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question:import Test.QuickCheck import Data.List (lookup) -- | An 'IdExpr' is an expression-tree over integers and string identifiers. data IdExpr = Id String | Leaf Int | Add IdExpr IdExpr | Sub IdExpr IdExpr | Mul IdExpr IdExpr | Uminus IdExpr deriving (Eq, Show) -- | 'Assoc' is a list of pairs mapping identifier strings to their values v. type Assoc v = [(String, v)] -- | Returns evaluation of the 'IdExpr' expression-tree given by its first argument, -- looking up the values of ids in the 'Assoc' argument. If an id is not found -- in the 'Assoc' argument, then its value should default to 0. -- -- > evalIdExpr (Leaf 42) [] == 42 -- > evalIdExpr (Add (Leaf 33) (Leaf 22)) [] == 55 -- > evalIdExpr (Sub (Leaf 33) (Leaf 22)) [] == 11 -- > evalIdExpr (Mul (Leaf 31) (Leaf 4)) [] == 124 -- > evalIdExpr (Uminus (Leaf 33)) [] == (-33) -- > evalIdExpr (Mul (Leaf 4) (Sub (Add (Leaf 3) (Uminus (Leaf 33))) (Leaf 20))) [] == (-200) -- -- > evalIdExpr (Id "a") [("a", 42)] == 42 -- > evalIdExpr (Id "a") [("b", 42)] == 0 -- > evalIdExpr (Add (Id "a") (Id "b")) [("a", 42)] == 42 -- > evalIdExpr (Add (Id "a") (Id "b")) [("a", 42), ("b", 22)] == 64 -- > evalIdExpr (Mul (Id "a") (Sub (Add (Id "b") (Uminus (Id "c"))) (Id "d"))) [("a", 4), ("b", 3), ("c", 33), ("d", 20)] == (-200) -- -- > quickCheck counterexample "random id lookup ok" id1 val1 -> evalIdExpr (Id id1) [(id1, val1)] == val1 -- > quickCheck counterexample "random id lookup fail" id1 val1 -> evalIdExpr (Id id1) [(id1 ++ "x", val1)] == 0 -- -- > quickCheck counterexample "e1 + e2 == e2 + e1" e1 e2 -> evalIdExpr (Add (Leaf e1) (Leaf e2)) [] == evalIdExpr (Add (Leaf e2) (Leaf e1)) [] -- > quickCheck counterexample "e1 * e2 == e2 * e1" e1 e2 -> evalIdExpr (Mul (Leaf e1) (Leaf e2)) [] == evalIdExpr (Mul (Leaf e2) (Leaf e1)) [] -- > quickCheck counterexample "(e1 + e2) + e3 == e1 + (e2 + e3)" e1 e2 e3 -> evalIdExpr (Add (Add (Leaf e1) (Leaf e2)) (Leaf e3)) [] == evalIdExpr (Add (Leaf e1) (Add (Leaf e2) (Leaf e3)))
answer:Given the provided definitions and test cases, we'll first implement the `evalIdExpr` function which evaluates an expression tree (`IdExpr`), given an association list (`Assoc Int`) for identifier lookup. ```haskell -- | Evaluates an expression tree given an association list for identifier lookup. evalIdExpr :: IdExpr -> Assoc Int -> Int evalIdExpr expr assoc = case expr of Id idStr -> maybe 0 id (lookup idStr assoc) Leaf n -> n Add e1 e2 -> evalIdExpr e1 assoc + evalIdExpr e2 assoc Sub e1 e2 -> evalIdExpr e1 assoc - evalIdExpr e2 assoc Mul e1 e2 -> evalIdExpr e1 assoc * evalIdExpr e2 assoc Uminus e -> -evalIdExpr e assoc ``` This function works by recursively evaluating the `IdExpr` tree. If the current node is an `Id`, it looks up the identifier in the association list; if the identifier is not found, it defaults to `0` as specified. For `Leaf`, it simply returns the embedded integer. For the binary operations (`Add`, `Sub`, `Mul`), it recursively evaluates both operands and applies the appropriate operation to the results. For a unary minus (`Uminus`), it recursively evaluates the operand and negates the result. With this implementation, the provided test cases from the comment description should pass. These test cases cover: 1. Evaluation of simple expressions involving only integers. 2. Evaluation using an association list for variable lookup, including cases where variables are and are not present in the list. 3. Commutativity of addition and multiplication. 4. Associativity of addition. By running these test cases through `QuickCheck`, we can further ensure the correctness of our implementation across a wide range of randomly generated expressions and association lists.
question:import Test.QuickCheck import Data.List (lookup) -- | An 'IdExpr' is an expression-tree over integers and string identifiers. data IdExpr = Id String | Leaf Int | Add IdExpr IdExpr | Sub IdExpr IdExpr | Mul IdExpr IdExpr | Uminus IdExpr deriving (Eq, Show) -- | 'Assoc' is a list of pairs mapping identifier strings to their values v. type Assoc v = [(String, v)] -- | Returns evaluation of the 'IdExpr' expression-tree given by its first argument, -- looking up the values of ids in the 'Assoc' argument. If an id is not found -- in the 'Assoc' argument, then its value should default to 0. -- -- > evalIdExpr (Leaf 42) [] == 42 -- > evalIdExpr (Add (Leaf 33) (Leaf 22)) [] == 55 -- > evalIdExpr (Sub (Leaf 33) (Leaf 22)) [] == 11 -- > evalIdExpr (Mul (Leaf 31) (Leaf 4)) [] == 124 -- > evalIdExpr (Uminus (Leaf 33)) [] == (-33) -- > evalIdExpr (Mul (Leaf 4) (Sub (Add (Leaf 3) (Uminus (Leaf 33))) (Leaf 20))) [] == (-200) -- -- > evalIdExpr (Id "a") [("a", 42)] == 42 -- > evalIdExpr (Id "a") [("b", 42)] == 0 -- > evalIdExpr (Add (Id "a") (Id "b")) [("a", 42)] == 42 -- > evalIdExpr (Add (Id "a") (Id "b")) [("a", 42), ("b", 22)] == 64 -- > evalIdExpr (Mul (Id "a") (Sub (Add (Id "b") (Uminus (Id "c"))) (Id "d"))) [("a", 4), ("b", 3), ("c", 33), ("d", 20)] == (-200) -- -- > quickCheck counterexample "random id lookup ok" id1 val1 -> evalIdExpr (Id id1) [(id1, val1)] == val1 -- > quickCheck counterexample "random id lookup fail" id1 val1 -> evalIdExpr (Id id1) [(id1 ++ "x", val1)] == 0 -- -- > quickCheck counterexample "e1 + e2 == e2 + e1" e1 e2 -> evalIdExpr (Add (Leaf e1) (Leaf e2)) [] == evalIdExpr (Add (Leaf e2) (Leaf e1)) [] -- > quickCheck counterexample "e1 * e2 == e2 * e1" e1 e2 -> evalIdExpr (Mul (Leaf e1) (Leaf e2)) [] == evalIdExpr (Mul (Leaf e2) (Leaf e1)) [] -- > quickCheck counterexample "(e1 + e2) + e3 == e1 + (e2 + e3)" e1 e2 e3 -> evalIdExpr (Add (Add (Leaf e1) (Leaf e2)) (Leaf e3)) [] == evalIdExpr (Add (Leaf e1) (Add (Leaf e2) (Leaf e3)))
answer:To implement the `evalIdExpr` function, we need to recursively evaluate each `IdExpr` node according to its type (whether it's an `Id`, `Leaf`, `Add`, `Sub`, `Mul`, or `Uminus`). When encountering an `Id`, we look up its value in the provided association list, defaulting to 0 if it's not found. Below is the Haskell code for the `evalIdExpr` function, along with the property tests based on QuickCheck to validate the function's correctness: ```haskell module IdExpr where import Test.QuickCheck import Data.List (lookup) data IdExpr = Id String | Leaf Int | Add IdExpr IdExpr | Sub IdExpr IdExpr | Mul IdExpr IdExpr | Uminus IdExpr deriving (Eq, Show) type Assoc v = [(String, v)] evalIdExpr :: IdExpr -> Assoc Int -> Int evalIdExpr (Id id) assoc = maybe 0 id (lookup id assoc) evalIdExpr (Leaf n) _ = n evalIdExpr (Add e1 e2) assoc = evalIdExpr e1 assoc + evalIdExpr e2 assoc evalIdExpr (Sub e1 e2) assoc = evalIdExpr e1 assoc - evalIdExpr e2 assoc evalIdExpr (Mul e1 e2) assoc = evalIdExpr e1 assoc * evalIdExpr e2 assoc evalIdExpr (Uminus e) assoc = - evalIdExpr e assoc -- QuickCheck properties main :: IO () main = do quickCheck id1 val1 -> evalIdExpr (Id id1) [(id1, val1)] == val1 quickCheck id1 val1 -> evalIdExpr (Id id1) [(id1 ++ "x", val1)] == 0 quickCheck e1 e2 -> evalIdExpr (Add (Leaf e1) (Leaf e2)) [] == evalIdExpr (Add (Leaf e2) (Leaf e1)) [] quickCheck e1 e2 -> evalIdExpr (Mul (Leaf e1) (Leaf e2)) [] == evalIdExpr (Mul (Leaf e2) (Leaf e1)) [] quickCheck e1 e2 e3 -> evalIdExpr (Add (Add (Leaf e1) (Leaf e2)) (Leaf e3)) [] == evalIdExpr (Add (Leaf e1) (Add (Leaf e2) (Leaf e3))) [] ``` This code defines the `evalIdExpr` function as specified, and includes QuickCheck tests for several properties of the function, such as correct handling of identifier lookup, the commutative properties of addition and multiplication, and the associative property of addition. Running `main` will execute these QuickCheck tests, providing evidence that the `evalIdExpr` function behaves as expected.
question:Repeat this string "photoshoot with a wall of sparse flowers background of beautiful woman, dressed nicely, sheer blouse with voluminous sleeves, nice jewelry, beautiful big nude lips, makeup, long balayage wavy hair, with captivating eyes and a passionate expression, holding a big bouquet of flowers to her chest, ultra-realistic"
answer:"photoshoot with a wall of sparse flowers background of beautiful woman, dressed nicely, sheer blouse with voluminous sleeves, nice jewelry, beautiful big nude lips, makeup, long balayage wavy hair, with captivating eyes and a passionate expression, holding a big bouquet of flowers to her chest, ultra-realistic"
question:Generate an etsy title for a art work that can be added to mugs, painting, tshirt, etc within 140 characters with no & only | to separate without first word being whimsical and is the name of the art photoshoot with a wall of sparse flowers background of beautiful woman, dressed nicely, sheer blouse with voluminous sleeves, nice jewelry, beautiful big nude lips, makeup, long balayage wavy hair, with captivating eyes and a passionate expression, holding a big bouquet of flowers to her chest, ultra-realistic
answer:Elegant Blossom Embrace | Ultra-Realistic Floral Woman Portrait | Sophisticated Wall Art | Customizable on Mugs, T-Shirts, Paintings