[AST] fix statement vs expression

Fixes #51, #52

We make the following changes to the AST by adding
- a newly introduced a top-level `Program` node, which is parent to
- a newly introduced `Statements` node, which is parent to
- a `Statement` node, which is chaned to be a parent of
- an `Expr` node.

We make the following changes to Statement by
- introduce a `EFor` node to the typed AST.

We update update the evaluator by
- providing an explicit transformer stack (`EvalT`),
- fixing the semantics for for loops, and
- switching to CPS both in evaluator and normaliser.

We also add minor improvements to the codebase by
- fixing `Sign` vs `Sig` naming issue,
- cleaning up some naming conventions, and
- providing `stack bench` benchmark for testing generators for the new
  AST.

bench/Main.hs

@@ -0,0 +1,81 @@
+import           TinyLang.Field.Generator  ()
+import           TinyLang.Field.Typed.Core
+
+import           Control.Monad
+import           Data.List
+import           Test.QuickCheck
+
+-- A couple of functions for checking the output of generators
+progNodes :: Program f -> Int
+progNodes = stmtsNodes . unProgram
+
+stmtsNodes :: Statements f -> Int
+stmtsNodes = sum . map stmtNodes . unStatements
+
+stmtNodes :: Statement f -> Int
+stmtNodes (ELet _ e)         = 1 + exprNodes e
+stmtNodes (EAssert e)        = 1 + exprNodes e
+stmtNodes (EFor _ _ _ stmts) = 1 + stmtsNodes stmts
+
+exprNodes :: Expr f a -> Int
+exprNodes (EConst _)          = 1
+exprNodes (EVar   _)          = 1
+exprNodes (EAppUnOp _ e)      = 1 + exprNodes e
+exprNodes (EAppBinOp _ e1 e2) = 1 + exprNodes e1 + exprNodes e2
+exprNodes (EIf e e1 e2)       = 1 + exprNodes e + exprNodes e1 + exprNodes e2
+
+progDepth :: Program f -> Int
+progDepth = stmtsDepth . unProgram
+
+stmtsDepth :: Statements f -> Int
+stmtsDepth = maximum . (0:) . map stmtDepth . unStatements
+
+stmtDepth :: Statement f -> Int
+stmtDepth (ELet _ e)         = 1 + exprDepth e
+stmtDepth (EAssert e)        = 1 + exprDepth e
+stmtDepth (EFor _ _ _ stmts) = 1 + stmtsDepth stmts
+
+exprDepth :: Expr f a -> Int
+exprDepth (EConst _)          = 1
+exprDepth (EVar _)            = 1
+exprDepth (EAppUnOp _ e)      = 1 + exprDepth e
+exprDepth (EAppBinOp _ e1 e2) = 1 + max (exprDepth e1) (exprDepth e2)
+exprDepth (EIf e e1 e2)       = 1 + max (exprDepth e)  (max (exprDepth e1) (exprDepth e2))
+
+data TestResult = TestResult { nodes :: Int
+                             , depth :: Int
+                             }
+                  deriving (Show)
+
+runGen :: Int -> IO TestResult
+runGen size = do
+    prog <- generate (resize size arbitrary) :: IO (Program (AField Rational))
+    pure $ TestResult (progNodes prog) (progDepth prog)
+
+average :: (Real a, Fractional b) => [a] -> b
+average xs = realToFrac (sum xs) / genericLength xs
+
+main :: IO ()
+main = do
+    let size = 1000
+    let runs = 1000 :: Int
+    putStrLn $ "Requested runs:  " ++ show runs
+    putStrLn $ "Requested size:  " ++ show size
+    results <- forM [1 .. runs] $ \_ -> runGen size
+    let nodess = map nodes results
+    let depths = map depth results
+    let minn = minimum nodess
+    let maxn = maximum nodess
+    let avgn = average nodess :: Double
+    let maxd = maximum depths
+    let mind = minimum depths
+    let avgd = average depths :: Double
+    putStrLn ""
+    putStrLn $ "Minimum depth = " ++ show mind
+    putStrLn $ "Maximum depth = " ++ show maxd
+    putStrLn $ "Mean depth    = " ++ show avgd
+    putStrLn ""
+    putStrLn $ "Minimum number of nodes = " ++ show minn
+    putStrLn $ "Maximum number of nodes = " ++ show maxn
+    putStrLn $ "Mean number of nodes    = " ++ show avgn
+    putStrLn ""

field/TinyLang/Field/Core.hs

@@ -0,0 +1,19 @@
+-- | Basic structure of our programs
+
+module TinyLang.Field.Core
+    ( Program (..)
+    , Statements (..)
+    ) where
+
+import           GHC.Generics
+import           Quiet
+
+-- | Basic wrapper of statements
+newtype Statements stmt = Statements { unStatements :: [stmt] }
+    deriving (Generic, Eq, Functor, Foldable, Traversable)
+    deriving (Show) via (Quiet (Statements stmt))
+
+-- | Basic wrapper of program
+newtype Program stmt = Program { unProgram :: (Statements stmt) }
+    deriving (Generic, Eq, Functor, Foldable, Traversable)
+    deriving (Show) via (Quiet (Program stmt))