diff options
Diffstat (limited to 'src/Soat/FirstOrder/Algebra.idr')
| -rw-r--r-- | src/Soat/FirstOrder/Algebra.idr | 8 |
1 files changed, 5 insertions, 3 deletions
diff --git a/src/Soat/FirstOrder/Algebra.idr b/src/Soat/FirstOrder/Algebra.idr index 6f9389b..b9c02c5 100644 --- a/src/Soat/FirstOrder/Algebra.idr +++ b/src/Soat/FirstOrder/Algebra.idr @@ -8,6 +8,8 @@ import Soat.FirstOrder.Signature %default total %hide Control.Relation.Equivalence +infix 5 ~> + public export 0 algebraOver : (sig : Signature) -> (U : sig.T -> Type) -> Type algebraOver sig x = {t : sig.T} -> (op : Op sig t) -> x ^ op.arity -> x t @@ -62,7 +64,7 @@ record IsHomomorphism -> b.relation t (f t (a.raw.sem op tms)) (b.raw.sem op (map f tms)) public export -record Homomorphism {0 sig : Signature} (a, b : Algebra sig) +record (~>) {0 sig : Signature} (a, b : Algebra sig) where constructor MkHomomorphism func : IFunc a.raw.U b.raw.U @@ -79,7 +81,7 @@ idIsHomo = MkIsHomomorphism mapId tms) public export -idHomo : {a : Algebra sig} -> Homomorphism a a +idHomo : {a : Algebra sig} -> a ~> a idHomo = MkHomomorphism _ idIsHomo public export @@ -98,5 +100,5 @@ compIsHomo fHomo gHomo = MkIsHomomorphism mapComp tms) public export -compHomo : {a, b, c : Algebra sig} -> Homomorphism b c -> Homomorphism a b -> Homomorphism a c +compHomo : {a, b, c : Algebra sig} -> b ~> c -> a ~> b -> a ~> c compHomo f g = MkHomomorphism _ $ compIsHomo f.homo g.homo |