diff options
Diffstat (limited to 'backends/lean/Base/Primitives')
| -rw-r--r-- | backends/lean/Base/Primitives/Alloc.lean | 4 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/ArraySlice.lean | 54 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Base.lean | 30 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 144 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Vec.lean | 26 |
5 files changed, 128 insertions, 130 deletions
diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean index 1f470fe1..15fe1ff9 100644 --- a/backends/lean/Base/Primitives/Alloc.lean +++ b/backends/lean/Base/Primitives/Alloc.lean @@ -11,8 +11,8 @@ namespace boxed -- alloc.boxed namespace Box -- alloc.boxed.Box -def deref (T : Type) (x : T) : Result T := ret x -def deref_mut (T : Type) (x : T) : Result (T × (T → Result T)) := ret (x, λ x => ret x) +def deref (T : Type) (x : T) : Result T := ok x +def deref_mut (T : Type) (x : T) : Result (T × (T → Result T)) := ok (x, λ x => ok x) /-- Trait instance -/ def coreopsDerefInst (Self : Type) : diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean index e1a39d40..ef658e1b 100644 --- a/backends/lean/Base/Primitives/ArraySlice.lean +++ b/backends/lean/Base/Primitives/ArraySlice.lean @@ -50,7 +50,7 @@ abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i def Array.index_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result α := match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds - | some x => ret x + | some x => ok x -- For initialization def Array.repeat (α : Type u) (n : Usize) (x : α) : Array α n := @@ -69,7 +69,7 @@ theorem Array.repeat_spec {α : Type u} (n : Usize) (x : α) : @[pspec] theorem Array.index_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize) (hbound : i.val < v.length) : - ∃ x, v.index_usize α n i = ret x ∧ x = v.val.index i.val := by + ∃ x, v.index_usize α n i = ok x ∧ x = v.val.index i.val := by simp only [index_usize] -- TODO: dependent rewrite have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) @@ -79,12 +79,12 @@ def Array.update_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x: match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds | some _ => - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ + ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ @[pspec] theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Usize) (x : α) (hbound : i.val < v.length) : - ∃ nv, v.update_usize α n i x = ret nv ∧ + ∃ nv, v.update_usize α n i x = ok nv ∧ nv.val = v.val.update i.val x := by simp only [update_usize] @@ -96,12 +96,12 @@ theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Us def Array.index_mut_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result (α × (α -> Result (Array α n))) := do let x ← index_usize α n v i - ret (x, update_usize α n v i) + ok (x, update_usize α n v i) @[pspec] theorem Array.index_mut_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize) (hbound : i.val < v.length) : - ∃ x back, v.index_mut_usize α n i = ret (x, back) ∧ + ∃ x back, v.index_mut_usize α n i = ok (x, back) ∧ x = v.val.index i.val ∧ back = update_usize α n v i := by simp only [index_mut_usize, Bind.bind, bind] @@ -148,7 +148,7 @@ abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : Lis def Slice.index_usize (α : Type u) (v: Slice α) (i: Usize) : Result α := match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds - | some x => ret x + | some x => ok x /- In the theorems below: we don't always need the `∃ ..`, but we use one so that `progress` introduces an opaque variable and an equality. This @@ -158,7 +158,7 @@ def Slice.index_usize (α : Type u) (v: Slice α) (i: Usize) : Result α := @[pspec] theorem Slice.index_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize) (hbound : i.val < v.length) : - ∃ x, v.index_usize α i = ret x ∧ x = v.val.index i.val := by + ∃ x, v.index_usize α i = ok x ∧ x = v.val.index i.val := by simp only [index_usize] -- TODO: dependent rewrite have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) @@ -168,12 +168,12 @@ def Slice.update_usize (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result ( match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds | some _ => - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ + ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ @[pspec] theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α) (hbound : i.val < v.length) : - ∃ nv, v.update_usize α i x = ret nv ∧ + ∃ nv, v.update_usize α i x = ok nv ∧ nv.val = v.val.update i.val x := by simp only [update_usize] @@ -185,12 +185,12 @@ theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α) def Slice.index_mut_usize (α : Type u) (v: Slice α) (i: Usize) : Result (α × (α → Result (Slice α))) := do let x ← Slice.index_usize α v i - ret (x, Slice.update_usize α v i) + ok (x, Slice.update_usize α v i) @[pspec] theorem Slice.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize) (hbound : i.val < v.length) : - ∃ x back, v.index_mut_usize α i = ret (x, back) ∧ + ∃ x back, v.index_mut_usize α i = ok (x, back) ∧ x = v.val.index i.val ∧ back = Slice.update_usize α v i := by simp only [index_mut_usize, Bind.bind, bind] @@ -204,30 +204,30 @@ theorem Slice.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i `progress` tactic), meaning `Array.to_slice` should be considered as opaque. All what the spec theorem reveals is that the "representative" lists are the same. -/ def Array.to_slice (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) := - ret ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩ + ok ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩ @[pspec] theorem Array.to_slice_spec {α : Type u} {n : Usize} (v : Array α n) : - ∃ s, to_slice α n v = ret s ∧ v.val = s.val := by simp [to_slice] + ∃ s, to_slice α n v = ok s ∧ v.val = s.val := by simp [to_slice] def Array.from_slice (α : Type u) (n : Usize) (_ : Array α n) (s : Slice α) : Result (Array α n) := if h: s.val.len = n.val then - ret ⟨ s.val, by simp [← List.len_eq_length, *] ⟩ + ok ⟨ s.val, by simp [← List.len_eq_length, *] ⟩ else fail panic @[pspec] theorem Array.from_slice_spec {α : Type u} {n : Usize} (a : Array α n) (ns : Slice α) (h : ns.val.len = n.val) : - ∃ na, from_slice α n a ns = ret na ∧ na.val = ns.val + ∃ na, from_slice α n a ns = ok na ∧ na.val = ns.val := by simp [from_slice, *] def Array.to_slice_mut (α : Type u) (n : Usize) (a : Array α n) : Result (Slice α × (Slice α → Result (Array α n))) := do let s ← Array.to_slice α n a - ret (s, Array.from_slice α n a) + ok (s, Array.from_slice α n a) @[pspec] theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) : - ∃ s back, to_slice_mut α n v = ret (s, back) ∧ + ∃ s back, to_slice_mut α n v = ok (s, back) ∧ v.val = s.val ∧ back = Array.from_slice α n v := by simp [to_slice_mut, to_slice] @@ -235,7 +235,7 @@ theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) : def Array.subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) := -- TODO: not completely sure here if r.start.val < r.end_.val ∧ r.end_.val ≤ a.val.len then - ret ⟨ a.val.slice r.start.val r.end_.val, + ok ⟨ a.val.slice r.start.val r.end_.val, by simp [← List.len_eq_length] have := a.val.slice_len_le r.start.val r.end_.val @@ -246,7 +246,7 @@ def Array.subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) @[pspec] theorem Array.subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize) (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ a.val.len) : - ∃ s, subslice α n a r = ret s ∧ + ∃ s, subslice α n a r = ok s ∧ s.val = a.val.slice r.start.val r.end_.val ∧ (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → s.val.index i = a.val.index (r.start.val + i)) := by @@ -270,7 +270,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range . scalar_tac let na := s_beg.append (s.val.append s_end) have : na.len = a.val.len := by simp [*] - ret ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩ + ok ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩ else fail panic @@ -282,7 +282,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range @[pspec] theorem Array.update_subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize) (s : Slice α) (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : s.length = r.end_.val - r.start.val) : - ∃ na, update_subslice α n a r s = ret na ∧ + ∃ na, update_subslice α n a r s = ok na ∧ (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧ (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = s.index_s (i - r.start.val)) ∧ (∀ i, r.end_.val ≤ i → i < n.val → na.index_s i = a.index_s i) := by @@ -306,7 +306,7 @@ theorem Array.update_subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : def Slice.subslice (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) := -- TODO: not completely sure here if r.start.val < r.end_.val ∧ r.end_.val ≤ s.length then - ret ⟨ s.val.slice r.start.val r.end_.val, + ok ⟨ s.val.slice r.start.val r.end_.val, by simp [← List.len_eq_length] have := s.val.slice_len_le r.start.val r.end_.val @@ -317,7 +317,7 @@ def Slice.subslice (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slic @[pspec] theorem Slice.subslice_spec {α : Type u} [Inhabited α] (s : Slice α) (r : Range Usize) (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ s.val.len) : - ∃ ns, subslice α s r = ret ns ∧ + ∃ ns, subslice α s r = ok ns ∧ ns.val = s.slice r.start.val r.end_.val ∧ (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index_s i = s.index_s (r.start.val + i)) := by @@ -344,14 +344,14 @@ def Slice.update_subslice (α : Type u) (s : Slice α) (r : Range Usize) (ss : S . scalar_tac let ns := s_beg.append (ss.val.append s_end) have : ns.len = s.val.len := by simp [*] - ret ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩ + ok ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩ else fail panic @[pspec] theorem Slice.update_subslice_spec {α : Type u} [Inhabited α] (a : Slice α) (r : Range Usize) (ss : Slice α) (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : ss.length = r.end_.val - r.start.val) : - ∃ na, update_subslice α a r ss = ret na ∧ + ∃ na, update_subslice α a r ss = ok na ∧ (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧ (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = ss.index_s (i - r.start.val)) ∧ (∀ i, r.end_.val ≤ i → i < a.length → na.index_s i = a.index_s i) := by @@ -393,7 +393,7 @@ def core.slice.index.Slice.index let x ← inst.get i slice match x with | none => fail panic - | some x => ret x + | some x => ok x /- [core::slice::index::Range:::get]: forward function -/ def core.slice.index.RangeUsize.get (T : Type) (i : Range Usize) (slice : Slice T) : diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean index 0c64eca1..4c5b2795 100644 --- a/backends/lean/Base/Primitives/Base.lean +++ b/backends/lean/Base/Primitives/Base.lean @@ -41,7 +41,7 @@ deriving Repr, BEq open Error inductive Result (α : Type u) where - | ret (v: α): Result α + | ok (v: α): Result α | fail (e: Error): Result α | div deriving Repr, BEq @@ -56,31 +56,31 @@ instance Result_Nonempty (α : Type u) : Nonempty (Result α) := /- HELPERS -/ -def ret? {α: Type u} (r: Result α): Bool := +def ok? {α: Type u} (r: Result α): Bool := match r with - | ret _ => true + | ok _ => true | fail _ | div => false def div? {α: Type u} (r: Result α): Bool := match r with | div => true - | ret _ | fail _ => false + | ok _ | fail _ => false def massert (b:Bool) : Result Unit := - if b then ret () else fail assertionFailure + if b then ok () else fail assertionFailure macro "prove_eval_global" : tactic => `(tactic| first | apply Eq.refl | decide) -def eval_global {α: Type u} (x: Result α) (_: ret? x := by prove_eval_global) : α := +def eval_global {α: Type u} (x: Result α) (_: ok? x := by prove_eval_global) : α := match x with | fail _ | div => by contradiction - | ret x => x + | ok x => x /- DO-DSL SUPPORT -/ def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Result β := match x with - | ret v => f v + | ok v => f v | fail v => fail v | div => div @@ -88,11 +88,11 @@ def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Resu instance : Bind Result where bind := bind --- Allows using return x in do-blocks +-- Allows using pure x in do-blocks instance : Pure Result where - pure := fun x => ret x + pure := fun x => ok x -@[simp] theorem bind_ret (x : α) (f : α → Result β) : bind (.ret x) f = f x := by simp [bind] +@[simp] theorem bind_ok (x : α) (f : α → Result β) : bind (.ok x) f = f x := by simp [bind] @[simp] theorem bind_fail (x : Error) (f : α → Result β) : bind (.fail x) f = .fail x := by simp [bind] @[simp] theorem bind_div (f : α → Result β) : bind .div f = .div := by simp [bind] @@ -103,14 +103,14 @@ instance : Pure Result where -- rely on subtype, and a custom let-binding operator, in effect recreating our -- own variant of the do-dsl -def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ok x } := match o with - | ret x => ret ⟨x, rfl⟩ + | ok x => ok ⟨x, rfl⟩ | fail e => fail e | div => div -@[simp] theorem bind_tc_ret (x : α) (f : α → Result β) : - (do let y ← .ret x; f y) = f x := by simp [Bind.bind, bind] +@[simp] theorem bind_tc_ok (x : α) (f : α → Result β) : + (do let y ← .ok x; f y) = f x := by simp [Bind.bind, bind] @[simp] theorem bind_tc_fail (x : Error) (f : α → Result β) : (do let y ← fail x; f y) = fail x := by simp [Bind.bind, bind] diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index 3d90f1a5..c298ba92 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -339,7 +339,7 @@ def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := -- ``` -- then normalization blocks (for instance, some proofs which use reflexivity fail). -- However, the version below doesn't block reduction (TODO: investigate): - return Scalar.ofIntCore x (Scalar.check_bounds_prop h) + ok (Scalar.ofIntCore x (Scalar.check_bounds_prop h)) else fail integerOverflow def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) @@ -573,7 +573,7 @@ instance {ty} : HAnd (Scalar ty) (Scalar ty) (Scalar ty) where theorem Scalar.add_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x + y.val) (hmax : ↑x + ↑y ≤ Scalar.max ty) : - (∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y) := by + (∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y) := by -- Applying the unfoldings only on the left conv => congr; ext; lhs; unfold HAdd.hAdd instHAddScalarResult; simp [add, tryMk] split @@ -582,7 +582,7 @@ theorem Scalar.add_spec {ty} {x y : Scalar ty} theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} (hmax : ↑x + ↑y ≤ Scalar.max ty) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by have hmin : Scalar.min ty ≤ ↑x + ↑y := by have hx := x.hmin have hy := y.hmin @@ -591,57 +591,57 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} /- Fine-grained theorems -/ @[pspec] theorem Usize.add_spec {x y : Usize} (hmax : ↑x + ↑y ≤ Usize.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U8.add_spec {x y : U8} (hmax : ↑x + ↑y ≤ U8.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U16.add_spec {x y : U16} (hmax : ↑x + ↑y ≤ U16.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U32.add_spec {x y : U32} (hmax : ↑x + ↑y ≤ U32.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U64.add_spec {x y : U64} (hmax : ↑x + ↑y ≤ U64.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U128.add_spec {x y : U128} (hmax : ↑x + ↑y ≤ U128.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem Isize.add_spec {x y : Isize} (hmin : Isize.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ Isize.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I8.add_spec {x y : I8} (hmin : I8.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I8.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I16.add_spec {x y : I16} (hmin : I16.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I16.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I32.add_spec {x y : I32} (hmin : I32.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I32.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I64.add_spec {x y : I64} (hmin : I64.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I64.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I128.add_spec {x y : I128} (hmin : I128.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I128.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax -- Generic theorem - shouldn't be used much @@ -649,7 +649,7 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} theorem Scalar.sub_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ Scalar.max ty) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by conv => congr; ext; lhs; simp [HSub.hSub, sub, tryMk, Sub.sub] split . simp [pure] @@ -658,7 +658,7 @@ theorem Scalar.sub_spec {ty} {x y : Scalar ty} theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned) {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by have : ↑x - ↑y ≤ Scalar.max ty := by have hx := x.hmin have hxm := x.hmax @@ -669,64 +669,64 @@ theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned) /- Fine-grained theorems -/ @[pspec] theorem Usize.sub_spec {x y : Usize} (hmin : Usize.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U8.sub_spec {x y : U8} (hmin : U8.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U16.sub_spec {x y : U16} (hmin : U16.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U32.sub_spec {x y : U32} (hmin : U32.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U64.sub_spec {x y : U64} (hmin : U64.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U128.sub_spec {x y : U128} (hmin : U128.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem Isize.sub_spec {x y : Isize} (hmin : Isize.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ Isize.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I8.sub_spec {x y : I8} (hmin : I8.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I8.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I16.sub_spec {x y : I16} (hmin : I16.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I16.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I32.sub_spec {x y : I32} (hmin : I32.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I32.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I64.sub_spec {x y : I64} (hmin : I64.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I64.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I128.sub_spec {x y : I128} (hmin : I128.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I128.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax -- Generic theorem - shouldn't be used much theorem Scalar.mul_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ Scalar.max ty) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by conv => congr; ext; lhs; simp [HMul.hMul] simp [mul, tryMk] split @@ -736,7 +736,7 @@ theorem Scalar.mul_spec {ty} {x y : Scalar ty} theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} (hmax : ↑x * ↑y ≤ Scalar.max ty) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by have : Scalar.min ty ≤ ↑x * ↑y := by have hx := x.hmin have hy := y.hmin @@ -745,57 +745,57 @@ theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} /- Fine-grained theorems -/ @[pspec] theorem Usize.mul_spec {x y : Usize} (hmax : ↑x * ↑y ≤ Usize.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U8.mul_spec {x y : U8} (hmax : ↑x * ↑y ≤ U8.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U16.mul_spec {x y : U16} (hmax : ↑x * ↑y ≤ U16.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U32.mul_spec {x y : U32} (hmax : ↑x * ↑y ≤ U32.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U64.mul_spec {x y : U64} (hmax : ↑x * ↑y ≤ U64.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U128.mul_spec {x y : U128} (hmax : ↑x * ↑y ≤ U128.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem Isize.mul_spec {x y : Isize} (hmin : Isize.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ Isize.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I8.mul_spec {x y : I8} (hmin : I8.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I8.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I16.mul_spec {x y : I16} (hmin : I16.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I16.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I32.mul_spec {x y : I32} (hmin : I32.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I32.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I64.mul_spec {x y : I64} (hmin : I64.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I64.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I128.mul_spec {x y : I128} (hmin : I128.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I128.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax -- Generic theorem - shouldn't be used much @@ -804,15 +804,14 @@ theorem Scalar.div_spec {ty} {x y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) (hmin : Scalar.min ty ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ Scalar.max ty) : - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := by simp [HDiv.hDiv, div, Div.div] simp [tryMk, *] - simp [pure] rfl theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at * have hx := x.hmin have hy := y.hmin @@ -828,69 +827,69 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S /- Fine-grained theorems -/ @[pspec] theorem Usize.div_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U8.div_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U16.div_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U32.div_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U64.div_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U128.div_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem Isize.div_spec (x : Isize) {y : Isize} (hnz : ↑y ≠ (0 : Int)) (hmin : Isize.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ Isize.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I8.div_spec (x : I8) {y : I8} (hnz : ↑y ≠ (0 : Int)) (hmin : I8.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I8.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I16.div_spec (x : I16) {y : I16} (hnz : ↑y ≠ (0 : Int)) (hmin : I16.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I16.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I32.div_spec (x : I32) {y : I32} (hnz : ↑y ≠ (0 : Int)) (hmin : I32.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I32.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I64.div_spec (x : I64) {y : I64} (hnz : ↑y ≠ (0 : Int)) (hmin : I64.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I64.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I128.div_spec (x : I128) {y : I128} (hnz : ↑y ≠ (0 : Int)) (hmin : I128.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I128.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax -- Generic theorem - shouldn't be used much @@ -899,15 +898,14 @@ theorem Scalar.rem_spec {ty} {x y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) (hmin : Scalar.min ty ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ Scalar.max ty) : - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by simp [HMod.hMod, rem] simp [tryMk, *] - simp [pure] rfl theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at * have hx := x.hmin have hy := y.hmin @@ -923,62 +921,62 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S simp [*] @[pspec] theorem Usize.rem_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U8.rem_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U16.rem_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U32.rem_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U64.rem_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U128.rem_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem I8.rem_spec (x : I8) {y : I8} (hnz : ↑y ≠ (0 : Int)) (hmin : I8.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I8.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I16.rem_spec (x : I16) {y : I16} (hnz : ↑y ≠ (0 : Int)) (hmin : I16.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I16.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I32.rem_spec (x : I32) {y : I32} (hnz : ↑y ≠ (0 : Int)) (hmin : I32.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I32.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I64.rem_spec (x : I64) {y : I64} (hnz : ↑y ≠ (0 : Int)) (hmin : I64.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I64.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I128.rem_spec (x : I128) {y : I128} (hnz : ↑y ≠ (0 : Int)) (hmin : I128.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I128.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax -- ofIntCore @@ -1152,6 +1150,6 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) := | isFalse h => isFalse (Scalar.ne_of_val_ne h) @[simp] theorem Scalar.neq_to_neq_val {ty} : ∀ {i j : Scalar ty}, (¬ i = j) ↔ ¬ i.val = j.val := by - intro i j; cases i; cases j; simp + simp [eq_equiv] end Primitives diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean index 65249c12..dbe5c8dd 100644 --- a/backends/lean/Base/Primitives/Vec.lean +++ b/backends/lean/Base/Primitives/Vec.lean @@ -61,34 +61,34 @@ def Vec.push (α : Type u) (v : Vec α) (x : α) : Result (Vec α) simp [Usize.max] at * have hm := Usize.refined_max.property cases h <;> cases hm <;> simp [U32.max, U64.max] at * <;> try linarith - return ⟨ List.concat v.val x, by simp at *; assumption ⟩ + ok ⟨ List.concat v.val x, by simp at *; assumption ⟩ else fail maximumSizeExceeded -- This shouldn't be used def Vec.insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit := if i.val < v.length then - .ret () + ok () else - .fail arrayOutOfBounds + fail arrayOutOfBounds -- This is actually the backward function def Vec.insert (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) := if i.val < v.length then - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ + ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ else - .fail arrayOutOfBounds + fail arrayOutOfBounds @[pspec] theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α) (hbound : i.val < v.length) : - ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by + ∃ nv, v.insert α i x = ok nv ∧ nv.val = v.val.update i.val x := by simp [insert, *] def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α := match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds - | some x => ret x + | some x => ok x /- In the theorems below: we don't always need the `∃ ..`, but we use one so that `progress` introduces an opaque variable and an equality. This @@ -98,7 +98,7 @@ def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α := @[pspec] theorem Vec.index_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize) (hbound : i.val < v.length) : - ∃ x, v.index_usize i = ret x ∧ x = v.val.index i.val := by + ∃ x, v.index_usize i = ok x ∧ x = v.val.index i.val := by simp only [index_usize] -- TODO: dependent rewrite have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) @@ -108,12 +108,12 @@ def Vec.update_usize {α : Type u} (v: Vec α) (i: Usize) (x: α) : Result (Vec match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds | some _ => - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ + ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ @[pspec] theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α) (hbound : i.val < v.length) : - ∃ nv, v.update_usize i x = ret nv ∧ + ∃ nv, v.update_usize i x = ok nv ∧ nv.val = v.val.update i.val x := by simp only [update_usize] @@ -125,15 +125,15 @@ theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α) def Vec.index_mut_usize {α : Type u} (v: Vec α) (i: Usize) : Result (α × (α → Result (Vec α))) := match Vec.index_usize v i with - | ret x => - ret (x, Vec.update_usize v i) + | ok x => + ok (x, Vec.update_usize v i) | fail e => fail e | div => div @[pspec] theorem Vec.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize) (hbound : i.val < v.length) : - ∃ x back, v.index_mut_usize i = ret (x, back) ∧ + ∃ x back, v.index_mut_usize i = ok (x, back) ∧ x = v.val.index i.val ∧ -- Backward function back = v.update_usize i |