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authorGravatar Stephane Glondu <steph@glondu.net>2012-01-12 16:04:54 +0100
committerGravatar Stephane Glondu <steph@glondu.net>2012-01-12 16:04:54 +0100
commit39efc41237ec906226a3a53d7396d51173495204 (patch)
tree87cd58d72d43469d2a2a0a127c1060d7c9e0206b /plugins/setoid_ring/Algebra_syntax.v
parent5fe4ac437bed43547b3695664974f492b55cb553 (diff)
parent97fefe1fcca363a1317e066e7f4b99b9c1e9987b (diff)
Remove non-DFSG contentsupstream/8.4_beta+dfsg
Diffstat (limited to 'plugins/setoid_ring/Algebra_syntax.v')
-rw-r--r--plugins/setoid_ring/Algebra_syntax.v25
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
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+++ 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).
+