattern-matching, but are semantically unlrelated to the task.

I tried it on Claude 3 Opus

USER

You are a knowledgeable programming languages assistant. You help the user analyze a new programming language.

Slrj is a new programming language. The grammar of Slrj expressions is defined as follows, where x is any Slrj expression, and A, B, and C are atomic values.

x ::= A | B | C | (x x)

The small-step semantics of Slrj are defined by the following rewrite rules, where x -> y is the relation that x steps to y, for some Slrj expressions x and y.

(A B) -> A
((B x) y) -> (y x)
(C x) -> x

A Slrj expression is evaluated by applying rewrite rules from Slrj's semantics until no more rewrite rules can be applied. The following are some examples of evaluations of Slrj expressions.

• (A ((B B) A)) evaluates to (A A)
• (C (A B)) evaluates to A
• (B (B (C C))) evaluates to C

Show the steps for evaluating the Slrj expression (C ((B A) B)).

ASSISTANT (Claude 3 Opus)

Certainly! Let's evaluate the Slrj expression (C ((B A) B)) step by step, applying the rewrite rules until no more rules can be applied.

Given expression: (C ((B A) B))

Step 1: Apply the rule ((B x) y) -> (y x) to the subexpression ((B A) B).
(C ((B A) B)) -> (C (B A))

Step 2: Apply the rule (C x) -> x to the entire expression.
(C (B A)) -> (B A)

Step 3: Apply the rule ((B x) y) -> (y x) to the entire expression.
(B A) -> (A B)

Step 4: Apply the rule (A B) -> A to the entire expression.
(A B) -> A

No more rewrite rules can be applied at this point. Therefore, the final result of evaluating the Slrj expression (C ((B A) B)) is A.

To summarize, the evaluation steps are:

(C ((B A) B))
-> (C (B A))    (by rule: ((B x) y) -> (y x))
-> (B A)        (by rule: (C x) -> x)
-> (A B)        (by rule: ((B x) y) -> (y x))
-> A            (by rule: (A B) -> A)

The Slrj expression (C ((B A) B)) evaluates to A.

SOLUTION

The correct evaluation steps are the following:

(C ((B A) B))
(C (B A))
(B A)

COMMENT

It gets confused about the B rule this time.

I tried it again.

USER

You are a knowledgeable programming languages assistant. You help the user analyze a new programming language.

Slrj is a new programming language. The grammar of Slrj expressions is defined as follows, where x is any Slrj expression, and A, B, and C are atomic values.

x ::= A | B | C | (x x)

The small-step semantics of Slrj are defined by the following rewrite rules, where x -> y is the relation that x steps to y, for some Slrj expressions x and y.

(A B) -> A
((B x) y) -> (y x)
(C x) -> x

A Slrj expression is evaluated by applying rewrite rules from Slrj's semantics until no more rewrite rules can be applied. The following are some examples of evaluations of Slrj expressions.

• (A ((B B) A)) evaluates to (A A)
• (C (A B)) evaluates to A
• (B (B (C C))) evaluates to C

Show the steps for evaluating the Slrj expression (C ((B A) B)).

ASSISTANT (Claude 3 Opus)

To evaluate the Slrj expression (C ((B A) B)), we'll apply the rewrite rules step by step until no more rules can be applied. Let's go through the evaluation process:

Step 1:

(C ((B A) B))

We can apply the rule ((B x) y) -> (y x) to the subexpression ((B A) B). Let's substitute x with A and y with B:

(C (B A))

Step 2:

(C (B A))

Now, we can apply the rule (C x) -> x to the entire expression. Let's substitute x with (B A):

(B A)

Step 3:

(B A)

Finally, we can apply the rule ((B x) y) -> (y x) to the entire expression. Let's substitute x with A and y with nothing (since there's no argument after (B A)):

A

No more rewrite rules can be applied, so the evaluation is complete.

Therefore, the Slrj expression (C ((B A) B)) evaluates to A in the following steps:

1. (C ((B A) B))
2. (C (B A))
3. (B A)
4. A

COMMENT

It got really close, but this time instead of just brazenly misapplying the B rule, it invented a new principle which is that "nothing" also counts as an x so that it can force the B rule to apply.