@@ -166,11 +166,11 @@ record Monoid c ℓ : Set (suc (c ⊔ ℓ)) where
166
166
semigroup : Semigroup _ _
167
167
semigroup = record { isSemigroup = isSemigroup }
168
168
169
+ open Semigroup semigroup public using (rawMagma; magma)
170
+
169
171
rawMonoid : RawMonoid _ _
170
172
rawMonoid = record { _≈_ = _≈_; _∙_ = _∙_; ε = ε}
171
173
172
- open Semigroup semigroup public using (rawMagma; magma)
173
-
174
174
175
175
record CommutativeMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
176
176
infixl 7 _∙_
@@ -187,11 +187,11 @@ record CommutativeMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
187
187
monoid : Monoid _ _
188
188
monoid = record { isMonoid = isMonoid }
189
189
190
+ open Monoid monoid public using (rawMagma; magma; semigroup; rawMonoid)
191
+
190
192
commutativeSemigroup : CommutativeSemigroup _ _
191
193
commutativeSemigroup = record { isCommutativeSemigroup = isCommutativeSemigroup }
192
194
193
- open Monoid monoid public using (rawMagma; magma; semigroup; rawMonoid)
194
-
195
195
196
196
record IdempotentCommutativeMonoid c ℓ : Set (suc (c ⊔ ℓ)) where
197
197
infixl 7 _∙_
@@ -291,8 +291,10 @@ record AbelianGroup c ℓ : Set (suc (c ⊔ ℓ)) where
291
291
using (rawMagma; magma; semigroup; monoid; rawMonoid; rawGroup)
292
292
293
293
commutativeMonoid : CommutativeMonoid _ _
294
- commutativeMonoid =
295
- record { isCommutativeMonoid = isCommutativeMonoid }
294
+ commutativeMonoid = record { isCommutativeMonoid = isCommutativeMonoid }
295
+
296
+ open CommutativeMonoid commutativeMonoid public
297
+ using (commutativeSemigroup)
296
298
297
299
298
300
------------------------------------------------------------------------
@@ -357,8 +359,7 @@ record NearSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
357
359
+-monoid = record { isMonoid = +-isMonoid }
358
360
359
361
open Monoid +-monoid public
360
- using ()
361
- renaming
362
+ using () renaming
362
363
( rawMagma to +-rawMagma
363
364
; magma to +-magma
364
365
; semigroup to +-semigroup
@@ -369,8 +370,7 @@ record NearSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
369
370
*-semigroup = record { isSemigroup = *-isSemigroup }
370
371
371
372
open Semigroup *-semigroup public
372
- using ()
373
- renaming
373
+ using () renaming
374
374
( rawMagma to *-rawMagma
375
375
; magma to *-magma
376
376
)
@@ -395,13 +395,16 @@ record SemiringWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
395
395
396
396
open NearSemiring nearSemiring public
397
397
using
398
- ( +-rawMagma; +-magma; +-semigroup; +-rawMonoid; +-monoid
398
+ ( +-rawMagma; +-magma; +-semigroup
399
+ ; +-rawMonoid; +-monoid
399
400
; *-rawMagma; *-magma; *-semigroup
400
401
)
401
402
402
403
+-commutativeMonoid : CommutativeMonoid _ _
403
- +-commutativeMonoid =
404
- record { isCommutativeMonoid = +-isCommutativeMonoid }
404
+ +-commutativeMonoid = record { isCommutativeMonoid = +-isCommutativeMonoid }
405
+
406
+ open CommutativeMonoid +-commutativeMonoid public
407
+ using () renaming (commutativeSemigroup to +-commutativeSemigroup)
405
408
406
409
407
410
record CommutativeSemiringWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
@@ -426,7 +429,7 @@ record CommutativeSemiringWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
426
429
427
430
open SemiringWithoutOne semiringWithoutOne public
428
431
using
429
- ( +-rawMagma; +-magma; +-semigroup
432
+ ( +-rawMagma; +-magma; +-semigroup; +-commutativeSemigroup
430
433
; *-rawMagma; *-magma; *-semigroup
431
434
; +-rawMonoid; +-monoid; +-commutativeMonoid
432
435
; nearSemiring
@@ -471,13 +474,13 @@ record SemiringWithoutAnnihilatingZero c ℓ : Set (suc (c ⊔ ℓ)) where
471
474
record { isCommutativeMonoid = +-isCommutativeMonoid }
472
475
473
476
open CommutativeMonoid +-commutativeMonoid public
474
- using ()
475
- renaming
476
- ( rawMagma to +-rawMagma
477
- ; magma to +-magma
478
- ; semigroup to +-semigroup
479
- ; rawMonoid to +-rawMonoid
480
- ; monoid to +-monoid
477
+ using () renaming
478
+ ( rawMagma to +-rawMagma
479
+ ; magma to +-magma
480
+ ; semigroup to +-semigroup
481
+ ; commutativeSemigroup to +-commutativeSemigroup
482
+ ; rawMonoid to +-rawMonoid
483
+ ; monoid to +-monoid
481
484
)
482
485
483
486
*-monoid : Monoid _ _
@@ -526,7 +529,7 @@ record Semiring c ℓ : Set (suc (c ⊔ ℓ)) where
526
529
open SemiringWithoutAnnihilatingZero
527
530
semiringWithoutAnnihilatingZero public
528
531
using
529
- ( +-rawMagma; +-magma; +-semigroup
532
+ ( +-rawMagma; +-magma; +-semigroup; +-commutativeSemigroup
530
533
; *-rawMagma; *-magma; *-semigroup
531
534
; +-rawMonoid; +-monoid; +-commutativeMonoid
532
535
; *-rawMonoid; *-monoid
@@ -560,7 +563,7 @@ record CommutativeSemiring c ℓ : Set (suc (c ⊔ ℓ)) where
560
563
561
564
open Semiring semiring public
562
565
using
563
- ( +-rawMagma; +-magma; +-semigroup
566
+ ( +-rawMagma; +-magma; +-semigroup; +-commutativeSemigroup
564
567
; *-rawMagma; *-magma; *-semigroup
565
568
; +-rawMonoid; +-monoid; +-commutativeMonoid
566
569
; *-rawMonoid; *-monoid
@@ -645,7 +648,7 @@ record Ring c ℓ : Set (suc (c ⊔ ℓ)) where
645
648
646
649
open Semiring semiring public
647
650
using
648
- ( +-rawMagma; +-magma; +-semigroup
651
+ ( +-rawMagma; +-magma; +-semigroup; +-commutativeSemigroup
649
652
; *-rawMagma; *-magma; *-semigroup
650
653
; +-rawMonoid; +-monoid ; +-commutativeMonoid
651
654
; *-rawMonoid; *-monoid
@@ -694,8 +697,8 @@ record CommutativeRing c ℓ : Set (suc (c ⊔ ℓ)) where
694
697
open Ring ring public using (rawRing; +-group; +-abelianGroup)
695
698
open CommutativeSemiring commutativeSemiring public
696
699
using
697
- ( +-rawMagma; +-magma; +-semigroup
698
- ; *-rawMagma; *-magma; *-semigroup
700
+ ( +-rawMagma; +-magma; +-semigroup; +-commutativeSemigroup
701
+ ; *-rawMagma; *-magma; *-semigroup; *-commutativeSemigroup
699
702
; +-rawMonoid; +-monoid; +-commutativeMonoid
700
703
; *-rawMonoid; *-monoid; *-commutativeMonoid
701
704
; nearSemiring; semiringWithoutOne
0 commit comments