Additional conv tactics.

def Mathlib.Tactic.Conv.convLHS : Lean.ParserDescr

conv_lhs => cs runs the conv tactic sequence cs on the left hand side of the target.

In general, for an n-ary operator as the target, it traverses into the second to last argument. It is a synonym for conv => arg -2; cs.

• conv_lhs at h => cs runs cs on the left hand side of hypothesis h.
• conv_lhs in pat => cs first looks for a subexpression matching pat (see also the pattern conv tactic) and then traverses into the left hand side of this subexpression. This syntax also supports the occs clause for the pattern.

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def Mathlib.Tactic.Conv.convRHS : Lean.ParserDescr

conv_rhs => cs runs the conv tactic sequence cs on the right hand side of the target.

In general, for an n-ary operator as the target, it traverses into the last argument. It is a synonym for conv => arg -1; cs.

• conv_rhs at h => cs runs cs on the right hand side of hypothesis h.
• conv_rhs in pat => cs first looks for a subexpression matching pat (see the pattern conv tactic) and then traverses into the right hand side of this subexpression. This syntax also supports the occs clause for the pattern.

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def Mathlib.Tactic.Conv.convRun_conv_ : Lean.ParserDescr

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def Mathlib.Tactic.Conv.«convConvIn__=>_» : Lean.ParserDescr

conv in pat => cs runs the conv tactic sequence cs on the first subexpression matching the pattern pat in the target. The converted expression becomes the new target subgoal, like conv => cs.

The arguments in are the same as those as the in pattern. In fact, conv in pat => cs is a macro for conv => pattern pat; cs.

The syntax also supports the occs clause. Example:

conv in (occs := *) x + y => rw [add_comm]

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def Mathlib.Tactic.Conv.dischargeConv : Lean.ParserDescr

• discharge => tac is a conv tactic which rewrites target p to True if tac is a tactic which proves the goal ⊢ p.
• discharge without argument returns ⊢ p as a subgoal.

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def Mathlib.Tactic.Conv.elabDischargeConv : Lean.Elab.Tactic.Tactic

Elaborator for the discharge tactic.

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def Mathlib.Tactic.Conv.convRefine_ : Lean.ParserDescr

Use refine in conv mode.

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def Mathlib.Tactic.Conv.«command#conv_=>_» : Lean.ParserDescr

The command #conv tac => e will run a conv tactic tac on e, and display the resulting expression (discarding the proof). For example, #conv rw [true_and_iff] => True ∧ False displays False. There are also shorthand commands for several common conv tactics:

• #whnf e is short for #conv whnf => e
• #simp e is short for #conv simp => e
• #norm_num e is short for #conv norm_num => e
• #push_neg e is short for #conv push_neg => e

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def Mathlib.Tactic.Conv.withReducible : Lean.ParserDescr

with_reducible tacs executes tacs using the reducible transparency setting. In this setting only definitions tagged as [reducible] are unfolded.

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def Mathlib.Tactic.Conv.«command#whnf_» : Lean.ParserDescr

The command #whnf e evaluates e to Weak Head Normal Form, which means that the "head" of the expression is reduced to a primitive - a lambda or forall, or an axiom or inductive type. It is similar to #reduce e, but it does not reduce the expression completely, only until the first constructor is exposed. For example:

open Nat List
set_option pp.notation false
#whnf [1, 2, 3].map succ
-- cons (succ 1) (map succ (cons 2 (cons 3 nil)))
#reduce [1, 2, 3].map succ
-- cons 2 (cons 3 (cons 4 nil))

The head of this expression is the List.cons constructor, so we can see from this much that the list is not empty, but the subterms Nat.succ 1 and List.map Nat.succ (List.cons 2 (List.cons 3 List.nil)) are still unevaluated. #reduce is equivalent to using #whnf on every subexpression.

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def Mathlib.Tactic.Conv.«command#whnfR_» : Lean.ParserDescr

The command #whnfR e evaluates e to Weak Head Normal Form with Reducible transparency, that is, it uses whnf but only unfolding reducible definitions.

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def Mathlib.Tactic.Conv.«command#simpOnly_=>__» : Lean.ParserDescr

• #simp => e runs simp on the expression e and displays the resulting expression after simplification.
• #simp only [lems] => e runs simp only [lems] on e.
• The => is optional, so #simp e and #simp only [lems] e have the same behavior. It is mostly useful for disambiguating the expression e from the lemmas.

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