cf527e05bd
This PR implements a `finally` section following a (potentially empty) `where` block. `where ... finally` opens a tactic sequence block in which the goals are the unassigned metavariables from the definition body and its auxiliary definitions that arise from use of `let rec` and `where`. This can be useful for discharging multiple proof obligations in the definition body by a single invocation of a tactic such as `all_goals`: ```lean example (i j : Nat) (xs : Array Nat) (hi : i < xs.size) (hj: j < xs.size) := match i with | 0 => x | _ => xs[i]'?_ + xs[j]'?_ where x := 13 finally all_goals assumption ``` --------- Co-authored-by: Sebastian Graf <sg@lean-fro.org>
115 lines
2.7 KiB
Text
115 lines
2.7 KiB
Text
example (i j : Nat) (xs : Array Nat) (hi : i < xs.size) (hj: j < xs.size) :=
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match i with
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| 0 => x
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| _ => xs[i]'?_ + xs[j]'?_
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where x := 13
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finally all_goals assumption
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def hole_in_def_body (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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xs[i]'?hole
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where finally
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case hole => exact h
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def hole_in_def_match (i : Nat) (xs : Array Nat) (h : i < xs.size) : Bool → Nat
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| true => xs[i]'?hole
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| false => i
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where finally
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case hole => exact h
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def hole_in_def_let_rhs (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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let f (_ : Nat) := xs[i]'?hole
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f i
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where finally
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case hole => exact h
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def hole_in_rec_def_body (n : Nat) (xs : Array Nat) (h : n < xs.size) : Nat :=
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match n with
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| 0 => xs[0]'?hole
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| n + 1 => hole_in_rec_def_body n xs (by omega)
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where finally
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case hole => exact h
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def hole_in_rec_let_rhs (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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let rec f (x : Nat) :=
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if x = 0 then xs[i]'?hole else f (x-1)
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f i
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where finally
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case hole => exact h
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theorem hole_in_thm_body (i : Nat) (xs : Array Nat) (h : i < xs.size) : True :=
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let _x := xs[i]'?hole
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True.intro
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where finally
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case hole => exact h
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set_option pp.rawOnError true in
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def hole_in_def_match_where (i : Nat) (xs : Array Nat) (h : i < xs.size) :=
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match i with
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| 0 => x
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| _ => xs[i]'?hole
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where x := 13
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finally case hole => assumption
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def hole_in_rec_let_rhs_match (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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let rec f (x : Nat) :=
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match x with
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| 0 => xs[i]'?hole
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| x + 1 => x
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f i
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where finally case hole => exact h
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def hole_in_rec_let_and_def (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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let rec f (x : Nat) :=
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match x with
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| 0 => xs[i]'?hole
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| x + 1 => x
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f i + xs[i]'?hole₂
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where finally
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case hole => exact h
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case hole₂ => exact h
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namespace hole_in_mutual_def
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mutual
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def even : Nat → Bool
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| 0 => ?zeroEven
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| n + 1 => odd n
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where finally
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case zeroEven => exact true
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def odd : Nat → Bool
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| 0 => ?zeroOdd
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| n + 1 => even n
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where finally
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case zeroOdd => exact false
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end
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mutual
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def even' (n : Nat) : Bool :=
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let rec go : Nat → Bool
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| 0 => ?zeroEven
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| n + 1 => not (go n)
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go n
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where finally
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case zeroEven => exact true
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def odd' n := not (even' n)
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end
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end hole_in_mutual_def
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structure S where
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a : Nat
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b : Nat
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def hole_in_struct_def : S where
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a := ?hole
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b := ?hole₂
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where finally
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all_goals exact 42
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/--
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error: `where ... finally` does not currently support any named sub-sections `| sectionName => ...`
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-/
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#guard_msgs in
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def hole_decreasing_does_not_exist (i : Nat) (xs : Array Nat) (h : i < xs.size) : Nat :=
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xs[i]'?hole
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where finally
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case hole => exact h
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| decreasing => skip
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