diff options
Diffstat (limited to 'backends/lean/Base/Primitives')
| -rw-r--r-- | backends/lean/Base/Primitives/Alloc.lean | 37 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Array.lean | 394 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/ArraySlice.lean | 552 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Base.lean | 11 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/CoreOps.lean | 37 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Range.lean | 2 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 169 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Vec.lean | 94 |
8 files changed, 843 insertions, 453 deletions
diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean new file mode 100644 index 00000000..6c89c6bb --- /dev/null +++ b/backends/lean/Base/Primitives/Alloc.lean @@ -0,0 +1,37 @@ +import Lean +import Base.Primitives.Base +import Base.Primitives.CoreOps + +open Primitives +open Result + +namespace alloc + +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 := ret x +def deref_mut_back (T : Type) (_ : T) (x : T) : Result T := ret x + +/-- Trait instance -/ +def coreopsDerefInst (Self : Type) : + core.ops.deref.Deref Self := { + Target := Self + deref := deref Self +} + +/-- Trait instance -/ +def coreopsDerefMutInst (Self : Type) : + core.ops.deref.DerefMut Self := { + derefInst := coreopsDerefInst Self + deref_mut := deref_mut Self + deref_mut_back := deref_mut_back Self +} + +end Box -- alloc.boxed.Box + +end boxed -- alloc.boxed + +end alloc diff --git a/backends/lean/Base/Primitives/Array.lean b/backends/lean/Base/Primitives/Array.lean deleted file mode 100644 index 6c95fd78..00000000 --- a/backends/lean/Base/Primitives/Array.lean +++ /dev/null @@ -1,394 +0,0 @@ -/- Arrays/slices -/ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd -import Mathlib.Tactic.Linarith -import Base.IList -import Base.Primitives.Scalar -import Base.Primitives.Range -import Base.Arith -import Base.Progress.Base - -namespace Primitives - -open Result Error - -def Array (α : Type u) (n : Usize) := { l : List α // l.length = n.val } - -instance (a : Type u) (n : Usize) : Arith.HasIntProp (Array a n) where - prop_ty := λ v => v.val.len = n.val - prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *] - -instance {α : Type u} {n : Usize} (p : Array α n → Prop) : Arith.HasIntProp (Subtype p) where - prop_ty := λ x => p x - prop := λ x => x.property - -@[simp] -abbrev Array.length {α : Type u} {n : Usize} (v : Array α n) : Int := v.val.len - -@[simp] -abbrev Array.v {α : Type u} {n : Usize} (v : Array α n) : List α := v.val - -example {α: Type u} {n : Usize} (v : Array α n) : v.length ≤ Scalar.max ScalarTy.Usize := by - scalar_tac - -def Array.make (α : Type u) (n : Usize) (init : List α) (hl : init.len = n.val := by decide) : - Array α n := ⟨ init, by simp [← List.len_eq_length]; apply hl ⟩ - -example : Array Int (Usize.ofInt 2) := Array.make Int (Usize.ofInt 2) [0, 1] - -@[simp] -abbrev Array.index {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i : Int) : α := - v.val.index i - -@[simp] -abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i j : Int) : List α := - v.val.slice i j - -def Array.index_shared (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 - -/- 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 - helps control the context. - -/ - -@[pspec] -theorem Array.index_shared_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize) - (hbound : i.val < v.length) : - ∃ x, v.index_shared α n i = ret x ∧ x = v.val.index i.val := by - simp only [index_shared] - -- TODO: dependent rewrite - have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) - simp [*] - --- This shouldn't be used -def Array.index_shared_back (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (_: α) : Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def Array.index_mut (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 - -@[pspec] -theorem Array.index_mut_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize) - (hbound : i.val < v.length) : - ∃ x, v.index_mut α n i = ret x ∧ x = v.val.index i.val := by - simp only [index_mut] - -- TODO: dependent rewrite - have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) - simp [*] - -def Array.index_mut_back (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x: α) : Result (Array α n) := - match v.val.indexOpt i.val with - | none => fail .arrayOutOfBounds - | some _ => - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ - -@[pspec] -theorem Array.index_mut_back_spec {α : Type u} {n : Usize} (v: Array α n) (i: Usize) (x : α) - (hbound : i.val < v.length) : - ∃ nv, v.index_mut_back α n i x = ret nv ∧ - nv.val = v.val.update i.val x - := by - simp only [index_mut_back] - have h := List.indexOpt_bounds v.val i.val - split - . simp_all [length]; cases h <;> scalar_tac - . simp_all - -def Slice (α : Type u) := { l : List α // l.length ≤ Usize.max } - -instance (a : Type u) : Arith.HasIntProp (Slice a) where - prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize - prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *] - -instance {α : Type u} (p : Slice α → Prop) : Arith.HasIntProp (Subtype p) where - prop_ty := λ x => p x - prop := λ x => x.property - -@[simp] -abbrev Slice.length {α : Type u} (v : Slice α) : Int := v.val.len - -@[simp] -abbrev Slice.v {α : Type u} (v : Slice α) : List α := v.val - -example {a: Type u} (v : Slice a) : v.length ≤ Scalar.max ScalarTy.Usize := by - scalar_tac - -def Slice.new (α : Type u): Slice α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩ - --- TODO: very annoying that the α is an explicit parameter -def Slice.len (α : Type u) (v : Slice α) : Usize := - Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac) - -@[simp] -theorem Slice.len_val {α : Type u} (v : Slice α) : (Slice.len α v).val = v.length := - by rfl - -@[simp] -abbrev Slice.index {α : Type u} [Inhabited α] (v: Slice α) (i: Int) : α := - v.val.index i - -@[simp] -abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : List α := - s.val.slice i j - -def Slice.index_shared (α : Type u) (v: Slice α) (i: Usize) : Result α := - match v.val.indexOpt i.val with - | none => fail .arrayOutOfBounds - | some x => ret 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 - helps control the context. - -/ - -@[pspec] -theorem Slice.index_shared_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize) - (hbound : i.val < v.length) : - ∃ x, v.index_shared α i = ret x ∧ x = v.val.index i.val := by - simp only [index_shared] - -- TODO: dependent rewrite - have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) - simp [*] - --- This shouldn't be used -def Slice.index_shared_back (α : Type u) (v: Slice α) (i: Usize) (_: α) : Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def Slice.index_mut (α : Type u) (v: Slice α) (i: Usize) : Result α := - match v.val.indexOpt i.val with - | none => fail .arrayOutOfBounds - | some x => ret x - -@[pspec] -theorem Slice.index_mut_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize) - (hbound : i.val < v.length) : - ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by - simp only [index_mut] - -- TODO: dependent rewrite - have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) - simp [*] - -def Slice.index_mut_back (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result (Slice α) := - match v.val.indexOpt i.val with - | none => fail .arrayOutOfBounds - | some _ => - .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ - -@[pspec] -theorem Slice.index_mut_back_spec {α : Type u} (v: Slice α) (i: Usize) (x : α) - (hbound : i.val < v.length) : - ∃ nv, v.index_mut_back α i x = ret nv ∧ - nv.val = v.val.update i.val x - := by - simp only [index_mut_back] - have h := List.indexOpt_bounds v.val i.val - split - . simp_all [length]; cases h <;> scalar_tac - . simp_all - -/- Array to slice/subslices -/ - -/- We could make this function not use the `Result` type. By making it monadic, we - push the user to use the `Array.to_slice_shared_spec` spec theorem below (through the - `progress` tactic), meaning `Array.to_slice_shared` should be considered as opaque. - All what the spec theorem reveals is that the "representative" lists are the same. -/ -def Array.to_slice_shared (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) := - ret ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩ - -@[pspec] -theorem Array.to_slice_shared_spec {α : Type u} {n : Usize} (v : Array α n) : - ∃ s, to_slice_shared α n v = ret s ∧ v.val = s.val := by simp [to_slice_shared] - -def Array.to_slice_mut (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) := - to_slice_shared α n v - -@[pspec] -theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) : - ∃ s, Array.to_slice_shared α n v = ret s ∧ v.val = s.val := to_slice_shared_spec v - -def Array.to_slice_mut_back (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, *] ⟩ - else fail panic - -@[pspec] -theorem Array.to_slice_mut_back_spec {α : Type u} {n : Usize} (a : Array α n) (ns : Slice α) (h : ns.val.len = n.val) : - ∃ na, to_slice_mut_back α n a ns = ret na ∧ na.val = ns.val - := by simp [to_slice_mut_back, *] - -def Array.subslice_shared (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, - by - simp [← List.len_eq_length] - have := a.val.slice_len_le r.start.val r.end_.val - scalar_tac ⟩ - else - fail panic - -@[pspec] -theorem Array.subslice_shared_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_shared α n a r = ret 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 - simp [subslice_shared, *] - intro i _ _ - have := List.index_slice r.start.val r.end_.val i a.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac) - simp [*] - -def Array.subslice_mut (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) := - Array.subslice_shared α n a r - -@[pspec] -theorem Array.subslice_mut_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_mut α n a r = ret s ∧ - s.val = a.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)) - := subslice_shared_spec a r h0 h1 - -def Array.subslice_mut_back (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) (s : Slice α) : Result (Array α n) := - -- TODO: not completely sure here - if h: r.start.val < r.end_.val ∧ r.end_.val ≤ a.length ∧ s.val.len = r.end_.val - r.start.val then - let s_beg := a.val.itake r.start.val - let s_end := a.val.idrop r.end_.val - have : s_beg.len = r.start.val := by - apply List.itake_len - . simp_all; scalar_tac - . scalar_tac - have : s_end.len = a.val.len - r.end_.val := by - apply List.idrop_len - . scalar_tac - . 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 ⟩ - else - fail panic - --- TODO: it is annoying to write `.val` everywhere. We could leverage coercions, --- but: some symbols like `+` are already overloaded to be notations for monadic --- operations/ --- We should introduce special symbols for the monadic arithmetic operations --- (the use will never write those symbols directly). -@[pspec] -theorem Array.subslice_mut_back_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, subslice_mut_back α n a r s = ret na ∧ - (∀ i, 0 ≤ i → i < r.start.val → na.index i = a.index i) ∧ - (∀ i, r.start.val ≤ i → i < r.end_.val → na.index i = s.index (i - r.start.val)) ∧ - (∀ i, r.end_.val ≤ i → i < n.val → na.index i = a.index i) := by - simp [subslice_mut_back, *] - have h := List.replace_slice_index r.start.val r.end_.val a.val s.val - (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac) - simp [List.replace_slice] at h - have ⟨ h0, h1, h2 ⟩ := h - clear h - split_conjs - . intro i _ _ - have := h0 i (by int_tac) (by int_tac) - simp [*] - . intro i _ _ - have := h1 i (by int_tac) (by int_tac) - simp [*] - . intro i _ _ - have := h2 i (by int_tac) (by int_tac) - simp [*] - -def Slice.subslice_shared (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, - by - simp [← List.len_eq_length] - have := s.val.slice_len_le r.start.val r.end_.val - scalar_tac ⟩ - else - fail panic - -@[pspec] -theorem Slice.subslice_shared_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_shared α s r = ret ns ∧ - ns.val = s.slice r.start.val r.end_.val ∧ - (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index i = s.index (r.start.val + i)) - := by - simp [subslice_shared, *] - intro i _ _ - have := List.index_slice r.start.val r.end_.val i s.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac) - simp [*] - -def Slice.subslice_mut (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) := - Slice.subslice_shared α s r - -@[pspec] -theorem Slice.subslice_mut_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_mut α s r = ret ns ∧ - ns.val = s.slice r.start.val r.end_.val ∧ - (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index i = s.index (r.start.val + i)) - := subslice_shared_spec s r h0 h1 - -attribute [pp_dot] List.len List.length List.index -- use the dot notation when printing -set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse) - -def Slice.subslice_mut_back (α : Type u) (s : Slice α) (r : Range Usize) (ss : Slice α) : Result (Slice α) := - -- TODO: not completely sure here - if h: r.start.val < r.end_.val ∧ r.end_.val ≤ s.length ∧ ss.val.len = r.end_.val - r.start.val then - let s_beg := s.val.itake r.start.val - let s_end := s.val.idrop r.end_.val - have : s_beg.len = r.start.val := by - apply List.itake_len - . simp_all; scalar_tac - . scalar_tac - have : s_end.len = s.val.len - r.end_.val := by - apply List.idrop_len - . scalar_tac - . 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 ⟩ - else - fail panic - -@[pspec] -theorem Slice.subslice_mut_back_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, subslice_mut_back α a r ss = ret na ∧ - (∀ i, 0 ≤ i → i < r.start.val → na.index i = a.index i) ∧ - (∀ i, r.start.val ≤ i → i < r.end_.val → na.index i = ss.index (i - r.start.val)) ∧ - (∀ i, r.end_.val ≤ i → i < a.length → na.index i = a.index i) := by - simp [subslice_mut_back, *] - have h := List.replace_slice_index r.start.val r.end_.val a.val ss.val - (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac) - simp [List.replace_slice, *] at h - have ⟨ h0, h1, h2 ⟩ := h - clear h - split_conjs - . intro i _ _ - have := h0 i (by int_tac) (by int_tac) - simp [*] - . intro i _ _ - have := h1 i (by int_tac) (by int_tac) - simp [*] - . intro i _ _ - have := h2 i (by int_tac) (by int_tac) - simp [*] - -end Primitives diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean new file mode 100644 index 00000000..f68c0846 --- /dev/null +++ b/backends/lean/Base/Primitives/ArraySlice.lean @@ -0,0 +1,552 @@ +/- Arrays/Slices -/ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd +import Mathlib.Tactic.Linarith +import Base.IList +import Base.Primitives.Scalar +import Base.Primitives.Range +import Base.Primitives.CoreOps +import Base.Arith +import Base.Progress.Base + +namespace Primitives + +open Result Error core.ops.range + +def Array (α : Type u) (n : Usize) := { l : List α // l.length = n.val } + +instance (a : Type u) (n : Usize) : Arith.HasIntProp (Array a n) where + prop_ty := λ v => v.val.len = n.val + prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *] + +instance {α : Type u} {n : Usize} (p : Array α n → Prop) : Arith.HasIntProp (Subtype p) where + prop_ty := λ x => p x + prop := λ x => x.property + +@[simp] +abbrev Array.length {α : Type u} {n : Usize} (v : Array α n) : Int := v.val.len + +@[simp] +abbrev Array.v {α : Type u} {n : Usize} (v : Array α n) : List α := v.val + +example {α: Type u} {n : Usize} (v : Array α n) : v.length ≤ Scalar.max ScalarTy.Usize := by + scalar_tac + +def Array.make (α : Type u) (n : Usize) (init : List α) (hl : init.len = n.val := by decide) : + Array α n := ⟨ init, by simp [← List.len_eq_length]; apply hl ⟩ + +example : Array Int (Usize.ofInt 2) := Array.make Int (Usize.ofInt 2) [0, 1] + +@[simp] +abbrev Array.index_s {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i : Int) : α := + v.val.index i + +@[simp] +abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i j : Int) : List α := + v.val.slice i j + +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 + +-- For initialization +def Array.repeat (α : Type u) (n : Usize) (x : α) : Array α n := + ⟨ List.ireplicate n.val x, by have h := n.hmin; simp_all [Scalar.min] ⟩ + +@[pspec] +theorem Array.repeat_spec {α : Type u} (n : Usize) (x : α) : + ∃ a, Array.repeat α n x = a ∧ a.val = List.ireplicate n.val x := by + simp [Array.repeat] + +/- 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 + helps control the context. + -/ + +@[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 + simp only [index_usize] + -- TODO: dependent rewrite + have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) + simp [*] + +def Array.update_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x: α) : Result (Array α n) := + match v.val.indexOpt i.val with + | none => fail .arrayOutOfBounds + | some _ => + .ret ⟨ 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.val = v.val.update i.val x + := by + simp only [update_usize] + have h := List.indexOpt_bounds v.val i.val + split + . simp_all [length]; cases h <;> scalar_tac + . simp_all + +def Slice (α : Type u) := { l : List α // l.length ≤ Usize.max } + +instance (a : Type u) : Arith.HasIntProp (Slice a) where + prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize + prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *] + +instance {α : Type u} (p : Slice α → Prop) : Arith.HasIntProp (Subtype p) where + prop_ty := λ x => p x + prop := λ x => x.property + +@[simp] +abbrev Slice.length {α : Type u} (v : Slice α) : Int := v.val.len + +@[simp] +abbrev Slice.v {α : Type u} (v : Slice α) : List α := v.val + +example {a: Type u} (v : Slice a) : v.length ≤ Scalar.max ScalarTy.Usize := by + scalar_tac + +def Slice.new (α : Type u): Slice α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩ + +-- TODO: very annoying that the α is an explicit parameter +def Slice.len (α : Type u) (v : Slice α) : Usize := + Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac) + +@[simp] +theorem Slice.len_val {α : Type u} (v : Slice α) : (Slice.len α v).val = v.length := + by rfl + +@[simp] +abbrev Slice.index_s {α : Type u} [Inhabited α] (v: Slice α) (i: Int) : α := + v.val.index i + +@[simp] +abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : List α := + s.val.slice i j + +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 + +/- 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 + helps control the context. + -/ + +@[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 + simp only [index_usize] + -- TODO: dependent rewrite + have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) + simp [*] + +-- This shouldn't be used +def Slice.index_shared_back (α : Type u) (v: Slice α) (i: Usize) (_: α) : Result Unit := + if i.val < List.length v.val then + .ret () + else + .fail arrayOutOfBounds + +def Slice.update_usize (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result (Slice α) := + match v.val.indexOpt i.val with + | none => fail .arrayOutOfBounds + | some _ => + .ret ⟨ 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.val = v.val.update i.val x + := by + simp only [update_usize] + have h := List.indexOpt_bounds v.val i.val + split + . simp_all [length]; cases h <;> scalar_tac + . simp_all + +/- Array to slice/subslices -/ + +/- We could make this function not use the `Result` type. By making it monadic, we + push the user to use the `Array.to_slice_spec` spec theorem below (through the + `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 ⟩ + +@[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] + +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, *] ⟩ + 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 + := by simp [from_slice, *] + +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, + by + simp [← List.len_eq_length] + have := a.val.slice_len_le r.start.val r.end_.val + scalar_tac ⟩ + else + fail panic + +@[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.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 + simp [subslice, *] + intro i _ _ + have := List.index_slice r.start.val r.end_.val i a.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac) + simp [*] + +def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) (s : Slice α) : Result (Array α n) := + -- TODO: not completely sure here + if h: r.start.val < r.end_.val ∧ r.end_.val ≤ a.length ∧ s.val.len = r.end_.val - r.start.val then + let s_beg := a.val.itake r.start.val + let s_end := a.val.idrop r.end_.val + have : s_beg.len = r.start.val := by + apply List.itake_len + . simp_all; scalar_tac + . scalar_tac + have : s_end.len = a.val.len - r.end_.val := by + apply List.idrop_len + . scalar_tac + . 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 ⟩ + else + fail panic + +-- TODO: it is annoying to write `.val` everywhere. We could leverage coercions, +-- but: some symbols like `+` are already overloaded to be notations for monadic +-- operations/ +-- We should introduce special symbols for the monadic arithmetic operations +-- (the use will never write those symbols directly). +@[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 ∧ + (∀ 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 + simp [update_subslice, *] + have h := List.replace_slice_index r.start.val r.end_.val a.val s.val + (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac) + simp [List.replace_slice] at h + have ⟨ h0, h1, h2 ⟩ := h + clear h + split_conjs + . intro i _ _ + have := h0 i (by int_tac) (by int_tac) + simp [*] + . intro i _ _ + have := h1 i (by int_tac) (by int_tac) + simp [*] + . intro i _ _ + have := h2 i (by int_tac) (by int_tac) + simp [*] + +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, + by + simp [← List.len_eq_length] + have := s.val.slice_len_le r.start.val r.end_.val + scalar_tac ⟩ + else + fail panic + +@[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.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 + simp [subslice, *] + intro i _ _ + have := List.index_slice r.start.val r.end_.val i s.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac) + simp [*] + +attribute [pp_dot] List.len List.length List.index -- use the dot notation when printing +set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse) + +def Slice.update_subslice (α : Type u) (s : Slice α) (r : Range Usize) (ss : Slice α) : Result (Slice α) := + -- TODO: not completely sure here + if h: r.start.val < r.end_.val ∧ r.end_.val ≤ s.length ∧ ss.val.len = r.end_.val - r.start.val then + let s_beg := s.val.itake r.start.val + let s_end := s.val.idrop r.end_.val + have : s_beg.len = r.start.val := by + apply List.itake_len + . simp_all; scalar_tac + . scalar_tac + have : s_end.len = s.val.len - r.end_.val := by + apply List.idrop_len + . scalar_tac + . 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 ⟩ + 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 ∧ + (∀ 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 + simp [update_subslice, *] + have h := List.replace_slice_index r.start.val r.end_.val a.val ss.val + (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac) + simp [List.replace_slice, *] at h + have ⟨ h0, h1, h2 ⟩ := h + clear h + split_conjs + . intro i _ _ + have := h0 i (by int_tac) (by int_tac) + simp [*] + . intro i _ _ + have := h1 i (by int_tac) (by int_tac) + simp [*] + . intro i _ _ + have := h2 i (by int_tac) (by int_tac) + simp [*] + +/- Trait declaration: [core::slice::index::private_slice_index::Sealed] -/ +structure core.slice.index.private_slice_index.Sealed (Self : Type) where + +/- Trait declaration: [core::slice::index::SliceIndex] -/ +structure core.slice.index.SliceIndex (Self T : Type) where + sealedInst : core.slice.index.private_slice_index.Sealed Self + Output : Type + get : Self → T → Result (Option Output) + get_mut : Self → T → Result (Option Output) + get_mut_back : Self → T → Option Output → Result T + get_unchecked : Self → ConstRawPtr T → Result (ConstRawPtr Output) + get_unchecked_mut : Self → MutRawPtr T → Result (MutRawPtr Output) + index : Self → T → Result Output + index_mut : Self → T → Result Output + index_mut_back : Self → T → Output → Result T + +/- [core::slice::index::[T]::index]: forward function -/ +def core.slice.index.Slice.index + (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) + (slice : Slice T) (i : I) : Result inst.Output := do + let x ← inst.get i slice + match x with + | none => fail panic + | some x => ret x + +/- [core::slice::index::Range:::get]: forward function -/ +def core.slice.index.RangeUsize.get (T : Type) (i : Range Usize) (slice : Slice T) : + Result (Option (Slice T)) := + sorry -- TODO + +/- [core::slice::index::Range::get_mut]: forward function -/ +def core.slice.index.RangeUsize.get_mut + (T : Type) : Range Usize → Slice T → Result (Option (Slice T)) := + sorry -- TODO + +/- [core::slice::index::Range::get_mut]: backward function 0 -/ +def core.slice.index.RangeUsize.get_mut_back + (T : Type) : + Range Usize → Slice T → Option (Slice T) → Result (Slice T) := + sorry -- TODO + +/- [core::slice::index::Range::get_unchecked]: forward function -/ +def core.slice.index.RangeUsize.get_unchecked + (T : Type) : + Range Usize → ConstRawPtr (Slice T) → Result (ConstRawPtr (Slice T)) := + -- Don't know what the model should be - for now we always fail to make + -- sure code which uses it fails + fun _ _ => fail panic + +/- [core::slice::index::Range::get_unchecked_mut]: forward function -/ +def core.slice.index.RangeUsize.get_unchecked_mut + (T : Type) : + Range Usize → MutRawPtr (Slice T) → Result (MutRawPtr (Slice T)) := + -- Don't know what the model should be - for now we always fail to make + -- sure code which uses it fails + fun _ _ => fail panic + +/- [core::slice::index::Range::index]: forward function -/ +def core.slice.index.RangeUsize.index + (T : Type) : Range Usize → Slice T → Result (Slice T) := + sorry -- TODO + +/- [core::slice::index::Range::index_mut]: forward function -/ +def core.slice.index.RangeUsize.index_mut + (T : Type) : Range Usize → Slice T → Result (Slice T) := + sorry -- TODO + +/- [core::slice::index::Range::index_mut]: backward function 0 -/ +def core.slice.index.RangeUsize.index_mut_back + (T : Type) : Range Usize → Slice T → Slice T → Result (Slice T) := + sorry -- TODO + +/- [core::slice::index::[T]::index_mut]: forward function -/ +def core.slice.index.Slice.index_mut + (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) : + Slice T → I → Result inst.Output := + sorry -- TODO + +/- [core::slice::index::[T]::index_mut]: backward function 0 -/ +def core.slice.index.Slice.index_mut_back + (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) : + Slice T → I → inst.Output → Result (Slice T) := + sorry -- TODO + +/- [core::array::[T; N]::index]: forward function -/ +def core.array.Array.index + (T I : Type) (N : Usize) (inst : core.ops.index.Index (Slice T) I) + (a : Array T N) (i : I) : Result inst.Output := + sorry -- TODO + +/- [core::array::[T; N]::index_mut]: forward function -/ +def core.array.Array.index_mut + (T I : Type) (N : Usize) (inst : core.ops.index.IndexMut (Slice T) I) + (a : Array T N) (i : I) : Result inst.indexInst.Output := + sorry -- TODO + +/- [core::array::[T; N]::index_mut]: backward function 0 -/ +def core.array.Array.index_mut_back + (T I : Type) (N : Usize) (inst : core.ops.index.IndexMut (Slice T) I) + (a : Array T N) (i : I) (x : inst.indexInst.Output) : Result (Array T N) := + sorry -- TODO + +/- Trait implementation: [core::slice::index::private_slice_index::Range] -/ +def core.slice.index.private_slice_index.SealedRangeUsizeInst + : core.slice.index.private_slice_index.Sealed (Range Usize) := {} + +/- Trait implementation: [core::slice::index::Range] -/ +def core.slice.index.SliceIndexRangeUsizeSliceTInst (T : Type) : + core.slice.index.SliceIndex (Range Usize) (Slice T) := { + sealedInst := core.slice.index.private_slice_index.SealedRangeUsizeInst + Output := Slice T + get := core.slice.index.RangeUsize.get T + get_mut := core.slice.index.RangeUsize.get_mut T + get_mut_back := core.slice.index.RangeUsize.get_mut_back T + get_unchecked := core.slice.index.RangeUsize.get_unchecked T + get_unchecked_mut := core.slice.index.RangeUsize.get_unchecked_mut T + index := core.slice.index.RangeUsize.index T + index_mut := core.slice.index.RangeUsize.index_mut T + index_mut_back := core.slice.index.RangeUsize.index_mut_back T +} + +/- Trait implementation: [core::slice::index::[T]] -/ +def core.ops.index.IndexSliceTIInst (T I : Type) + (inst : core.slice.index.SliceIndex I (Slice T)) : + core.ops.index.Index (Slice T) I := { + Output := inst.Output + index := core.slice.index.Slice.index T I inst +} + +/- Trait implementation: [core::slice::index::[T]] -/ +def core.ops.index.IndexMutSliceTIInst (T I : Type) + (inst : core.slice.index.SliceIndex I (Slice T)) : + core.ops.index.IndexMut (Slice T) I := { + indexInst := core.ops.index.IndexSliceTIInst T I inst + index_mut := core.slice.index.Slice.index_mut T I inst + index_mut_back := core.slice.index.Slice.index_mut_back T I inst +} + +/- Trait implementation: [core::array::[T; N]] -/ +def core.ops.index.IndexArrayIInst (T I : Type) (N : Usize) + (inst : core.ops.index.Index (Slice T) I) : + core.ops.index.Index (Array T N) I := { + Output := inst.Output + index := core.array.Array.index T I N inst +} + +/- Trait implementation: [core::array::[T; N]] -/ +def core.ops.index.IndexMutArrayIInst (T I : Type) (N : Usize) + (inst : core.ops.index.IndexMut (Slice T) I) : + core.ops.index.IndexMut (Array T N) I := { + indexInst := core.ops.index.IndexArrayIInst T I N inst.indexInst + index_mut := core.array.Array.index_mut T I N inst + index_mut_back := core.array.Array.index_mut_back T I N inst +} + +/- [core::slice::index::usize::get]: forward function -/ +def core.slice.index.Usize.get + (T : Type) : Usize → Slice T → Result (Option T) := + sorry -- TODO + +/- [core::slice::index::usize::get_mut]: forward function -/ +def core.slice.index.Usize.get_mut + (T : Type) : Usize → Slice T → Result (Option T) := + sorry -- TODO + +/- [core::slice::index::usize::get_mut]: backward function 0 -/ +def core.slice.index.Usize.get_mut_back + (T : Type) : Usize → Slice T → Option T → Result (Slice T) := + sorry -- TODO + +/- [core::slice::index::usize::get_unchecked]: forward function -/ +def core.slice.index.Usize.get_unchecked + (T : Type) : Usize → ConstRawPtr (Slice T) → Result (ConstRawPtr T) := + sorry -- TODO + +/- [core::slice::index::usize::get_unchecked_mut]: forward function -/ +def core.slice.index.Usize.get_unchecked_mut + (T : Type) : Usize → MutRawPtr (Slice T) → Result (MutRawPtr T) := + sorry -- TODO + +/- [core::slice::index::usize::index]: forward function -/ +def core.slice.index.Usize.index (T : Type) : Usize → Slice T → Result T := + sorry -- TODO + +/- [core::slice::index::usize::index_mut]: forward function -/ +def core.slice.index.Usize.index_mut (T : Type) : Usize → Slice T → Result T := + sorry -- TODO + +/- [core::slice::index::usize::index_mut]: backward function 0 -/ +def core.slice.index.Usize.index_mut_back + (T : Type) : Usize → Slice T → T → Result (Slice T) := + sorry -- TODO + +/- Trait implementation: [core::slice::index::private_slice_index::usize] -/ +def core.slice.index.private_slice_index.SealedUsizeInst + : core.slice.index.private_slice_index.Sealed Usize := {} + +/- Trait implementation: [core::slice::index::usize] -/ +def core.slice.index.SliceIndexUsizeSliceTInst (T : Type) : + core.slice.index.SliceIndex Usize (Slice T) := { + sealedInst := core.slice.index.private_slice_index.SealedUsizeInst + Output := T + get := core.slice.index.Usize.get T + get_mut := core.slice.index.Usize.get_mut T + get_mut_back := core.slice.index.Usize.get_mut_back T + get_unchecked := core.slice.index.Usize.get_unchecked T + get_unchecked_mut := core.slice.index.Usize.get_unchecked_mut T + index := core.slice.index.Usize.index T + index_mut := core.slice.index.Usize.index_mut T + index_mut_back := core.slice.index.Usize.index_mut_back T +} + +end Primitives diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean index 7c0fa3bb..7fc33251 100644 --- a/backends/lean/Base/Primitives/Base.lean +++ b/backends/lean/Base/Primitives/Base.lean @@ -120,11 +120,18 @@ def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := -- MISC -- ---------- -@[simp] def mem.replace (a : Type) (x : a) (_ : a) : a := x -@[simp] def mem.replace_back (a : Type) (_ : a) (y : a) : a := y +@[simp] def core.mem.replace (a : Type) (x : a) (_ : a) : a := x +@[simp] def core.mem.replace_back (a : Type) (_ : a) (y : a) : a := y /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas +-- We don't really use raw pointers for now +structure MutRawPtr (T : Type) where + v : T + +structure ConstRawPtr (T : Type) where + v : T + end Primitives diff --git a/backends/lean/Base/Primitives/CoreOps.lean b/backends/lean/Base/Primitives/CoreOps.lean new file mode 100644 index 00000000..da458f66 --- /dev/null +++ b/backends/lean/Base/Primitives/CoreOps.lean @@ -0,0 +1,37 @@ +import Lean +import Base.Primitives.Base + +open Primitives +open Result + +namespace core.ops + +namespace index -- core.ops.index + +/- Trait declaration: [core::ops::index::Index] -/ +structure Index (Self Idx : Type) where + Output : Type + index : Self → Idx → Result Output + +/- Trait declaration: [core::ops::index::IndexMut] -/ +structure IndexMut (Self Idx : Type) where + indexInst : Index Self Idx + index_mut : Self → Idx → Result indexInst.Output + index_mut_back : Self → Idx → indexInst.Output → Result Self + +end index -- core.ops.index + +namespace deref -- core.ops.deref + +structure Deref (Self : Type) where + Target : Type + deref : Self → Result Target + +structure DerefMut (Self : Type) where + derefInst : Deref Self + deref_mut : Self → Result derefInst.Target + deref_mut_back : Self → derefInst.Target → Result Self + +end deref -- core.ops.deref + +end core.ops diff --git a/backends/lean/Base/Primitives/Range.lean b/backends/lean/Base/Primitives/Range.lean index 26cbee42..a268bcba 100644 --- a/backends/lean/Base/Primitives/Range.lean +++ b/backends/lean/Base/Primitives/Range.lean @@ -11,7 +11,7 @@ import Base.Progress.Base namespace Primitives -structure Range (α : Type u) where +structure core.ops.range.Range (α : Type u) where mk :: start: α end_: α diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index fecb0d1d..f74fecd4 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -230,6 +230,20 @@ def Scalar.cMax (ty : ScalarTy) : Int := | .Usize => Scalar.max .U32 | _ => Scalar.max ty +theorem Scalar.min_lt_max (ty : ScalarTy) : Scalar.min ty < Scalar.max ty := by + cases ty <;> simp [Scalar.min, Scalar.max] + . simp [Isize.min, Isize.max] + have h1 := Isize.refined_min.property + have h2 := Isize.refined_max.property + cases h1 <;> cases h2 <;> simp [*] + . simp [Usize.max] + have h := Usize.refined_max.property + cases h <;> simp [*] + +theorem Scalar.min_le_max (ty : ScalarTy) : Scalar.min ty ≤ Scalar.max ty := by + have := Scalar.min_lt_max ty + int_tac + theorem Scalar.cMin_bound ty : Scalar.min ty ≤ Scalar.cMin ty := by cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at * have h := Isize.refined_min.property @@ -372,10 +386,28 @@ def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (x.val * y.val) --- TODO: instances of +, -, * etc. for scalars +-- TODO: shift left +def Scalar.shiftl {ty0 ty1 : ScalarTy} (x : Scalar ty0) (y : Scalar ty1) : Result (Scalar ty0) := + sorry + +-- TODO: shift right +def Scalar.shiftr {ty0 ty1 : ScalarTy} (x : Scalar ty0) (y : Scalar ty1) : Result (Scalar ty0) := + sorry + +-- TODO: xor +def Scalar.xor {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry + +-- TODO: and +def Scalar.and {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry + +-- TODO: or +def Scalar.or {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry -- Cast an integer from a [src_ty] to a [tgt_ty] --- TODO: check the semantics of casts in Rust +-- TODO: double-check the semantics of casts in Rust def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := Scalar.tryMk tgt_ty x.val @@ -398,6 +430,34 @@ def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Re instance (ty : ScalarTy) : Inhabited (Scalar ty) := by constructor; cases ty <;> apply (Scalar.ofInt 0) +-- TODO: reducible? +@[reducible] def core_isize_min : Isize := Scalar.ofInt Isize.min (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize)) +@[reducible] def core_isize_max : Isize := Scalar.ofInt Isize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize)) +@[reducible] def core_i8_min : I8 := Scalar.ofInt I8.min +@[reducible] def core_i8_max : I8 := Scalar.ofInt I8.max +@[reducible] def core_i16_min : I16 := Scalar.ofInt I16.min +@[reducible] def core_i16_max : I16 := Scalar.ofInt I16.max +@[reducible] def core_i32_min : I32 := Scalar.ofInt I32.min +@[reducible] def core_i32_max : I32 := Scalar.ofInt I32.max +@[reducible] def core_i64_min : I64 := Scalar.ofInt I64.min +@[reducible] def core_i64_max : I64 := Scalar.ofInt I64.max +@[reducible] def core_i128_min : I128 := Scalar.ofInt I128.min +@[reducible] def core_i128_max : I128 := Scalar.ofInt I128.max + +-- TODO: reducible? +@[reducible] def core_usize_min : Usize := Scalar.ofInt Usize.min +@[reducible] def core_usize_max : Usize := Scalar.ofInt Usize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Usize)) +@[reducible] def core_u8_min : U8 := Scalar.ofInt U8.min +@[reducible] def core_u8_max : U8 := Scalar.ofInt U8.max +@[reducible] def core_u16_min : U16 := Scalar.ofInt U16.min +@[reducible] def core_u16_max : U16 := Scalar.ofInt U16.max +@[reducible] def core_u32_min : U32 := Scalar.ofInt U32.min +@[reducible] def core_u32_max : U32 := Scalar.ofInt U32.max +@[reducible] def core_u64_min : U64 := Scalar.ofInt U64.min +@[reducible] def core_u64_max : U64 := Scalar.ofInt U64.max +@[reducible] def core_u128_min : U128 := Scalar.ofInt U128.min +@[reducible] def core_u128_max : U128 := Scalar.ofInt U128.max + -- TODO: below: not sure this is the best way. -- Should we rather overload operations like +, -, etc.? -- Also, it is possible to automate the generation of those definitions @@ -447,6 +507,26 @@ instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where hMod x y := Scalar.rem x y +-- Shift left +instance {ty0 ty1} : HShiftLeft (Scalar ty0) (Scalar ty1) (Result (Scalar ty0)) where + hShiftLeft x y := Scalar.shiftl x y + +-- Shift right +instance {ty0 ty1} : HShiftRight (Scalar ty0) (Scalar ty1) (Result (Scalar ty0)) where + hShiftRight x y := Scalar.shiftr x y + +-- Xor +instance {ty} : HXor (Scalar ty) (Scalar ty) (Scalar ty) where + hXor x y := Scalar.xor x y + +-- Or +instance {ty} : HOr (Scalar ty) (Scalar ty) (Scalar ty) where + hOr x y := Scalar.or x y + +-- And +instance {ty} : HAnd (Scalar ty) (Scalar ty) (Scalar ty) where + hAnd x y := Scalar.and x y + -- Generic theorem - shouldn't be used much @[cpspec] theorem Scalar.add_spec {ty} {x y : Scalar ty} @@ -864,33 +944,33 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S -- ofIntCore -- TODO: typeclass? -@[reducible] def Isize.ofIntCore := @Scalar.ofIntCore .Isize -@[reducible] def I8.ofIntCore := @Scalar.ofIntCore .I8 -@[reducible] def I16.ofIntCore := @Scalar.ofIntCore .I16 -@[reducible] def I32.ofIntCore := @Scalar.ofIntCore .I32 -@[reducible] def I64.ofIntCore := @Scalar.ofIntCore .I64 -@[reducible] def I128.ofIntCore := @Scalar.ofIntCore .I128 -@[reducible] def Usize.ofIntCore := @Scalar.ofIntCore .Usize -@[reducible] def U8.ofIntCore := @Scalar.ofIntCore .U8 -@[reducible] def U16.ofIntCore := @Scalar.ofIntCore .U16 -@[reducible] def U32.ofIntCore := @Scalar.ofIntCore .U32 -@[reducible] def U64.ofIntCore := @Scalar.ofIntCore .U64 -@[reducible] def U128.ofIntCore := @Scalar.ofIntCore .U128 +def Isize.ofIntCore := @Scalar.ofIntCore .Isize +def I8.ofIntCore := @Scalar.ofIntCore .I8 +def I16.ofIntCore := @Scalar.ofIntCore .I16 +def I32.ofIntCore := @Scalar.ofIntCore .I32 +def I64.ofIntCore := @Scalar.ofIntCore .I64 +def I128.ofIntCore := @Scalar.ofIntCore .I128 +def Usize.ofIntCore := @Scalar.ofIntCore .Usize +def U8.ofIntCore := @Scalar.ofIntCore .U8 +def U16.ofIntCore := @Scalar.ofIntCore .U16 +def U32.ofIntCore := @Scalar.ofIntCore .U32 +def U64.ofIntCore := @Scalar.ofIntCore .U64 +def U128.ofIntCore := @Scalar.ofIntCore .U128 -- ofInt -- TODO: typeclass? -@[reducible] def Isize.ofInt := @Scalar.ofInt .Isize -@[reducible] def I8.ofInt := @Scalar.ofInt .I8 -@[reducible] def I16.ofInt := @Scalar.ofInt .I16 -@[reducible] def I32.ofInt := @Scalar.ofInt .I32 -@[reducible] def I64.ofInt := @Scalar.ofInt .I64 -@[reducible] def I128.ofInt := @Scalar.ofInt .I128 -@[reducible] def Usize.ofInt := @Scalar.ofInt .Usize -@[reducible] def U8.ofInt := @Scalar.ofInt .U8 -@[reducible] def U16.ofInt := @Scalar.ofInt .U16 -@[reducible] def U32.ofInt := @Scalar.ofInt .U32 -@[reducible] def U64.ofInt := @Scalar.ofInt .U64 -@[reducible] def U128.ofInt := @Scalar.ofInt .U128 +abbrev Isize.ofInt := @Scalar.ofInt .Isize +abbrev I8.ofInt := @Scalar.ofInt .I8 +abbrev I16.ofInt := @Scalar.ofInt .I16 +abbrev I32.ofInt := @Scalar.ofInt .I32 +abbrev I64.ofInt := @Scalar.ofInt .I64 +abbrev I128.ofInt := @Scalar.ofInt .I128 +abbrev Usize.ofInt := @Scalar.ofInt .Usize +abbrev U8.ofInt := @Scalar.ofInt .U8 +abbrev U16.ofInt := @Scalar.ofInt .U16 +abbrev U32.ofInt := @Scalar.ofInt .U32 +abbrev U64.ofInt := @Scalar.ofInt .U64 +abbrev U128.ofInt := @Scalar.ofInt .U128 postfix:max "#isize" => Isize.ofInt postfix:max "#i8" => I8.ofInt @@ -908,9 +988,46 @@ postfix:max "#u128" => U128.ofInt -- Testing the notations example : Result Usize := 0#usize + 1#usize +-- TODO: factor those lemmas out @[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by simp [Scalar.ofInt, Scalar.ofIntCore] +@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + +@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by + apply Scalar.ofInt_val_eq h + -- Comparisons instance {ty} : LT (Scalar ty) where lt a b := LT.lt a.val b.val diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean index 2d48a641..2c3fce91 100644 --- a/backends/lean/Base/Primitives/Vec.lean +++ b/backends/lean/Base/Primitives/Vec.lean @@ -6,7 +6,7 @@ import Mathlib.Tactic.RunCmd import Mathlib.Tactic.Linarith import Base.IList import Base.Primitives.Scalar -import Base.Primitives.Array +import Base.Primitives.ArraySlice import Base.Arith import Base.Progress.Base @@ -14,6 +14,8 @@ namespace Primitives open Result Error +namespace alloc.vec + def Vec (α : Type u) := { l : List α // l.length ≤ Usize.max } instance (a : Type u) : Arith.HasIntProp (Vec a) where @@ -83,7 +85,7 @@ theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α) ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by simp [insert, *] -def Vec.index_shared (α : Type u) (v: Vec α) (i: Usize) : Result α := +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 @@ -94,51 +96,83 @@ def Vec.index_shared (α : Type u) (v: Vec α) (i: Usize) : Result α := -/ @[pspec] -theorem Vec.index_shared_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize) - (hbound : i.val < v.length) : - ∃ x, v.index_shared α i = ret x ∧ x = v.val.index i.val := by - simp only [index_shared] - -- TODO: dependent rewrite - have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*]) - simp [*] - --- This shouldn't be used -def Vec.index_back (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def Vec.index_mut (α : Type u) (v: Vec α) (i: Usize) : Result α := - match v.val.indexOpt i.val with - | none => fail .arrayOutOfBounds - | some x => ret x - -@[pspec] -theorem Vec.index_mut_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize) +theorem Vec.index_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize) (hbound : i.val < v.length) : - ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by - simp only [index_mut] + ∃ x, v.index_usize i = ret 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 [*]) simp [*] -def Vec.index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) := +def Vec.update_usize {α : Type u} (v: Vec α) (i: Usize) (x: α) : Result (Vec α) := match v.val.indexOpt i.val with | none => fail .arrayOutOfBounds | some _ => .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩ @[pspec] -theorem Vec.index_mut_back_spec {α : Type u} (v: Vec α) (i: Usize) (x : α) +theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α) (hbound : i.val < v.length) : - ∃ nv, v.index_mut_back α i x = ret nv ∧ + ∃ nv, v.update_usize i x = ret nv ∧ nv.val = v.val.update i.val x := by - simp only [index_mut_back] + simp only [update_usize] have h := List.indexOpt_bounds v.val i.val split . simp_all [length]; cases h <;> scalar_tac . simp_all +/- [alloc::vec::Vec::index]: forward function -/ +def Vec.index (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) + (self : Vec T) (i : I) : Result inst.Output := + sorry -- TODO + +/- [alloc::vec::Vec::index_mut]: forward function -/ +def Vec.index_mut (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) + (self : Vec T) (i : I) : Result inst.Output := + sorry -- TODO + +/- [alloc::vec::Vec::index_mut]: backward function 0 -/ +def Vec.index_mut_back + (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) + (self : Vec T) (i : I) (x : inst.Output) : Result (alloc.vec.Vec T) := + sorry -- TODO + +/- Trait implementation: [alloc::vec::Vec] -/ +def Vec.coreopsindexIndexInst (T I : Type) + (inst : core.slice.index.SliceIndex I (Slice T)) : + core.ops.index.Index (alloc.vec.Vec T) I := { + Output := inst.Output + index := Vec.index T I inst +} + +/- Trait implementation: [alloc::vec::Vec] -/ +def Vec.coreopsindexIndexMutInst (T I : Type) + (inst : core.slice.index.SliceIndex I (Slice T)) : + core.ops.index.IndexMut (alloc.vec.Vec T) I := { + indexInst := Vec.coreopsindexIndexInst T I inst + index_mut := Vec.index_mut T I inst + index_mut_back := Vec.index_mut_back T I inst +} + +@[simp] +theorem Vec.index_slice_index {α : Type} (v : Vec α) (i : Usize) : + Vec.index α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i = + Vec.index_usize v i := + sorry + +@[simp] +theorem Vec.index_mut_slice_index {α : Type} (v : Vec α) (i : Usize) : + Vec.index_mut α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i = + Vec.index_usize v i := + sorry + +@[simp] +theorem Vec.index_mut_back_slice_index {α : Type} (v : Vec α) (i : Usize) (x : α) : + Vec.index_mut_back α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i x = + Vec.update_usize v i x := + sorry + +end alloc.vec + end Primitives |