diff options
author | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /plugins/setoid_ring/Algebra_syntax.v | |
parent | 300293c119981054c95182a90c829058530a6b6f (diff) |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'plugins/setoid_ring/Algebra_syntax.v')
-rw-r--r-- | plugins/setoid_ring/Algebra_syntax.v | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/plugins/setoid_ring/Algebra_syntax.v b/plugins/setoid_ring/Algebra_syntax.v new file mode 100644 index 00000000..e896554e --- /dev/null +++ b/plugins/setoid_ring/Algebra_syntax.v @@ -0,0 +1,25 @@ + +Class Zero (A : Type) := zero : A. +Notation "0" := zero. +Class One (A : Type) := one : A. +Notation "1" := one. +Class Addition (A : Type) := addition : A -> A -> A. +Notation "_+_" := addition. +Notation "x + y" := (addition x y). +Class Multiplication {A B : Type} := multiplication : A -> B -> B. +Notation "_*_" := multiplication. +Notation "x * y" := (multiplication x y). +Class Subtraction (A : Type) := subtraction : A -> A -> A. +Notation "_-_" := subtraction. +Notation "x - y" := (subtraction x y). +Class Opposite (A : Type) := opposite : A -> A. +Notation "-_" := opposite. +Notation "- x" := (opposite(x)). +Class Equality {A : Type}:= equality : A -> A -> Prop. +Notation "_==_" := equality. +Notation "x == y" := (equality x y) (at level 70, no associativity). +Class Bracket (A B: Type):= bracket : A -> B. +Notation "[ x ]" := (bracket(x)). +Class Power {A B: Type} := power : A -> B -> A. +Notation "x ^ y" := (power x y). + |