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Questions and Answers
What is the main reduction rule of the semantic of the lambda-calculus?
What is the main reduction rule of the semantic of the lambda-calculus?
- beta-reduction (correct)
- delta-reduction
- alpha-reduction
- gamma-reduction
In Haskell, which list representation is syntactic sugar for [1,2,3]?
In Haskell, which list representation is syntactic sugar for [1,2,3]?
- [1:2:3:[]]
- [1,2,3,[]]
- [1,2:3:[]] (correct)
- [1,2,3:[]]
Which concept is not a key feature of functional programming?
Which concept is not a key feature of functional programming?
- tail recursion
- algebraic data types
- mutable variables (correct)
- side-effects in evaluation
Why is Haskell considered a pure functional programming language?
Why is Haskell considered a pure functional programming language?
Which technique is NOT used to convert a recursive function into a tail recursive one?
Which technique is NOT used to convert a recursive function into a tail recursive one?
In the Haskell function definition product [] = 1 product (x:xs) = x * product xs, what concept is illustrated?
In the Haskell function definition product [] = 1 product (x:xs) = x * product xs, what concept is illustrated?
What is the value of the expression foldr (-) 0 [1, 2, 3]?
What is the value of the expression foldr (-) 0 [1, 2, 3]?
What is the type of the polymorphic Haskell function head?
What is the type of the polymorphic Haskell function head?
What is the type of the const function?
What is the type of the const function?
What is the value of the expression flip (-) 1 2?
What is the value of the expression flip (-) 1 2?
What kind of algebraic data type is (a, b) in Haskell?
What kind of algebraic data type is (a, b) in Haskell?
What does the foldl (flip (:)) [] "drawer" expression evaluate to?
What does the foldl (flip (:)) [] "drawer" expression evaluate to?
Flashcards
Single Recursive Call
Single Recursive Call
A function call with one recursive call returns the value immediately.
Section Function
Section Function
A function that takes a value and applies it to another function, creating a new function.
Fold Expressions
Fold Expressions
A recursive process that combines elements of a list with an initial value.
Polymorphic Functions
Polymorphic Functions
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Const Function
Const Function
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++ Function
++ Function
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Flip Function
Flip Function
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Algebraic Data Types
Algebraic Data Types
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Beta-Reduction
Beta-Reduction
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List in Haskell
List in Haskell
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Tail Recursion
Tail Recursion
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Haskell
Haskell
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Study Notes
Haskell Functions
- A function with exactly one recursive call and its return value is immediately returned by the calling function.
Section Function
- The section (^2) is equivalent to \x -> 2^x.
Fold Expressions
- Evaluation of foldr (+) 0 [1, 2, 3] = 6
- Evaluation of foldr (-) 0 [1, 2, 3] = 2
- Evaluation of foldl (+) 0 [1, 2, 3] = 6
- Evaluation of foldl (-) 0 [1, 2, 3] = -6
- Evaluation of foldr (+) 5 [1, 2, 3] = 11
- Evaluation of foldl (-) 5 [1, 2, 3] = -1
Polymorphic Functions
- Type of max a b = if a > b then a else b is a -> a -> a
- Type of head (x:xs) = x is [a] -> a
- Type of length [] = 0; length (x:xs) = 1 + length xs is Num n => [a] -> n
- Type of maximum = foldl max where max a b = if a > b then a else b is (Foldable t, Ord a) => t a -> a
Const Function
- Evaluation of const (1+) 10 100 = 101
- Type of const x _ = x is a -> b -> a
- Evaluation of foldr (const (1+)) 0 [2, 31, 1] = 3
- Evaluation of foldl (const (1+)) 0 [2, 31, 1] = 2
++ Function
- Evaluation of "c" ++ "++" = "c++"
- Type of (++) is [a] -> [a] -> [a]
- foldr (++) [] flattens a list of lists
Flip Function
- Evaluation of flip (-) 1 2 = 1
- Type of flip f a b = f b a is (a -> b -> c) -> (b -> a -> c)
Algebraic Data Types
- Type (a, b) is a product
- fst and snd are projection functions
Lambda-Calculus
- The main reduction rule of the semantic of lambda-calculus is beta-reduction
List in Haskell
- A list [1,2,3] is syntactic sugar for 1 : 2 : 3 : [] which is equivalent to 1 : (2 : (3 : []))
Recursion in Functional Programming
- Tail recursion is an important concept in functional programming
- Techniques to transform a recursive function into an equivalent tail recursive function include accumulating parameters
Properties of Haskell
- Haskell is a pure functional programming language, meaning the evaluation of expressions has no side-effects
- Mutable variables are not a feature of Haskell
- Algebraic data types, particularly co-products, are used where other languages would use NULL pointers
- Pattern matching is used in the Haskell function definition product [] = 1; product (x:xs) = x * product xs
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Description
Test your knowledge on lambda calculus and functional programming concepts with this quiz. From reduction rules to recursion, see how well you understand these fundamental principles in computer science.
