213 lines
5.4 KiB
Text
213 lines
5.4 KiB
Text
module
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public axiom testSorry : α
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/-! Module docstring -/
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/-- A definition (not exposed). -/
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public def f := 1
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/-- An definition (exposed) -/
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@[expose] public def fexp := 1
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#guard_msgs(drop warning) in
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/-- A theorem. -/
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public theorem t : f = 1 := testSorry
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public class X
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/-- A local instance of a public class. -/
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instance : X := ⟨⟩
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-- Check that the theorem types are checked in exported context, where `f` is not defeq to `1`
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-- (but `fexp` is)
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/--
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error: type mismatch
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y
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has type
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Vector Unit 1
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but is expected to have type
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Vector Unit f
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-/
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#guard_msgs in
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public theorem v (x : Vector Unit f) (y : Vector Unit 1) : x = y := testSorry
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theorem v' (x : Vector Unit f) (y : Vector Unit 1) : x = y := testSorry
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theorem v'' (x : Vector Unit fexp) (y : Vector Unit 1) : x = y := testSorry
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-- Check that rfl theorems are complained about if they aren't rfl in the context of their type
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/--
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error: Not a definitional equality: the left-hand side
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f
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is not definitionally equal to the right-hand side
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1
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Note: This theorem is exported from the current module. This requires that all definitions that need to be unfolded to prove this theorem must be exposed.
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-/
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#guard_msgs in
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public theorem trfl : f = 1 := rfl
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/--
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error: Not a definitional equality: the left-hand side
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f
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is not definitionally equal to the right-hand side
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1
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Note: This theorem is exported from the current module. This requires that all definitions that need to be unfolded to prove this theorem must be exposed.
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-/
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#guard_msgs in
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@[defeq] public theorem trfl' : f = 1 := (rfl)
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theorem trflprivate : f = 1 := rfl
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def trflprivate' : f = 1 := rfl
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@[defeq] def trflprivate''' : f = 1 := rfl
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theorem trflprivate'''' : f = 1 := (rfl)
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public theorem fexp_trfl : fexp = 1 := rfl
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@[defeq] public theorem fexp_trfl' : fexp = 1 := rfl
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public opaque P : Nat → Prop
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public axiom hP1 : P 1
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/-- error: dsimp made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [t]; exact hP1
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example : P f := by simp only [t]; exact hP1
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/-- error: dsimp made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [trfl]; exact hP1
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/-- error: dsimp made no progress -/
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#guard_msgs in
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example : P f := by dsimp only [trfl']; exact hP1
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example : P f := by dsimp only [trflprivate]; exact hP1
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example : P f := by dsimp only [trflprivate']; exact hP1
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example : P fexp := by dsimp only [fexp_trfl]; exact hP1
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example : P fexp := by dsimp only [fexp_trfl]; exact hP1
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-- Check that the error message does not mention the export issue if
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-- it wouldn’t be a rfl otherwise either
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/--
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error: Not a definitional equality: the left-hand side
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f
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is not definitionally equal to the right-hand side
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2
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-/
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#guard_msgs in
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@[defeq] public theorem not_rfl : f = 2 := testSorry
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def priv := 2
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/-! Private decls should not be accessible in exported contexts. -/
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/-- error: unknown identifier 'priv' -/
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#guard_msgs in
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public abbrev h := priv
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/-! Equational theorems tests. -/
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public def f_struct : Nat → Nat
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| 0 => 0
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| n + 1 => f_struct n
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termination_by structural n => n
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public def f_wfrec : Nat → Nat → Nat
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| 0, acc => acc
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| n + 1, acc => f_wfrec n (acc + 1)
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termination_by n => n
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@[expose] public def f_exp_wfrec : Nat → Nat → Nat
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| 0, acc => acc
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| n + 1, acc => f_exp_wfrec n (acc + 1)
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termination_by n => n
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@[inline] protected def Test.Option.map (f : α → β) : Option α → Option β
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| some x => some (f x)
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| none => none
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/-- error: 'f.eq_def' is a reserved name -/
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#guard_msgs in
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public def f.eq_def := 1
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/-- error: 'fexp.eq_def' is a reserved name -/
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#guard_msgs in
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public def fexp.eq_def := 1
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/-- info: @[defeq] private theorem f.eq_def : f = 1 -/
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#guard_msgs in #print sig f.eq_def
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/-- info: @[defeq] private theorem f.eq_unfold : f = 1 -/
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#guard_msgs in #print sig f.eq_unfold
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/-- info: @[defeq] theorem fexp.eq_def : fexp = 1 -/
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#guard_msgs in #print sig fexp.eq_def
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/-- info: @[defeq] theorem fexp.eq_unfold : fexp = 1 -/
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#guard_msgs in #print sig fexp.eq_unfold
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/-- info: @[defeq] private theorem f_struct.eq_1 : f_struct 0 = 0 -/
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#guard_msgs in #print sig f_struct.eq_1
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/--
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info: private theorem f_struct.eq_def : ∀ (x : Nat),
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f_struct x =
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match x with
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| 0 => 0
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| n.succ => f_struct n
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-/
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#guard_msgs in #print sig f_struct.eq_def
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/--
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info: private theorem f_struct.eq_unfold : f_struct = fun x =>
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match x with
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| 0 => 0
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| n.succ => f_struct n
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-/
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#guard_msgs(pass trace, all) in #print sig f_struct.eq_unfold
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/-- info: private theorem f_wfrec.eq_1 : ∀ (x : Nat), f_wfrec 0 x = x -/
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#guard_msgs(pass trace, all) in #print sig f_wfrec.eq_1
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/--
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info: private theorem f_wfrec.eq_def : ∀ (x x_1 : Nat),
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f_wfrec x x_1 =
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_wfrec.eq_def
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/--
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info: private theorem f_wfrec.eq_unfold : f_wfrec = fun x x_1 =>
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_wfrec.eq_unfold
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/-- info: theorem f_exp_wfrec.eq_1 : ∀ (x : Nat), f_exp_wfrec 0 x = x -/
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#guard_msgs in #print sig f_exp_wfrec.eq_1
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/--
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info: theorem f_exp_wfrec.eq_def : ∀ (x x_1 : Nat),
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f_exp_wfrec x x_1 =
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_exp_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_exp_wfrec.eq_def
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/--
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info: theorem f_exp_wfrec.eq_unfold : f_exp_wfrec = fun x x_1 =>
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match x, x_1 with
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| 0, acc => acc
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| n.succ, acc => f_exp_wfrec n (acc + 1)
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-/
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#guard_msgs in #print sig f_exp_wfrec.eq_unfold
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