111 lines
3.5 KiB
Text
111 lines
3.5 KiB
Text
/-
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Copyright (c) 2015 Jeremy Avigad. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Jeremy Avigad
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Bundled structures
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-/
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import algebra.group homotopy.interval
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open algebra
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namespace algebra
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structure Semigroup :=
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(carrier : Type) (struct : semigroup carrier)
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attribute Semigroup.carrier [coercion]
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attribute Semigroup.struct [instance]
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structure CommSemigroup :=
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(carrier : Type) (struct : comm_semigroup carrier)
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attribute CommSemigroup.carrier [coercion]
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attribute CommSemigroup.struct [instance]
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structure Monoid :=
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(carrier : Type) (struct : monoid carrier)
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attribute Monoid.carrier [coercion]
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attribute Monoid.struct [instance]
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structure CommMonoid :=
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(carrier : Type) (struct : comm_monoid carrier)
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attribute CommMonoid.carrier [coercion]
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attribute CommMonoid.struct [instance]
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abbreviation signature := interval
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structure Group (i : signature) :=
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(carrier : Type) (struct : group carrier)
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definition MulGroup : Type := Group interval.zero
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definition AddGroup : Type := Group interval.one
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attribute Group.carrier [coercion]
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definition MulGroup.mk [constructor] [reducible] (G : Type) (H : group G) : MulGroup :=
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Group.mk _ G _
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definition AddGroup.mk [constructor] [reducible] (G : Type) (H : add_group G) : AddGroup :=
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Group.mk _ G add_group.to_group
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definition MulGroup.struct [reducible] (G : MulGroup) : group G := Group.struct G
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definition AddGroup.struct [reducible] (G : AddGroup) : add_group G :=
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@group.to_add_group _ (Group.struct G)
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attribute MulGroup.struct AddGroup.struct [instance] [priority 2000]
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attribute Group.struct [instance] [priority 800]
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structure CommGroup (i : signature) :=
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(carrier : Type) (struct : comm_group carrier)
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definition MulCommGroup : Type := CommGroup interval.zero
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definition AddCommGroup : Type := CommGroup interval.one
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attribute CommGroup.carrier [coercion]
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definition MulCommGroup.mk [constructor] [reducible] (G : Type) (H : comm_group G) : MulCommGroup :=
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CommGroup.mk _ G _
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definition AddCommGroup.mk [constructor] [reducible] (G : Type) (H : add_comm_group G) :
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AddCommGroup :=
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CommGroup.mk _ G add_comm_group.to_comm_group
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definition MulCommGroup.struct [reducible] (G : MulCommGroup) : comm_group G := CommGroup.struct G
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definition AddCommGroup.struct [reducible] (G : AddCommGroup) : add_comm_group G :=
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@comm_group.to_add_comm_group _ (CommGroup.struct G)
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attribute MulCommGroup.struct AddCommGroup.struct [instance] [priority 2000]
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attribute CommGroup.struct [instance] [priority 800]
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-- structure AddSemigroup :=
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-- (carrier : Type) (struct : add_semigroup carrier)
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-- attribute AddSemigroup.carrier [coercion]
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-- attribute AddSemigroup.struct [instance]
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-- structure AddCommSemigroup :=
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-- (carrier : Type) (struct : add_comm_semigroup carrier)
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-- attribute AddCommSemigroup.carrier [coercion]
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-- attribute AddCommSemigroup.struct [instance]
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-- structure AddMonoid :=
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-- (carrier : Type) (struct : add_monoid carrier)
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-- attribute AddMonoid.carrier [coercion]
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-- attribute AddMonoid.struct [instance]
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-- structure AddCommMonoid :=
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-- (carrier : Type) (struct : add_comm_monoid carrier)
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-- attribute AddCommMonoid.carrier [coercion]
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-- attribute AddCommMonoid.struct [instance]
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-- structure AddGroup :=
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-- (carrier : Type) (struct : add_group carrier)
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-- attribute AddGroup.carrier [coercion]
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-- attribute AddGroup.struct [instance]
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-- structure AddCommGroup :=
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-- (carrier : Type) (struct : add_comm_group carrier)
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-- attribute AddCommGroup.carrier [coercion]
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-- attribute AddCommGroup.struct [instance]
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end algebra
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