[fix] added raw bundles to Data.Nat.Base

CHANGELOG.md

@@ -1739,6 +1739,13 @@ Other minor changes
   _⊓′_ : ℕ → ℕ → ℕ
   ∣_-_∣′ : ℕ → ℕ → ℕ
   _! : ℕ → ℕ
+
+  +-rawMagma          : RawMagma 0ℓ 0ℓ
+  +-0-rawMonoid       : RawMonoid 0ℓ 0ℓ
+  *-rawMagma          : RawMagma 0ℓ 0ℓ
+  *-1-rawMonoid       : RawMonoid 0ℓ 0ℓ
+  +-*-rawNearSemiring : RawNearSemiring 0ℓ 0ℓ
+  +-*-rawSemiring     : RawSemiring 0ℓ 0ℓ
   ```
 
 

src/Data/Nat/Base.agda

@@ -11,7 +11,7 @@
 
 module Data.Nat.Base where
 
-open import Algebra.Bundles.Raw using (RawMagma; RawMonoid)
+open import Algebra.Bundles.Raw using (RawMagma; RawMonoid; RawNearSemiring; RawSemiring)
 open import Data.Bool.Base using (Bool; true; false; T; not)
 open import Level using (0ℓ)
 open import Relation.Binary.Core using (Rel)
@@ -323,3 +323,36 @@ compare (suc m) (suc n) with compare m n
   ; _∙_ = _+_
   ; ε   = 0
   }
+
+*-rawMagma : RawMagma 0ℓ 0ℓ
+*-rawMagma = record
+  { _≈_ = _≡_
+  ; _∙_ = _*_
+  }
+
+*-1-rawMonoid : RawMonoid 0ℓ 0ℓ
+*-1-rawMonoid = record
+  { _≈_ = _≡_
+  ; _∙_ = _*_
+  ; ε = 1
+  }
+
++-*-rawNearSemiring : RawNearSemiring 0ℓ 0ℓ
++-*-rawNearSemiring = record
+  { Carrier = _
+  ; _≈_ = _≡_
+  ; _+_ = _+_
+  ; _*_ = _*_
+  ; 0# = 0
+  }
+
++-*-rawSemiring : RawSemiring 0ℓ 0ℓ
++-*-rawSemiring = record
+  { Carrier = _
+  ; _≈_ = _≡_
+  ; _+_ = _+_
+  ; _*_ = _*_
+  ; 0# = 0
+  ; 1# = 1
+  }
+

src/Data/Nat/Binary/Properties.agda

@@ -983,19 +983,19 @@ toℕ-homo-* x y =  aux x y (size x ℕ.+ size y) ℕₚ.≤-refl
     |y|+1+|x|≤cnt = subst (ℕ._≤ cnt) eq |x|+1+|y|≤cnt
 
 
-toℕ-isMagmaHomomorphism-* : IsMagmaHomomorphism *-rawMagma ℕₚ.*-rawMagma toℕ
+toℕ-isMagmaHomomorphism-* : IsMagmaHomomorphism *-rawMagma ℕᵇ.*-rawMagma toℕ
 toℕ-isMagmaHomomorphism-* = record
   { isRelHomomorphism = toℕ-isRelHomomorphism
   ; homo              = toℕ-homo-*
   }
 
-toℕ-isMonoidHomomorphism-* : IsMonoidHomomorphism *-1-rawMonoid ℕₚ.*-1-rawMonoid toℕ
+toℕ-isMonoidHomomorphism-* : IsMonoidHomomorphism *-1-rawMonoid ℕᵇ.*-1-rawMonoid toℕ
 toℕ-isMonoidHomomorphism-* = record
   { isMagmaHomomorphism = toℕ-isMagmaHomomorphism-*
   ; ε-homo              = refl
   }
 
-toℕ-isMonoidMonomorphism-* : IsMonoidMonomorphism *-1-rawMonoid ℕₚ.*-1-rawMonoid toℕ
+toℕ-isMonoidMonomorphism-* : IsMonoidMonomorphism *-1-rawMonoid ℕᵇ.*-1-rawMonoid toℕ
 toℕ-isMonoidMonomorphism-* = record
   { isMonoidHomomorphism = toℕ-isMonoidHomomorphism-*
   ; injective            = toℕ-injective

src/Data/Nat/Properties.agda

@@ -845,19 +845,6 @@ m+n≮m m n = subst (_≮ m) (+-comm n m) (m+n≮n n m)
 ------------------------------------------------------------------------
 -- Bundles
 
-*-rawMagma : RawMagma 0ℓ 0ℓ
-*-rawMagma = record
-  { _≈_ = _≡_
-  ; _∙_ = _*_
-  }
-
-*-1-rawMonoid : RawMonoid 0ℓ 0ℓ
-*-1-rawMonoid = record
-  { _≈_ = _≡_
-  ; _∙_ = _*_
-  ; ε   = 1
-  }
-
 *-magma : Magma 0ℓ 0ℓ
 *-magma = record
   { isMagma = *-isMagma