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

## Equations

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

## Equations

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

## Equations

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

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

## Equations

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

## Equations

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

## Equations

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

(aesop) Only for use by Aesop developers. Enables dynamic script structuring.

(aesop) Only for use by Aesop developers. Uses static structuring instead of dynamic structuring if no metavariables appear in the proof.

(aesop) Only for use by Aesop developers. Generates a script even if none was requested.

(aesop) Warn when apply builder is applied to a rule with conclusion of the form A ↔ B