This module defines data structures to represent the syntax of the "Lu" programming language. You should read this file carefully to understand the Lu language, but you do not need to edit this file. For more details, you may also wish to refer to the Lu Manual.

This module contains:

The definitions of the datatypes that represent the syntax of Lu
Sample programs written in Lu
A pretty-printer that displays these datatypes as concise text
Arbitrary instances for these datatypes that can be used for property based testing

> {-# LANGUAGE FlexibleInstances #-}
> {-# LANGUAGE TypeSynonymInstances #-}

> module LuSyntax where

> import Data.Map (Map)
> import qualified Data.Map as Map
> import Text.PrettyPrint hiding (parens,braces,sep,(<>))
> import qualified Text.PrettyPrint as PP
> import Test.QuickCheck(Arbitrary(..),Gen)
> import qualified Test.QuickCheck as QC
> import Control.Monad(mapM_)
> import qualified Data.Char as Char

What is a Lu Program?

The general idea is that Lu is a very, very cut down version of the Lua scripting language.

Programs are sequences of statements in a block:

> newtype Block = Block [ Statement ]                 -- s1 ... sn 
>   deriving (Eq, Show)

For convenience, we create these instances to join blocks together:

> instance Semigroup Block where
>    Block s1 <> Block s2 = Block (s1 <> s2)
> instance Monoid Block where
>    mempty = Block []

Statements themselves have the following forms:

> data Statement =
>     Assign Var Expression             -- x = e
>   | If Expression Block Block         -- if e then s1 else s2 end
>   | While Expression Block            -- while e do s end
>   | Empty                             -- ';'
>   | Repeat Block Expression           -- repeat s until e
>   deriving (Eq, Show)

Expressions are variables, literal constants, operators applied to sub-expressions, or table constructions:

> data Expression =
>     Var Var                            -- global variables x and table indexing
>   | Val Value                          -- literal values
>   | Op1 Uop Expression                 -- unary operators
>   | Op2 Expression Bop Expression      -- binary operators
>   | TableConst [TableField]            -- table construction, { x = 3 , y = 5 }
>   deriving (Eq, Show)

The literal values include nil, ints, booleans, strings and a special value for tables that should not appear directly in source programs, but is used by the interpreter.

> data Value =
>     NilVal             -- nil
>   | IntVal Int         -- 1
>   | BoolVal Bool       -- false, true
>   | StringVal String   -- "abd"
>   | TableVal Name      -- <not used in source programs>
>   deriving (Eq, Show, Ord)

Unary operators are single argument functions: arithmetic negation, logical not, and an overloaded length/size operation.

> data Uop =
>     Neg   -- `-` :: Int -> Int
>   | Not   -- not` :: a -> Bool
>   | Len   -- `#` :: String -> Int / Table -> Int
>   deriving (Eq, Show, Enum, Bounded)

Binary operators are two-argument functions: arithmetic operators that work with int values only, overloaded equality and ordering operations that work for anything, and string concatenation.

> data Bop =
>     Plus     -- `+`  :: Int -> Int -> Int
>   | Minus    -- `-`  :: Int -> Int -> Int
>   | Times    -- `*`  :: Int -> Int -> Int
>   | Divide   -- `//` :: Int -> Int -> Int   -- floor division
>   | Modulo   -- `%`  :: Int -> Int -> Int   -- modulo
>   | Eq       -- `==` :: a -> a -> Bool
>   | Gt       -- `>`  :: a -> a -> Bool
>   | Ge       -- `>=` :: a -> a -> Bool
>   | Lt       -- `<`  :: a -> a -> Bool
>   | Le       -- `<=` :: a -> a -> Bool
>   | Concat   -- `..` :: String -> String -> String 
>   deriving (Eq, Show, Enum, Bounded)

Variables and Tables

Variables are places that store values. There are two kinds of variables in Lu: globals and table fields.

Tables are a primitive part of the language. They are heterogeneous finite maps from values to values; i.e. a data structure that can be accessed by looking up the value associated with a key, in a variable expression

t[1]    -- any value except nil can be used as a key
t[true]
t["x"]

or modified by introducing a new value associated with a key, using an assignment statement:

t[1] = 3      -- any value except nil can be stored in a table
t[true] = t
t["y"] = true
t[0] = nil    -- assigning a field to nil removes the association from the table

In the case that the key is a string, Lu supports syntactic sugar for table projection and assignment, allowing users to write t.x instead of t["x"] and t.y = true instead of t["y"] = true.

We represent these globals and table fields, using the following datatype definitions.

> type Name = String            -- either the name of a variable or the name of a field

> data Var =
>     Name Name                  -- x, global variable
>   | Dot Expression Name        -- t.x, access table using string key   
>   | Proj Expression Expression -- t[1], access table table using any type of key
>   deriving (Eq, Show)

> data TableField =
>     FieldName Name Expression      -- x = 3, 
>   | FieldKey Expression Expression -- ["x"] = true , [1] = 4 , [true] = "a"
>   deriving (Eq, Show)

Test Programs

Below are some test programs that you can use in this assignment. These programs can also be found in the corresponding files. Please take a look at these files to familiarize yourself with the syntax of Lu.

> var :: String -> Expression
> var = Var . Name

> -- test.lu
> wTest :: Block
> wTest = Block [
>     Assign (Name "x") (Op2 (Op2 (Op2 (Val (IntVal 1)) Plus (Val (IntVal 2)))
>                        Minus
>                        (Val (IntVal 3)))
>                    Plus
>                    (Op2 (Val (IntVal 1)) Plus (Val (IntVal 3)))),
>     Assign (Name "y") (Val (IntVal 0)),
>     While (Op2 (var "x") Gt (Val (IntVal 0))) (Block [
>         Assign (Name "y") (Op2 (var "y") Plus (var "x")),
>         Assign (Name "x") (Op2 (var "x") Minus (Val (IntVal 1)))
>     ])]

> 
> -- fact.lu
> wFact :: Block
> wFact = Block [
>     Assign (Name "n") (Val (IntVal 5)),
>     Assign (Name "f") (Val (IntVal 1)),
>     While (Op2 (var "n") Gt (Val (IntVal 0))) (Block [
>         Assign (Name "x") (Var (Name "n")),
>         Assign (Name "z") (Var (Name "f")),
>         While (Op2 (var "x") Gt (Val (IntVal 1))) (Block [
>             Assign (Name "f") (Op2 (var "z") Plus (Var (Name "f"))),
>             Assign (Name "x") (Op2 (var "x") Minus (Val (IntVal 1)))
>         ]),
>         Assign (Name "n") (Op2 (Var (Name "n")) Minus (Val (IntVal 1)))
>     ]) ]

> -- abs.lu
> wAbs :: Block
> wAbs = Block [
>     Assign (Name "x") (Op2 (Val (IntVal 0)) Minus (Val (IntVal 3))),
>     If (Op2 (Var (Name "x")) Lt (Val (IntVal 0)))
>         (Block [Assign (Name "x") (Op2 (Val (IntVal 0)) Minus (Var (Name "x")))])
>         (Block [])]

> -- times.lu
> wTimes :: Block
> wTimes = Block [
>     Assign (Name "x") (Val (IntVal 10)),
>     Assign (Name "y") (Val (IntVal 3)),
>     Assign (Name "z") (Val (IntVal 0)),
>     While (Op2 (Var (Name "x")) Gt (Val (IntVal 0))) (Block [
>         Assign (Name "z") (Op2 (Var (Name "z")) Plus (Var (Name "y"))),
>         Assign (Name "x") (Op2 (Var (Name "x")) Minus (Val (IntVal 1)))
>     ])]

> -- table.lu
> wTable :: Block
> wTable = Block [Assign (Name "a") (TableConst []),Assign (Name "k") (Val (StringVal "x")),Assign (Proj (Var (Name "a")) (Var (Name "k"))) (Val (IntVal 10)),Assign (Proj (Var (Name "a")) (Val (IntVal 20))) (Val (StringVal "great")),Assign (Name "o1") (Var (Proj (Var (Name "a")) (Val (StringVal "x")))),Assign (Name "k") (Val (IntVal 20)),Assign (Name "o2") (Var (Proj (Var (Name "a")) (Var (Name "k")))),Assign (Proj (Var (Name "a")) (Val (StringVal "x"))) (Op2 (Var (Proj (Var (Name "a")) (Val (StringVal "x")))) Plus (Val (IntVal 1))),Assign (Name "o3") (Var (Proj (Var (Name "a")) (Val (StringVal "x"))))]

> -- bfs.lu
> wBfs :: Block
> wBfs = Block [Assign (Name "start") (Val (IntVal 1)),Assign (Name "goal") (Val (IntVal 10)),Empty,Assign (Name "graph") (TableConst []),Assign (Proj (Var (Name "graph")) (Val (IntVal 1))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 2)),FieldKey (Val (IntVal 2)) (Val (IntVal 3))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 2))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 6)),FieldKey (Val (IntVal 2)) (Val (IntVal 5)),FieldKey (Val (IntVal 3)) (Val (IntVal 1))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 3))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 1))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 4))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 7)),FieldKey (Val (IntVal 2)) (Val (IntVal 8))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 5))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 9)),FieldKey (Val (IntVal 2)) (Val (IntVal 10)),FieldKey (Val (IntVal 3)) (Val (IntVal 2))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 6))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 2))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 7))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 4)),FieldKey (Val (IntVal 2)) (Val (IntVal 11)),FieldKey (Val (IntVal 3)) (Val (IntVal 12))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 8))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 4))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 9))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 5))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 10))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 5))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 11))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 7))]),Assign (Proj (Var (Name "graph")) (Val (IntVal 12))) (TableConst [FieldKey (Val (IntVal 1)) (Val (IntVal 7))]),Empty,Assign (Name "q") (TableConst [FieldName "elements" (TableConst []),FieldName "first" (Val (IntVal 0)),FieldName "last" (Val (IntVal 0))]),Assign (Proj (Var (Dot (Var (Name "q")) "elements")) (Var (Dot (Var (Name "q")) "last"))) (Var (Name "start")),Assign (Dot (Var (Name "q")) "last") (Op2 (Var (Dot (Var (Name "q")) "last")) Plus (Val (IntVal 1))),Empty,Assign (Name "visited") (TableConst []),Assign (Proj (Var (Name "visited")) (Var (Name "start"))) (Val (BoolVal True)),Assign (Name "found") (Val (BoolVal False)),Empty,Repeat (Block [Assign (Name "node") (Var (Proj (Var (Dot (Var (Name "q")) "elements")) (Var (Dot (Var (Name "q")) "first")))),Assign (Proj (Var (Dot (Var (Name "q")) "elements")) (Var (Dot (Var (Name "q")) "first"))) (Val NilVal),Assign (Dot (Var (Name "q")) "first") (Op2 (Var (Dot (Var (Name "q")) "first")) Plus (Val (IntVal 1))),Empty,Assign (Proj (Var (Name "visited")) (Var (Name "node"))) (Val (BoolVal True)),If (Op2 (Var (Name "goal")) Eq (Var (Name "node"))) (Block [Assign (Name "found") (Val (BoolVal True)),Assign (Dot (Var (Name "q")) "first") (Var (Dot (Var (Name "q")) "last"))]) (Block [Assign (Name "i") (Val (IntVal 1)),While (Op2 (Var (Name "i")) Le (Op1 Len (Var (Proj (Var (Name "graph")) (Var (Name "node")))))) (Block [Assign (Name "next") (Var (Proj (Var (Proj (Var (Name "graph")) (Var (Name "node")))) (Var (Name "i")))),If (Op1 Not (Var (Proj (Var (Name "visited")) (Var (Name "next"))))) (Block [Assign (Proj (Var (Dot (Var (Name "q")) "elements")) (Var (Dot (Var (Name "q")) "last"))) (Var (Name "next")),Assign (Dot (Var (Name "q")) "last") (Op2 (Var (Dot (Var (Name "q")) "last")) Plus (Val (IntVal 1)))]) (Block [Empty]),Assign (Name "i") (Op2 (Var (Name "i")) Plus (Val (IntVal 1)))])])]) (Op2 (Op2 (Var (Dot (Var (Name "q")) "last")) Minus (Var (Dot (Var (Name "q")) "first"))) Eq (Val (IntVal 0)))]

A Pretty Printer for Lu

The derived Show instances for the datatypes above are pretty hard to read, especially when programs get long. Really, who wants to read this...

> -- >>> wTest

Block [Assign (Name "x") (Op2 (Op2 (Op2 (Val (IntVal 1)) Plus (Val (IntVal 2))) Minus (Val (IntVal 3))) Plus (Op2 (Val (IntVal 1)) Plus (Val (IntVal 3)))),Assign (Name "y") (Val (IntVal 0)),While (Op2 (Var (Name "x")) Gt (Val (IntVal 0))) (Block [Assign (Name "y") (Op2 (Var (Name "y")) Plus (Var (Name "x"))),Assign (Name "x") (Op2 (Var (Name "x")) Minus (Val (IntVal 1)))])]

instead of this...

> -- >>> pretty wTest

x = 1 + 2 - 3 + (1 + 3)
y = 0
while x > 0 do
  y = y + x
  x = x - 1
end

A pretty printer is a function that formats an abstract syntax tree into a readable representation of the concrete syntax.

The pretty library, imported above as PP, provides the following to assist in the development of pretty printers:

An abstract type Doc of "pretty documents" that know how to lay themselves out prettily. We can use this type to define a class of of types that support pretty printing---those that define a function mapping any value of that type to a suitable Doc.

> class PP a where
>   pp :: a -> Doc

Operations for rendering, or converting a Doc to text at the top level. The rendering functions are parameterized over display options, such as the maximum line length, so that they can figure out how to best display the text.

> -- | Default operation for the pretty printer. Displays using standard formatting
> -- rules, with generous use of indentation and newlines.
> pretty :: PP a => a -> String
> pretty = PP.render . pp

> -- | Compact version. Displays its argument without newlines.
> oneLine :: PP a => a -> String
> oneLine = PP.renderStyle (PP.style {PP.mode=PP.OneLineMode}) . pp

Primitive documents and operations for constructing Docs from primitive types, such as characters and string.

For example, we can use the text function to define the Uop instance of the PP class. This instance converts each unary operator into a document.

> instance PP Uop where
>   pp Neg = PP.char '-'
>   pp Not = PP.text "not"
>   pp Len = PP.char '#'

Combinators for combining Docs in various ways, providing constraints on the textual layout. For example, some are listed below. (See the library documentation for many more.)

 -- An empty document, with no width and no height.
 empty :: Doc

 -- Beside. Combines two documents horizontally with no space between.
 (<>) :: Doc -> Doc -> Doc

 -- Beside, separated by space, unless one of the arguments is `empty`.
 (<+>) :: Doc -> Doc -> Doc

 -- Nest (or indent) a document by a given number of positions
 -- (which may also be negative).
 nest :: Int -> Doc -> Doc

 -- Above. Combines two documents vertically (with overlap if
 -- possible: if the last line of the first argument stops at
 -- least one position before the first line of the second begins,
 -- these two lines are overlapped).
 ($$) :: Doc -> Doc -> Doc

 -- List version of $$.
 vcat :: [Doc] -> Doc

 -- wrap document in (..)
 parens :: Doc -> Doc

Pretty-Pretter implementation

> instance PP Bool where
>   pp True = PP.text "true"
>   pp False = PP.text "false"

> instance PP String where
>   pp = PP.text

> instance PP Int where
>   pp = PP.int

> instance PP Var where
>   pp (Name n) = PP.text n
>   pp (Dot (Var v) k) = pp v <> PP.text "." <> pp k
>   pp (Dot t k) = PP.parens (pp t) <> PP.text "." <> pp k
>   pp (Proj (Var v) k) = pp v <> brackets (pp k)
>   pp (Proj t k) = PP.parens (pp t) <> brackets (pp k)

> instance PP Value where
>   pp (IntVal i)  = pp i
>   pp (BoolVal b) = pp b
>   pp NilVal = PP.text "nil"
>   pp (StringVal s) = PP.text ("\"" <> s <> "\"")
>   pp (TableVal t)  = PP.text "<" <> PP.text t <> PP.text ">"

> isBase :: Expression -> Bool
> isBase TableConst{} = True
> isBase Val{} = True
> isBase Var{} = True
> isBase Op1{} = True
> isBase _ = False

> instance PP Bop where
>   pp Plus   = PP.char '+'
>   pp Minus  = PP.char '-'
>   pp Times  = PP.char '*'
>   pp Divide = PP.text "//"
>   pp Modulo = PP.text "%"
>   pp Gt     = PP.char '>'
>   pp Ge     = PP.text ">="
>   pp Lt     = PP.char '<'
>   pp Le     = PP.text "<="
>   pp Eq     = PP.text "=="
>   pp Concat = PP.text ".."

> instance PP Expression where
>   pp (Var v) = pp v
>   pp (Val v) = pp v
>   pp (Op1 o v) = pp o <+> if isBase v then pp v else PP.parens (pp v)
>   pp e@Op2{} = ppPrec 0 e  where
>      ppPrec n (Op2 e1 bop e2) =
>         ppParens (level bop < n) $
>            ppPrec (level bop) e1 <+> pp bop <+> ppPrec (level bop + 1) e2
>      ppPrec _ e' = pp e'
>      ppParens b = if b then PP.parens else id
>   pp (TableConst fs) = PP.braces (PP.sep (PP.punctuate PP.comma (map pp fs)))

> instance PP TableField where
>    pp (FieldName name e) = pp name <+> equals <+> pp e
>    pp (FieldKey e1 e2) = PP.brackets (pp e1) <+> PP.equals <+> pp e2

> instance PP Block where
>   pp (Block [s])  = pp s
>   pp (Block ss)   = PP.vcat (map pp ss)

> ppSS :: [Statement] -> Doc
> ppSS ss  = PP.vcat (map pp ss)

> instance PP Statement where
>   pp (Assign x e) = pp x <+> PP.equals <+> pp e 
>   pp (If guard b1 b2)
>     = PP.hang (PP.text "if" <+> pp guard <+> PP.text "then") 2 (pp b1)
>       PP.$$ PP.nest 2 (PP.text "else" PP.$$ pp b2 )
>       PP.$$ PP.text "end"
>   pp (While guard e)
>     = PP.hang (PP.text "while" <+> pp guard <+> PP.text "do") 2 (pp e)
>                 PP.$+$ PP.text "end"
>   pp Empty = PP.semi
>   pp (Repeat b e)
>     = PP.hang (PP.text "repeat") 2 (pp b)
>               PP.$+$ PP.text "until" <+> pp e

> level :: Bop -> Int
> level Times  = 7
> level Divide = 7
> level Plus   = 5
> level Minus  = 5
> level Concat = 4
> level _      = 3    -- comparison operators

> instance PP a => PP (Map Value a) where
>   pp m = PP.braces (PP.vcat (map ppa (Map.toList m))) where
>     ppa (StringVal s, v2) = PP.text s <+> PP.text "=" <+> pp v2
>     ppa (v1 , v2) = PP.brackets (pp v1) <+> PP.text "=" <+> pp v2

> instance PP a => PP (Map Name a) where
>   pp m = PP.braces (PP.vcat (map ppa (Map.toList m))) where
>     ppa (s, v2) = PP.text s <+> PP.text "=" <+> pp v2

Arbitrary Lu

As usual with QuickCheck, we need an Arbitrary instance for Lu programs. We've provided these instances for you If you'd like to see what sorts of expressions and programs are being generated, you can try running the following commands in the terminal.

> sampleVar :: IO ()
> sampleVar = QC.sample' (arbitrary :: Gen Var) >>= mapM_ (print . pp)

> sampleExp :: IO ()
> sampleExp = QC.sample' (arbitrary :: Gen Expression) >>= mapM_ (print . pp)

> sampleStat :: IO ()
> sampleStat = QC.sample' (arbitrary :: Gen Statement) >>= mapM_ (print . pp)

To test with a lot of tests while still making sure that our Lu programs don't get too big, we can limit the size used by quickcheck.

> quickCheckN :: QC.Testable prop => Int -> prop -> IO ()
> quickCheckN n = QC.quickCheckWith $ QC.stdArgs { QC.maxSuccess = n , QC.maxSize = 100 }

Generators

> -- | Generate a small set of names for generated tests. These names are guaranteed to not include
> -- reserved words
> genName :: Gen Name
> genName = QC.elements [ "_", "_G", "x", "X", "y", "x0",  "X0", "xy", "XY", "_x" ]

> -- | Generate a string literal, being careful about the characters that it may contain 
> genStringLit :: Gen String
> genStringLit = escape <$> QC.listOf (QC.elements stringLitChars) where
>     -- escape special characters appearing in the string,
>     escape :: String -> String
>     escape = foldr Char.showLitChar "" 
>     -- generate strings containing printable characters or spaces, but not including '\"'
>     stringLitChars :: [Char]
>     stringLitChars = filter (\c -> c /= '\"' && (Char.isSpace c || Char.isPrint c)) ['\NUL' .. '~']

> -- | Generate a size-controlled global variable or table field
> genVar :: Int -> Gen Var
> genVar 0 = Name <$> genName
> genVar n = QC.frequency [(1, Name <$> genName)
>                         ,(n, Dot <$> genExp n' <*> genName)
>                         ,(n, Proj <$> genExp n' <*> genExp n')]
>    where n' = n `div` 2

> -- | Generate a size-controlled expression
> genExp :: Int -> Gen Expression
> genExp 0 = QC.oneof [ Var <$> genVar 0, Val <$> arbitrary ]
> genExp n = QC.frequency [ (1, Var <$> genVar n)
>                      , (1, Val <$> arbitrary)
>                      , (n, Op1  <$> arbitrary <*> genExp n') 
>                      , (n, Op2  <$> genExp n' <*> arbitrary <*> genExp n') 
>                      , (n', TableConst <$> genTableFields n') ]
>     where n' = n `div` 2

> -- | Generate a list of fields in a table constructor epression. 
> -- We limit the size of the table to avoid size blow up. 
> genTableFields :: Int -> Gen [TableField]
> genTableFields n = do
>    len <- QC.elements [0 .. 3]
>    take len <$> QC.infiniteListOf (genTableField n)

> genTableField :: Int -> Gen TableField
> genTableField n = QC.oneof [FieldName <$> genName <*> genExp n',
>                             FieldKey <$> genExp n' <*> genExp n' ]
>     where n' = n `div` 2

> -- | Generate a size-controlled statement
> genStatement :: Int -> Gen Statement
> genStatement n | n <= 1 = QC.oneof [Assign <$> genVar 0 <*> genExp 0, return Empty]
> genStatement n = QC.frequency [ (1, Assign <$> genVar n' <*> genExp n')
>                               , (1, return Empty)
>                               , (n, If <$> genExp n' <*> genBlock n' <*> genBlock n')
>                               -- generate loops half as frequently as if statements
>                               , (n', While <$> genExp n' <*> genBlock n')
>                               , (n', Repeat <$> genBlock n' <*> genExp n')
>                               
>                            ]
>     where n' = n `div` 2

> genBlock :: Int -> Gen Block
> genBlock n = Block <$> genStmts n where
>     genStmts 0 = pure []
>     genStmts n = QC.frequency [ (1, return []),
>                                 (n, (:) <$> genStatement n' <*> genStmts n')]
>            where n' = n `div` 2

Instances

> instance Arbitrary Var where
>   arbitrary = QC.sized genVar
>   shrink (Name n)  = []
>   shrink (Dot e n) = [Dot e' n | e' <- shrink e]
>   shrink (Proj e1 e2) = [Proj e1' e2 | e1' <- shrink e1] ++
>                         [Proj e1 e2' | e2' <- shrink e2]

> instance Arbitrary Statement where
>   arbitrary = QC.sized genStatement
>   shrink (Assign v e) = [ Assign v' e | v'  <- shrink v ] ++
>                         [ Assign v e' | e'  <- shrink e ]
>   shrink (If e b1 b2) = first b1 ++ first b2 ++
>                         [ If e' b1 b2 | e'  <- shrink e ] ++
>                         [ If e b1' b2 | b1' <- shrink b1 ] ++
>                         [ If e b1 b2' | b2' <- shrink b2 ]
>   shrink (While e b) = first b ++
>                         [ While e' b   | e'  <- shrink e ] ++
>                         [ While e b'   | b'  <- shrink b ]
>   shrink Empty = []
>   shrink (Repeat b e) = first b ++
>                       [ Repeat b' e | b' <- shrink b] ++
>                       [ Repeat b e' | e' <- shrink e]

> -- | access the first statement in a block, if one exists
> first :: Block -> [Statement]
> first (Block []) = []
> first (Block (x:_)) = [x]

> -- | access expressions in a table field
> getExp :: TableField -> [Expression]
> getExp (FieldName _ e) = [e]
> getExp (FieldKey e1 e2) = [e1, e2]

> instance Arbitrary TableField where
>   arbitrary = QC.sized genTableField
>   shrink (FieldName n e1) = [FieldName n e1' | e1' <- shrink e1] 
>   shrink (FieldKey e1 e2) = [FieldKey e1' e2 | e1' <- shrink e1] ++
>                             [FieldKey e1 e2' | e2' <- shrink e2]

> instance Arbitrary Block where
>   arbitrary = QC.sized genBlock
>   shrink (Block ss) = [ Block ss' | ss' <- shrink ss ]

> instance Arbitrary Expression where
>   arbitrary = QC.sized genExp

>   shrink (Val v)          = Val <$> shrink v
>   shrink (Var v)          = Var <$> shrink v
>   shrink (Op1 o e)        = e : [Op1 o e' | e' <- shrink e]
>   shrink (Op2 e1 o e2)    =
>     [ Op2 e1' o e2 | e1' <- shrink e1 ] ++
>     [ Op2 e1 o e2' | e2' <- shrink e2 ] ++
>     [ e1, e2 ]
>   shrink (TableConst fs) = concatMap getExp fs ++ (TableConst <$> shrink fs)

> instance Arbitrary Uop where
>   arbitrary = QC.arbitraryBoundedEnum

> instance Arbitrary Bop where
>   arbitrary = QC.arbitraryBoundedEnum

> shrinkStringLit :: String -> [String]
> shrinkStringLit s = filter (/= '\"') <$> shrink s

> instance Arbitrary Value where
>   arbitrary = QC.oneof [ IntVal <$> arbitrary
>                        , BoolVal <$> arbitrary
>                        , pure NilVal
>                        , StringVal <$> genStringLit
>                        -- note: do not generate table values
>                        ]

>   shrink (IntVal n) = IntVal <$> shrink n
>   shrink (BoolVal b) = BoolVal <$> shrink b
>   shrink NilVal = []
>   shrink (StringVal s) = StringVal <$> shrinkStringLit s
>   shrink (TableVal _) = []

CIS 552: Advanced Programming

Fall 2021