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2 files changed +48
-6
lines changed Original file line number Diff line number Diff line change 11
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module Data.Integer.Base where
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+ open import Algebra.Bundles.Raw
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+ using (RawMagma; RawMonoid; RawNearSemiring; RawSemiring; RawRing)
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open import Data.Bool.Base using (Bool; T; true; false)
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open import Data.Nat.Base as ℕ using (ℕ; z≤n; s≤s)
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open import Data.Sign.Base as Sign using (Sign)
@@ -293,3 +295,49 @@ _%ℕ_ : (dividend : ℤ) (divisor : ℕ) .{{_ : ℕ.NonZero divisor}} → ℕ
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_%_ : (dividend divisor : ℤ) .{{_ : NonZero divisor}} → ℕ
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i % j = i %ℕ ∣ j ∣
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+
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+ ------------------------------------------------------------------------
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+ -- Bundles
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+
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+ +-rawMagma : RawMagma 0ℓ 0ℓ
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+ +-rawMagma = record { _≈_ = _≡_ ; _∙_ = _+_ }
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+
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+ +-0-rawMonoid : RawMonoid 0ℓ 0ℓ
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+ +-0-rawMonoid = record { _≈_ = _≡_ ; _∙_ = _+_ ; ε = 0ℤ }
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+
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+ *-rawMagma : RawMagma 0ℓ 0ℓ
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+ *-rawMagma = record { _≈_ = _≡_ ; _∙_ = _*_ }
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+
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+ *-1-rawMonoid : RawMonoid 0ℓ 0ℓ
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+ *-1-rawMonoid = record { _≈_ = _≡_ ; _∙_ = _*_ ; ε = 1ℤ }
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+
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+ +-*-rawNearSemiring : RawNearSemiring 0ℓ 0ℓ
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+ +-*-rawNearSemiring = record
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+ { Carrier = _
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+ ; _≈_ = _≡_
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+ ; _+_ = _+_
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+ ; _*_ = _*_
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+ ; 0# = 0ℤ
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+ }
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+
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+ +-*-rawSemiring : RawSemiring 0ℓ 0ℓ
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+ +-*-rawSemiring = record
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+ { Carrier = _
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+ ; _≈_ = _≡_
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+ ; _+_ = _+_
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+ ; _*_ = _*_
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+ ; 0# = 0ℤ
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+ ; 1# = 1ℤ
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+ }
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+
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+ +-*-rawRing : RawRing 0ℓ 0ℓ
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+ +-*-rawRing = record
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+ { Carrier = _
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+ ; _≈_ = _≡_
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+ ; _+_ = _+_
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+ ; _*_ = _*_
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+ ; -_ = -_
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+ ; 0# = 0ℤ
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+ ; 1# = 1ℤ
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+ }
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+
Original file line number Diff line number Diff line change @@ -1539,12 +1539,6 @@ private
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------------------------------------------------------------------------
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-- Bundles
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- *-rawMagma : RawMagma 0ℓ 0ℓ
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- *-rawMagma = record { _≈_ = _≡_ ; _∙_ = _*_ }
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-
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- *-1-rawMonoid : RawMonoid 0ℓ 0ℓ
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- *-1-rawMonoid = record { _≈_ = _≡_ ; _∙_ = _*_ ; ε = 1ℤ }
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-
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*-magma : Magma 0ℓ 0ℓ
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*-magma = record
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{ isMagma = *-isMagma
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