inductive Aesop.Strategy : Type

Search strategies which Aesop can use.

• bestFirst: Aesop.Strategy

  Best-first search. This is the default strategy.

• depthFirst: Aesop.Strategy

  Depth-first search. Whenever a rule is applied, Aesop immediately tries to solve each of its subgoals (from left to right), up to the maximum rule application depth. Goal and rule priorities are ignored, except to decide which rule is applied first.

• breadthFirst: Aesop.Strategy

  Breadth-first search. Aesop always works on the oldest unsolved goal. Goal and rule priorities are ignored, except to decide which rule is applied first.

Instances For

• Aesop.instBEqStrategy
• Aesop.instInhabitedStrategy
• Aesop.instReprStrategy

instance Aesop.instInhabitedStrategy : Inhabited Aesop.Strategy

Equations

• Aesop.instInhabitedStrategy = { default := Aesop.Strategy.bestFirst }

instance Aesop.instBEqStrategy : BEq Aesop.Strategy

Equations

• Aesop.instBEqStrategy = { beq := Aesop.beqStrategy✝ }

instance Aesop.instReprStrategy : Repr Aesop.Strategy

Equations

• Aesop.instReprStrategy = { reprPrec := Aesop.reprStrategy✝ }

structure Aesop.Options : Type

Options which modify the behaviour of the aesop tactic.

• strategy : Aesop.Strategy

  The search strategy used by Aesop.

• maxRuleApplicationDepth : Nat

  The maximum number of rule applications in any branch of the search tree (i.e., the maximum search depth). When a branch exceeds this limit, it is considered unprovable, but other branches may still be explored. 0 means no limit.

• maxRuleApplications : Nat

  Maximum total number of rule applications in the search tree. When this limit is exceeded, the search ends. 0 means no limit.

• maxGoals : Nat

  Maximum total number of goals in the search tree. When this limit is exceeded, the search ends. 0 means no limit.

• maxNormIterations : Nat

  Maximum number of norm rules applied to a single goal. When this limit is exceeded, normalisation is likely stuck in an infinite loop, so Aesop fails. 0 means no limit.

• maxSafePrefixRuleApplications : Nat

  When Aesop fails to prove a goal, it reports the goals that remain after safe rules have been applied exhaustively to the root goal, the safe descendants of the root goal, and so on (i.e., after the "safe prefix" of the search tree has been unfolded). However, it is possible for the search to fail before the safe prefix has been completely generated. In this case, Aesop expands the safe prefix after the fact. This option limits the number of additional rule applications generated during this process. 0 means no limit.

• maxRuleHeartbeats : Nat

  Heartbeat limit for individual Aesop rules. If a rule goes over this limit, it fails, but Aesop itself continues until it reaches the limit set by the maxHeartbeats option. If maxRuleHeartbeats = 0, there is no per-rule limit.

• maxSimpHeartbeats : Nat

  Heartbeat limit for Aesop's builtin simp rule. If simp goes over this limit, Aesop fails. If maxSimpHeartbeats = 0, there is no limit for simp (but the global heartbeat limit still applies).

• maxUnfoldHeartbeats : Nat

  Heartbeat limit for Aesop's builtin unfold rule. If unfold goes over this limit, Aesop fails. If maxUnfoldHeartbeats = 0, there is no limit for unfold (but the global heartbeat limit still applies).

• applyHypsTransparency : Lean.Meta.TransparencyMode

  The transparency used by the applyHyps builtin rule. The rule applies a hypothesis h : T if T ≡ ∀ (x₁ : X₁) ... (xₙ : Xₙ), Y at the given transparency and if additionally the goal's target is defeq to Y at the given transparency.

• assumptionTransparency : Lean.Meta.TransparencyMode

  The transparency used by the assumption builtin rule. The rule applies a hypothesis h : T if T is defeq to the goal's target at the given transparency.

• destructProductsTransparency : Lean.Meta.TransparencyMode

  The transparency used by the destructProducts builtin rule. The rule splits a hypothesis h : T if T is defeq to a product-like type (e.g. T ≡ A ∧ B or T ≡ A × B) at the given transparency.

  Note: we can index this rule only if the transparency is .reducible. With any other transparency, the rule becomes unindexed and is applied to every goal.

• introsTransparency? : Option Lean.Meta.TransparencyMode

  If this option is not none, the builtin intros rule unfolds the goal's target with the given transparency to discover ∀ binders. For example, with def T := ∀ x y : Nat, x = y, introsTransparency? := some .default and goal ⊢ T, the intros rule produces the goal x, y : Nat ⊢ x = y. With introsTransparency? := some .reducible, it produces ⊢ T. With introsTransparency? := none, it only introduces arguments which are syntactically bound by ∀ binders, so it also produces ⊢ T.

• terminal : Bool

  If true, Aesop succeeds only if it proves the goal. If false, Aesop always succeeds and reports the goals remaining after safe rules were applied.

• warnOnNonterminal : Bool

  If true, print a warning when Aesop does not prove the goal.

• traceScript : Bool

  If Aesop proves a goal and this option is true, Aesop prints a tactic proof as a Try this: suggestion.

• enableSimp : Bool

  Enable the builtin simp normalisation rule.

• useSimpAll : Bool

  Use simp_all, rather than simp at *, for the builtin simp normalisation rule.

• useDefaultSimpSet : Bool

  Use simp theorems from the default simp set, i.e. those tagged with @[simp]. If this option is false, Aesop uses only Aesop-specific simp theorems, i.e. those tagged with @[aesop simp]. Note that the congruence lemmas from the default simp set are always used.

• enableUnfold : Bool

  Enable the builtin unfold normalisation rule.

Instances For

• Aesop.instBEqOptions
• Aesop.instInhabitedOptions
• Aesop.instReprOptions

instance Aesop.instInhabitedOptions : Inhabited Aesop.Options

Equations

• One or more equations did not get rendered due to their size.

instance Aesop.instBEqOptions : BEq Aesop.Options

Equations

• Aesop.instBEqOptions = { beq := Aesop.beqOptions✝ }

instance Aesop.instReprOptions : Repr Aesop.Options

Equations

• Aesop.instReprOptions = { reprPrec := Aesop.reprOptions✝ }