diff options
| author | Greg Brown <greg.brown01@ed.ac.uk> | 2022-12-17 10:26:37 +0000 |
|---|---|---|
| committer | Greg Brown <greg.brown01@ed.ac.uk> | 2022-12-17 10:41:24 +0000 |
| commit | 29c2714d5b5eddf053579d66d20c88daa7cd4859 (patch) | |
| tree | 771025814d33073dbe9a95b7caab615bdf4d4a1d | |
| parent | 4fa5948dafdb102ad0ab1cd3753d910929534673 (diff) | |
Define sorts.
| -rw-r--r-- | obs.ipkg | 3 | ||||
| -rw-r--r-- | src/Obs.idr | 0 | ||||
| -rw-r--r-- | src/Obs/Sort.idr | 44 |
3 files changed, 46 insertions, 1 deletions
@@ -2,4 +2,5 @@ package obs authors = "Greg Brown" sourcedir = "src" -modules = Obs +modules + = Obs.Sort diff --git a/src/Obs.idr b/src/Obs.idr deleted file mode 100644 index e69de29..0000000 --- a/src/Obs.idr +++ /dev/null diff --git a/src/Obs/Sort.idr b/src/Obs/Sort.idr new file mode 100644 index 0000000..16eaa96 --- /dev/null +++ b/src/Obs/Sort.idr @@ -0,0 +1,44 @@ +module Obs.Sort + +-- Definition ------------------------------------------------------------------ + +public export +data Sort : Type where + Prop : Sort + Set : Nat -> Sort + +%name Sort s, s', s'', s''' + +-- Interfaces ------------------------------------------------------------------ + +export +Eq Sort where + Prop == Prop = True + (Set i) == (Set j) = True + _ == _ = False + +export +Show Sort where + show Prop = "Prop" + show (Set 0) = "Set" + show (Set (S i)) = "Set \{show (S i)}" + +-- Operations ------------------------------------------------------------------ + +infix 5 ~> + +public export +suc : Sort -> Sort +suc Prop = Set 0 +suc (Set i) = Set (S i) + +public export +lub : Sort -> Sort -> Sort +lub Prop s' = s' +lub (Set i) Prop = Set i +lub (Set i) (Set j) = Set (max i j) + +public export +(~>) : Sort -> Sort -> Sort +s ~> Prop = Prop +s ~> (Set k) = lub s (Set k) |