196d899c02
This PR adds a monolithic `CommRing` class, for internal use by `grind`, and includes instances for `Int`/`BitVec`/`IntX`/`UIntX`.
60 lines
1.7 KiB
Text
60 lines
1.7 KiB
Text
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/- Simple Matrix -/
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def Matrix (m n : Nat) (α : Type u) : Type u :=
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Fin m → Fin n → α
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namespace Matrix
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/- Scoped notation for accessing values stored in matrices. -/
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scoped syntax:max (name := matrixAccess) (priority := high) term noWs "[" term ", " term "]" : term
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macro_rules (kind := matrixAccess)
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| `($x[$i, $j]) => `($x $i $j)
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def dotProduct [Mul α] [Add α] [Zero α] (u v : Fin m → α) : α :=
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loop m (Nat.le_refl ..) Zero.zero
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where
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loop (i : Nat) (h : i ≤ m) (acc : α) : α :=
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match i, h with
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| 0, _ => acc
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| i+1, h =>
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have : i < m := Nat.lt_of_lt_of_le (Nat.lt_succ_self _) h
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loop i (Nat.le_of_lt this) (acc + u ⟨i, this⟩ * v ⟨i, this⟩)
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instance [Zero α] : Zero (Matrix m n α) where
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zero _ _ := 0
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instance [Add α] : Add (Matrix m n α) where
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add x y i j := x[i, j] + y[i, j]
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instance [Mul α] [Add α] [Zero α] : HMul (Matrix m n α) (Matrix n p α) (Matrix m p α) where
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hMul x y i j := dotProduct (x[i, ·]) (y[·, j])
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instance [Mul α] : HMul α (Matrix m n α) (Matrix m n α) where
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hMul c x i j := c * x[i, j]
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end Matrix
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def m1 : Matrix 2 2 Int :=
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fun i j => #[#[1, 2], #[3, 4]][i]![j]!
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def m2 : Matrix 2 2 Int :=
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fun i j => #[#[5, 6], #[7, 8]][i]![j]!
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open Matrix -- activate .[.,.] notation
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#guard (m1*m2)[0, 0] == 19
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#guard (m1*m2)[0, 1] == 22
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#guard (m1*m2)[1, 0] == 43
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#guard (m1*m2)[1, 1] == 50
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def v := -2
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#guard (v*m1*m2)[0, 0] == -38
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def ex1 (a b : Nat) (x : Matrix 10 20 Nat) (y : Matrix 20 10 Nat) (z : Matrix 10 10 Nat) : Matrix 10 10 Nat :=
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a * x * y + b * z
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def ex2 (a b : Nat) (x : Matrix m n Nat) (y : Matrix n m Nat) (z : Matrix m m Nat) : Matrix m m Nat :=
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a * x * y + b * z
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