cabal

only doing this because Data.Set is not in the stdlib

lib/Logic/Language.hs

@@ -0,0 +1,40 @@
+module Logic.Language where
+
+-- Convenience newtype so strings of symbols are less ugly
+newtype ConcatShowList symbol = ConcatShowList [symbol]
+instance Show symbol => Show (ConcatShowList symbol) where
+  show (ConcatShowList xs) = concat $ map show xs
+
+-- Formal language (/grammar/production system/whatever)
+-- https://en.wikipedia.org/wiki/Post_canonical_system
+class Show symbol => Language symbol where
+  isWellFormed :: [symbol] -> Bool
+
+  -- If Haskell had dependent types these could be generalized.
+
+  -- axiomN : N wffs -> theorem
+  axiom0 :: [TypeAxiom0 symbol]
+  axiom1 :: [TypeAxiom1 symbol]
+  axiom2 :: [TypeAxiom2 symbol]
+  axiom3 :: [TypeAxiom3 symbol]
+
+  axiom0 = []
+  axiom1 = []
+  axiom2 = []
+  axiom3 = []
+
+  -- inferN : N theorems -> theorem
+  -- (axiom0 and infer0 would mean the same thing.)
+  infer1 :: [TypeInfer1 symbol]
+  infer2 :: [TypeInfer2 symbol]
+
+  infer1 = []
+  infer2 = []
+
+type TypeAxiom0 s = [s]
+type TypeAxiom1 s = [s] -> [s]
+type TypeAxiom2 s = [s] -> [s] -> [s]
+type TypeAxiom3 s = [s] -> [s] -> [s] -> [s]
+
+type TypeInfer1 s = [s] -> [[s]]
+type TypeInfer2 s = [s] -> [s] -> [[s]]