Runs a term elaborator inside a tactic.
This function ensures that term elaboration fails when backtracking,
i.e., in first| tac term | other
.
Tactics are productions in the syntax category tactic
.
Given the syntax of a tactic, the tactic interpreter is responsible for carrying out actions in the tactic monad TacticM
, which is a wrapper around Lean's term elaborator that keeps track of the additional state needed to execute tactics.
A custom tactic consists of an extension to the tactic
category along with either:
a macro that translates the new syntax into existing syntax, or
an elaborator that carries out TacticM
actions to implement the tactic.
The easiest way to define a new tactic is as a macro that expands into already-existing tactics. Macro expansion is interleaved with tactic execution. The tactic interpreter first expands tactic macros just before they are to be interpreted. Because tactic macros are not fully expanded prior to running a tactic script, they can use recursion; as long as the recursive occurrence of the macro syntax is beneath a tactic that can be executed, there will not be an infinite chain of expansion.
This recursive implementation of a tactic akin to repeat
is defined via macro expansion.
When the argument $t
fails, the recursive occurrence of rep
is never invoked, and is thus never macro expanded.
syntax "rep" tactic : tactic
macro_rules
| `(tactic|rep $t) =>
`(tactic|
first
| $t; rep $t
| skip)
example : 0 ≤ 4 := ⊢ 0 ≤ 4
rep (⊢ Nat.le 0 0)
All goals completed! 🐙
Like other Lean macros, tactic macros are hygienic. References to global names are resolved when the macro is defined, and names introduced by the tactic macro cannot capture names from its invocation site.
When defining a tactic macro, it's important to specify that the syntax being matched or constructed is for the syntax category tactic
.
Otherwise, the syntax will be interpreted as that of a term, which will match against or construct an incorrect AST for tactics.
Because macro expansion can fail, multiple macros can match the same syntax, allowing backtracking.
Tactic macros take this further: even if a tactic macro expands successfully, if the expansion fails when interpreted, the tactic interpreter will attempt the next expansion.
This is used to make a number of Lean's built-in tactics extensible—new behavior can be added to a tactic by adding a Lean.Parser.Command.macro_rules : command
macro_rules
declaration.
trivial
The trivial
, which is used by many other tactics to quickly dispatch subgoals that are not worth bothering the user with, is designed to be extended through new macro expansions.
Lean's default trivial
can't solve IsEmpty []
goals:
def IsEmpty (xs : List α) : Prop :=
¬ xs ≠ []
example (α : Type u) : IsEmpty (α := α) [] := α:Type u⊢ IsEmpty [] α:Type u⊢ IsEmpty []
The error message is an artifact of trivial
trying assumption
last.
Adding another expansion allows trivial
to take care of these goals:
def emptyIsEmpty : IsEmpty (α := α) [] := α:Type u_1⊢ IsEmpty [] All goals completed! 🐙
macro_rules | `(tactic|trivial) => `(tactic|exact emptyIsEmpty)
example (α : Type u) : IsEmpty (α := α) [] := α:Type u⊢ IsEmpty []
All goals completed! 🐙
Macro expansion can induce backtracking when the failure arises from any part of the expanded syntax.
An infix version of first
can be defined by providing multiple expansions in separate Lean.Parser.Command.macro_rules : command
macro_rules
declarations:
syntax tactic "<|||>" tactic : tactic
macro_rules
| `(tactic|$t1 <|||> $t2) => pure t1
macro_rules
| `(tactic|$t1 <|||> $t2) => pure t2
example : 2 = 2 := ⊢ 2 = 2
All goals completed! 🐙 <|||> apply And.intro
example : 2 = 2 := ⊢ 2 = 2
apply And.intro <|||> All goals completed! 🐙
Multiple Lean.Parser.Command.macro_rules : command
macro_rules
declarations are needed because each defines a pattern-matching function that will always take the first matching alternative.
Backtracking is at the granularity of Lean.Parser.Command.macro_rules : command
macro_rules
declarations, not their individual cases.
Relationship to Lean.Elab.Term.TermElabM
, Lean.Meta.MetaM
Overview of available effects
Checkpointing
Tracked at issue #67
Lean.Elab.Tactic.Tactic : Type
Lean.Elab.Tactic.TacticM (α : Type) : Type
Lean.Elab.Tactic.run (mvarId : Lean.MVarId) (x : TacticM Unit) : Lean.Elab.TermElabM (List Lean.MVarId)
Lean.Elab.Tactic.runTermElab {α : Type} (k : Lean.Elab.TermElabM α) (mayPostpone : Bool := false) : TacticM α
Runs a term elaborator inside a tactic.
This function ensures that term elaboration fails when backtracking,
i.e., in first| tac term | other
.
Lean.Elab.Tactic.getFVarId (id : Lean.Syntax) : TacticM Lean.FVarId
Lean.Elab.Tactic.getFVarIds (ids : Array Lean.Syntax) : TacticM (Array Lean.FVarId)
Lean.Elab.Tactic.withLocation (loc : Location) (atLocal : Lean.FVarId → TacticM Unit) (atTarget : TacticM Unit) (failed : Lean.MVarId → TacticM Unit) : TacticM Unit
Runs the given atLocal
and atTarget
methods on each of the locations selected by the given loc
.
If loc
is a list of locations, runs at each specified hypothesis (and finally the goal if ⊢
is included),
and fails if any of the tactic applications fail.
If loc
is *
, runs at the target first and then the hypotheses in reverse order.
If atTarget
closes the main goal, withLocation
does not run atLocal
.
If all tactic applications fail, withLocation
with call failed
with the main goal mvar.
Lean.Elab.Tactic.getGoals : TacticM (List Lean.MVarId)
Returns the list of goals. Goals may or may not already be assigned.
Lean.Elab.Tactic.closeMainGoal (tacName : Lean.Name) (val : Lean.Expr) (checkUnassigned : Bool := true) : TacticM Unit
Closes main goal using the given expression.
If checkUnassigned == true
, then val
must not contain unassigned metavariables.
Returns true
if val
was successfully used to close the goal.
Lean.Elab.Tactic.tagUntaggedGoals (parentTag newSuffix : Lean.Name) (newGoals : List Lean.MVarId) : TacticM Unit
Use parentTag
to tag untagged goals at newGoals
.
If there are multiple new untagged goals, they are named using <parentTag>.<newSuffix>_<idx>
where idx > 0
.
If there is only one new untagged goal, then we just use parentTag
Lean.Elab.Tactic.appendGoals (mvarIds : List Lean.MVarId) : TacticM Unit
Add the given goals at the end of the current list of goals.
Lean.Elab.Tactic.closeMainGoalUsing (tacName : Lean.Name) (x : Lean.Expr → Lean.Name → TacticM Lean.Expr) (checkNewUnassigned : Bool := true) : TacticM Unit
Try to close main goal using x target tag
, where target
is the type of the main goal and tag
is its user name.
If checkNewUnassigned
is true, then throws an error if the resulting value has metavariables that were created during the execution of x
.
If it is false, then it is the responsibility of x
to add such metavariables to the goal list.
During the execution of x
:
The local context is that of the main goal.
The goal list has the main goal removed.
It is allowable to modify the goal list, for example with Lean.Elab.Tactic.pushGoals
.
On failure, the main goal remains at the front of the goal list.
Lean.Elab.Tactic.elabTerm (stx : Lean.Syntax) (expectedType? : Option Lean.Expr) (mayPostpone : Bool := false) : TacticM Lean.Expr
Elaborate stx
in the current MVarContext
. If given, the expectedType
will be used to help
elaboration but not enforced (use elabTermEnsuringType
to enforce an expected type).
Lean.Elab.Tactic.elabTermEnsuringType (stx : Lean.Syntax) (expectedType? : Option Lean.Expr) (mayPostpone : Bool := false) : TacticM Lean.Expr
Elaborate stx
in the current MVarContext
. If given, the expectedType
will be used to help
elaboration and then a TypeMismatchError
will be thrown if the elaborated type doesn't match.
Lean.Elab.Tactic.elabTermWithHoles (stx : Lean.Syntax) (expectedType? : Option Lean.Expr) (tagSuffix : Lean.Name) (allowNaturalHoles : Bool := false) (parentTag? : Option Lean.Name := none) : TacticM (Lean.Expr × List Lean.MVarId)
Elaborates stx
and collects the MVarId
s of any holes that were created during elaboration.
With allowNaturalHoles := false
(the default), any new natural holes (_
) which cannot
be synthesized during elaboration cause elabTermWithHoles
to fail. (Natural goals appearing in
stx
which were created prior to elaboration are permitted.)
Unnamed MVarId
s are renamed to share the tag parentTag?
(or the main goal's tag if parentTag?
is none
).
If multiple unnamed goals are encountered, tagSuffix
is appended to this tag along with a numerical index.
Note:
Previously-created MVarId
s which appear in stx
are not returned.
All parts of elabTermWithHoles
operate at the current MCtxDepth
, and therefore may assign
metavariables.
When allowNaturalHoles := true
, stx
is elaborated under withAssignableSyntheticOpaque
,
meaning that .syntheticOpaque
metavariables might be assigned during elaboration. This is a
consequence of the implementation.
These operations are primarily used as part of the implementation of TacticM
or of particular tactics.
It's rare that they are useful when implementing new tactics.
These operations are exposed through standard Lean monad type classes.
Lean.Elab.Tactic.tryCatch {α : Type} (x : TacticM α) (h : Lean.Exception → TacticM α) : TacticM α
Non-backtracking try
/catch
.
Lean.Elab.Tactic.liftMetaMAtMain {α : Type} (x : Lean.MVarId → Lean.MetaM α) : TacticM α
Lean.Elab.Tactic.getMainModule : TacticM Lean.Name
Lean.Elab.Tactic.getCurrMacroScope : TacticM Lean.MacroScope
Lean.Elab.Tactic.adaptExpander (exp : Lean.Syntax → TacticM Lean.Syntax) : Tactic
Adapt a syntax transformation to a regular tactic evaluator.
Lean.Elab.Tactic.elabCasesTargets (targets : Array Lean.Syntax) : TacticM (Array Lean.Expr × Array (Lean.Ident × Lean.FVarId))
Lean.Elab.Tactic.elabSimpArgs (stx : Lean.Syntax) (ctx : Lean.Meta.Simp.Context) (simprocs : Lean.Meta.Simp.SimprocsArray) (eraseLocal : Bool) (kind : SimpKind) : TacticM ElabSimpArgsResult
Elaborate extra simp theorems provided to simp
. stx
is of the form "[" simpTheorem,* "]"
If eraseLocal == true
, then we consider local declarations when resolving names for erased theorems (- id
),
this option only makes sense for simp_all
or *
is used.
When recover := true
, try to recover from errors as much as possible so that users keep seeing
the current goal.
Lean.Elab.Tactic.elabSimpConfig (optConfig : Lean.Syntax) (kind : SimpKind) : TacticM Lean.Meta.Simp.Config
Lean.Elab.Tactic.elabSimpConfigCtxCore : Lean.Syntax → TacticM Lean.Meta.Simp.ConfigCtx
Lean.Elab.Tactic.dsimpLocation' (ctx : Lean.Meta.Simp.Context) (simprocs : Lean.Meta.Simp.SimprocsArray) (loc : Location) : TacticM Lean.Meta.Simp.Stats
Implementation of dsimp?
.
Lean.Elab.Tactic.elabDSimpConfigCore : Lean.Syntax → TacticM Lean.Meta.DSimp.Config
Lean.Elab.Tactic.tacticElabAttribute : Lean.KeyedDeclsAttribute Tactic