Merge remote-tracking branch 'origin/main' into brando
This commit is contained in:
Brando Miranda
commit
c73e56630e
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@ -1,10 +1,82 @@
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from pantograph.server import Server
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from pantograph.server import Server, ServerError
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from pantograph.expr import Variable, Goal, TacticCalc
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import unittest
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import sglang as sgl
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LEAN4_INTRO = '''/-- A sequence `u` of real numbers converges to `l` if `∀ ε > 0, ∃ N, ∀ n ≥ N, |u_n - l| ≤ ε`.
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This condition will be spelled `seq_limit u l`. -/
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def seq_limit (u : ℕ → ℝ) (l : ℝ) : Prop :=
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∀ ε > 0, ∃ N, ∀ n ≥ N, |u n - l| ≤ ε
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/- In the above definition, note that the `n`-th term of the sequence `u` is denoted
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simply by `u n`.
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Similarly, in the next definition, `f x` is what we would write `f(x)` on paper.
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Also note that implication is denoted by a single arrow (we'll explain why later). -/
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/-- A function`f : ℝ → ℝ` is continuous at `x₀` if
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`∀ ε > 0, ∃ δ > 0, ∀ x, |x - x₀| ≤ δ ⇒ |f(x) - f(x₀)| ≤ ε`.
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This condition will be spelled `continuous_at f x₀`.-/
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def continuous_at (f : ℝ → ℝ) (x₀ : ℝ) : Prop :=
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∀ ε > 0, ∃ δ > 0, ∀ x, |x - x₀| ≤ δ → |f x - f x₀| ≤ ε
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/-- Now we claim that if `f` is continuous at `x₀` then it is sequentially continuous
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at `x₀`: for any sequence `u` converging to `x₀`, the sequence `f ∘ u` converges
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to `f x₀`. -/
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example (f : ℝ → ℝ) (u : ℕ → ℝ) (x₀ : ℝ) (hu : seq_limit u x₀) (hf : continuous_at f x₀) :
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seq_limit (f ∘ u) (f x₀) := by { -- This `by` keyword marks the beginning of the proof
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-- Put your text cursor here and watch the Lean InfoView panel to the right.
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-- Then move your cursor from line to line in the proof while monitoring the Infoview.
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-- Our goal is to prove that, for any positive `ε`, there exists a natural
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-- number `N` such that, for any natural number `n` at least `N`,
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-- `|f(u_n) - f(x₀)|` is at most `ε`.
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unfold seq_limit
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-- Fix a positive number `ε`.
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intros ε hε
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-- By assumption on `f` applied to this positive `ε`, we get a positive `δ`
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-- such that, for all real number `x`, if `|x - x₀| ≤ δ` then `|f(x) - f(x₀)| ≤ ε` (1).
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obtain ⟨δ, δ_pos, Hf⟩ : ∃ δ > 0, ∀ x, |x - x₀| ≤ δ → |f x - f x₀| ≤ ε := hf ε hε
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-- The assumption on `u` applied to this `δ` gives a natural number `N` such that
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-- for every natural number `n`, if `n ≥ N` then `|u_n - x₀| ≤ δ` (2).
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obtain ⟨N, Hu⟩ : ∃ N, ∀ n ≥ N, |u n - x₀| ≤ δ := hu δ δ_pos
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-- Let's prove `N` is suitable.
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use N
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-- Fix `n` which is at least `N`. Let's prove `|f(u_n) - f(x₀)| ≤ ε`.
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intros n hn
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-- Thanks to (1) applied to `u_n`, it suffices to prove that `|u_n - x₀| ≤ δ`.
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apply Hf
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-- This follows from property (2) and our assumption on `n`.
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exact Hu n hn
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-- This finishes the proof!
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}
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/-
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Now that this proof is over, you can use the file explorer to the
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left of this panel to open the file `Exercises > 01Rewriting.lean`.
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-/'''
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LEAN4_REWRITE = '''Rewrite tactic tutorial:
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example (a b c : Nat) : a + b + c = a + c + b := by
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rw [Nat.add_assoc, Nat.add_comm b, ← Nat.add_assoc]
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example (a b c : Nat) : a + b + c = a + c + b := by
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rw [Nat.add_assoc, Nat.add_assoc, Nat.add_comm b]
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example (a b c : Nat) : a + b + c = a + c + b := by
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rw [Nat.add_assoc, Nat.add_assoc, Nat.add_comm _ b]
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example (f : Nat → Nat) (a : Nat) (h : a + 0 = 0) : f a = f 0 := by
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rw [Nat.add_zero] at h
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rw [h]
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def Tuple (α : Type) (n : Nat) :=
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{ as : List α // as.length = n }
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example (n : Nat) (h : n = 0) (t : Tuple α n) : Tuple α 0 := by
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rw [h] at t
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exact t
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'''
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@sgl.function
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def multi_turn_question(s, question_1, question_2):
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@ -16,22 +88,37 @@ def multi_turn_question(s, question_1, question_2):
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@sgl.function
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def select_tactic(s, state):
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def select_tactic(s, server, state, goal_id, feedback_turns = 5):
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s += sgl.system("You are an expert in Lean. Choose the next one tactic to run given the current proof state and goals.")
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s += sgl.user(LEAN4_REWRITE)
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s += sgl.user("The current proof state: GoalState(state_id=0, goals=[Goal(variables=[], target='∀ (a b: Nat), (b = 2) -> 1 + a + 1 = a + b', name=None, is_conversion=False)])")
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s += sgl.assistant("```intros a b h```")
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s += sgl.user("The current proof state: GoalState(state_id=1, goals=[Goal(variables=[Variable(t='Nat', v=None, name='a'), Variable(t='Nat', v=None, name='b'), Variable(t='b = 2', v=None, name='h')], target='1 + a + 1 = a + b', name=None, is_conversion=False)])")
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s += sgl.assistant('TacticCalc("1 + a + 1 = a + 1 + 1")')
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s += sgl.user("The current proof state: " + str(state))
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with s.copy() as tmp:
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tmp += sgl.assistant(sgl.gen("tactic", max_tokens=64))
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print("==tmp===")
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print(tmp["tactic"])
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tactic = extract_code_from_llm_output(tmp["tactic"])
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s += sgl.assistant("```"+tactic+"```")
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return tactic
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for i in range(feedback_turns):
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with s.copy() as tmp:
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tmp += sgl.assistant(sgl.gen("tactic", max_tokens=64))
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print("==tmp===")
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print(tmp["tactic"])
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tactic = extract_code_from_llm_output(tmp["tactic"])
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s += sgl.assistant("```"+tactic+"```")
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success, new_state = apply_tactic(server, state, goal_id, tactic)
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if not success:
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with s.user():
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s += "This answer got Lean compile error:\n" + str(new_state) + "\n"
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s += "Please try again by taking the Lean compiler feedback."
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else:
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return new_state
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def apply_tactic(server, state, goal_id, tactic):
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try:
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new_state = server.goal_tactic(state, goal_id=goal_id, tactic=tactic)
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except ServerError as e:
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return False, e
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return True, new_state
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def extract_code_from_llm_output(reply):
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i = reply.find("```lean")
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@ -51,6 +138,7 @@ def extract_code_from_llm_output(reply):
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class TestServerSGL(unittest.TestCase):
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def test_conv_calc_sgl(self):
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n_trails = 5
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sgl.set_default_backend(sgl.OpenAI("gpt-4"))
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server = Server()
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@ -80,43 +168,46 @@ class TestServerSGL(unittest.TestCase):
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target="a + 1 + 1 = a + b",
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),
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])
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state = select_tactic.run(str(state2))
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tactic = state.ret_value
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for m in state.messages():
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print(m["role"], ":", m["content"])
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state3 = None
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for i in range(n_trails):
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print(f"===============trail {str(i)}============")
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try:
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state = select_tactic.run(server, state2, goal_id = 1)
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state3 = state.ret_value
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for m in state.messages():
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print(m["role"], ":", m["content"])
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print("\n-- new state --\n", state3)
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break
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except ServerError as e:
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print(f"server error: {e}")
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continue
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state3 = server.goal_tactic(state2, goal_id=1, tactic=TacticCalc("_ = a + 2"))
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print("\n-- tactic --\n", tactic)
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state3 = server.goal_tactic(state2, goal_id=1, tactic=tactic)
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print("==========state3============")
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print(state3)
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# state4 = server.goal_tactic(state3, goal_id=0, tactic="rw [Nat.add_assoc]")
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# print("==========state4============")
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# print(state4)
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# self.assertTrue(state4.is_solved)
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state4 = None
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for i in range(n_trails):
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print(f"===============trail {str(i)}============")
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try:
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state = select_tactic.run(server, state3, goal_id = 0)
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state4 = state.ret_value
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for m in state.messages():
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print(m["role"], ":", m["content"])
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print("\n-- new state --\n", state4)
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break
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# print("==========state2============")
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# print(state2)
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# state_c1 = server.goal_conv_begin(state2, goal_id=0)
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# print("==========state c1============")
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# print(state_c1)
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# state_c2 = server.goal_tactic(state_c1, goal_id=0, tactic="rhs")
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# print("==========state c2============")
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# print(state_c2)
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# state_c3 = server.goal_tactic(state_c2, goal_id=0, tactic="rw [Nat.add_comm]")
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# print("==========state c3============")
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# print(state_c3)
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# state_c4 = server.goal_conv_end(state_c3)
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# print("==========state c4============")
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# print(state_c4)
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except ServerError as e:
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print(f"server error: {e}")
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continue
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# state_c5 = server.goal_tactic(state_c4, goal_id=0, tactic="rfl")
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# print("==========state c5============")
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# print(state_c5)
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# self.assertTrue(state_c5.is_solved)
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# print()
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state4 = server.goal_tactic(state3, goal_id=0, tactic="rw [Nat.add_assoc]")
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print("==========state4============")
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print(state4)
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self.assertTrue(state4.is_solved)
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def test_sglang_openai(self):
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