From 7fd22748735571a05903e0ce39beda693f8d093b Mon Sep 17 00:00:00 2001
From: Danila Fedorin <danila.fedorin@gmail.com>
Date: Mon, 28 Jan 2019 23:19:37 -0800
Subject: [PATCH] Add all solutions to HW3.

---
 HW3.fedorind.hs | 102 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 HW3.fedorind.hs

diff --git a/HW3.fedorind.hs b/HW3.fedorind.hs
new file mode 100644
index 0000000..8bd3785
--- /dev/null
+++ b/HW3.fedorind.hs
@@ -0,0 +1,102 @@
+-- Author: Danila Fedorin
+import Data.List
+
+-- Definitions
+type Var = String
+type Macro = String
+
+data PenMode = Up | Down
+
+data Expr = Variable Var
+          | Number Int
+          | Sum Expr Expr
+
+data Cmd = Pen PenMode
+         | Move Expr Expr
+         | Define Macro [Var] Prog
+         | Call Macro [Expr]
+
+type Prog = [Cmd]
+
+-- HW Code
+-- define line(x1, y1, x2, y2) {
+--     pen up; move (x1, y1);
+--     pen down; move(x2, y2);
+-- }
+lineMacro = Define "line" [ "x1", "y1", "x2", "y2" ]
+    [ Pen Up
+    , Move (Variable "x1") (Variable "y1")
+    , Pen Down
+    , Move (Variable "x2") (Variable "y2")
+    ]
+
+-- define nix(x, y, w, h) {
+--     call line(x, y, x + w, y + h);
+--     call line(x + w, y, x, y + h);
+-- }
+nixMacro = Define "nix" [ "x", "y", "w", "h" ]
+    [ Call "line"
+        [ Variable "x"
+        , Variable "y"
+        , Sum (Variable "x") (Variable "w")
+        , Sum (Variable "y") (Variable "h")
+        ]
+    , Call "line"
+        [ Sum (Variable "x") (Variable "w")
+        , Variable "y"
+        , Variable "x"
+        , Sum (Variable "y") (Variable "h")
+        ]
+    ]
+
+steps :: Int -> Prog
+steps n = base ++ stepList
+    where
+        base = [ Pen Up, Move (Number 0) (Number 0) ]
+        stepList = [1..n] >>= (\i -> [ Move (Number (i -1)) (Number i), Move (Number i) (Number i) ])
+
+prettyPrintExpr :: Expr -> String
+prettyPrintExpr (Variable v) = v
+prettyPrintExpr (Number i) = show i
+prettyPrintExpr (Sum l r) = prettyPrintExpr l ++ "+" ++ prettyPrintExpr r
+
+prettyPrintPenMode :: PenMode -> String
+prettyPrintPenMode Up = "up"
+prettyPrintPenMode Down = "down"
+
+prettyPrintCmd :: Cmd -> [String]
+prettyPrintCmd (Pen m) = [ "pen " ++ prettyPrintPenMode m ++ ";" ]
+prettyPrintCmd (Move l r) = [ "move(" ++ prettyPrintExpr l ++ ", " ++ prettyPrintExpr r ++ ");" ]
+prettyPrintCmd (Define m vs cmds) = ("define " ++ m ++ "(" ++ intercalate ", " vs ++ ") {") : map ("    " ++) (cmds >>= prettyPrintCmd) ++ [ "}" ]
+prettyPrintCmd (Call n xs) = [ "call " ++ n ++ "(" ++ intercalate ", " (map prettyPrintExpr xs) ++ ");" ]
+
+prettyPrint :: Prog -> String
+prettyPrint prog = intercalate "\n" $ (prog >>= prettyPrintCmd) ++ [ "" ]
+
+macros :: Prog -> [Macro]
+macros xs = xs >>= macrosC
+    where
+        macrosC (Define n vs cs) = n:(cs >>= macrosC)
+        macrosC _ = []
+
+sortWith :: Ord b => (a -> b) -> [a] -> [a]
+sortWith f = sortBy (\l r -> compare (f l) (f r))
+
+optE :: Expr -> Expr
+optE expr = mergeAll $ sortWith exprOrdinal $ listTerms expr
+    where
+        listTerms (Sum l r) = listTerms l ++ listTerms r
+        listTerms e = [ e ]
+        exprOrdinal (Number _) = 2
+        exprOrdinal _ = 1
+        mergeTwo (Number i1) (Number i2) = Number (i1 + i2)
+        mergeTwo l r = Sum l r
+        mergeAll [x] = x
+        mergeAll xs = foldr1 mergeTwo xs
+
+optP :: Prog -> Prog
+optP = map optC
+    where
+        optC (Move e1 e2) = Move (optE e1) (optE e2)
+        optC (Call n exs) = Call n (map optE exs)
+        optC c = c