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Manuel M T Chakravarty (Applicative & Tweag I/O) Gabriele Keller (UNSW Sydney) Demystifying Functional Programming And what that means for learning & teaching mchakravarty TacticalGrace justtesting.org haskellformac.com

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Structured Programming (1960s)

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Object-Oriented Programming (70s/80s)

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Functional Programming

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Functional Programming Too academic Impractical Too complicated Inefficient Not for the average developer

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Diffusion of Innovation [Everett Rogers 1962]

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How do we get them on board?

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There is still time to submit proposals (deadline 18 March)!

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There is still time to submit proposals (deadline 18 March)!

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“How do we teach FP to the early majority as opposed to early adopters (and innovators).”

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http://learninghaskell.com

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Advise to The Innovator

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“Liberation from the tyranny of syntax: focus on concepts instead of language constructs.”

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“Liberation from the tyranny of syntax: focus on concepts instead of language constructs.” —Felleisen et al, The Structure and Interpretation of the Computer Science Curriculum

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Beware of Historical Explanations

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Beware of Historical Explanations Category Theory

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Beware of Historical Explanations Category Theory Formal Semantics

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Beware of Historical Explanations Category Theory Formal Semantics Functional Programming

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Beware of Historical Explanations “A monad is a monoid in the category of endofunctors.” Category Theory Formal Semantics Functional Programming

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Beware of Historical Explanations “A monad is a monoid in the category of endofunctors.” Category Theory Formal Semantics Functional Programming We need explanations that can stand on their own

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Mindset of The Early Adopter

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Examples First

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Examples First Why?

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Examples First Why? Example #1 Example #2 Example #n ộ

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Examples First Why? Example #1 Example #2 Example #n ộ Problem statement

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Examples First Why? Example #1 Example #2 Example #n ộ Problem statement Example solution ộ

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Examples First Why? Example #1 Example #2 Example #n ộ Problem statement General concept Example solution ộ

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Math Later

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Math Later “If math is useful to a functional programmer, functional programming must be able to motivate math.”

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Math Later “If math is useful to a functional programmer, functional programming must be able to motivate math.”

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But the Jargon is Here to Stay

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But the Jargon is Here to Stay Burrito Warm fuzzy thing Workflow Computation builder Kleisli triple

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But the Jargon is Here to Stay Burrito Warm fuzzy thing Workflow Computation builder Kleisli triple Monad

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Teaching The Early Majority

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Examples first Generalise & abstract only after demonstrating a need

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Examples first Generalise & abstract only after demonstrating a need

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The Trouble with Recursion

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The Trouble with Recursion fix :: (a -> a) -> a fix f = let x = f x in x Simple. Elegant. Powerful.

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The Trouble with Recursion fix :: (a -> a) -> a fix f = let x = f x in x Simple. Elegant. Powerful. And utterly confusing…

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How does it work? How can I use it to solve a given problem?

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 natSum 3 = 3 + 2 + 1 + 0 natSum 4 = 4 + 3 + 2 + 1 + 0 natSum 5 = 5 + 4 + 3 + 2 + 1 + 0 ⋮

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 natSum 3 = 3 + 2 + 1 + 0 natSum 4 = 4 + 3 + 2 + 1 + 0 natSum 5 = 5 + 4 + 3 + 2 + 1 + 0 ⋮ we can reuse natSum 4

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum 1 = 1 + natSum 0 natSum 2 = 2 + natSum 1 natSum 3 = 3 + natSum 2 natSum 4 = 4 + natSum 3 natSum 5 = 5 + natSum 4 ⋮

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum 1 = 1 + natSum 0 natSum 2 = 2 + natSum 1 natSum 3 = 3 + natSum 2 natSum 4 = 4 + natSum 3 natSum 5 = 5 + natSum 4 ⋮ from here on all the same with different numbers

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum n = n + natSum (n - 1)

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First Recursion Example natSum n 㱺 n + (n-1) + ⋯ + 2 + 1 + 0 natSum 0 = 0 natSum n = n + natSum (n - 1) use variable instead of unbound sequence

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natSum 0 = 0 natSum n = n + natSum (n - 1)

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))        㱺 5 + (4 + (3 + (2 + (1 + natSum (1 - 1)))))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))        㱺 5 + (4 + (3 + (2 + (1 + natSum (1 - 1)))))        㱺 5 + (4 + (3 + (2 + (1 + natSum 0))))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))        㱺 5 + (4 + (3 + (2 + (1 + natSum (1 - 1)))))        㱺 5 + (4 + (3 + (2 + (1 + natSum 0))))        㱺 5 + (4 + (3 + (2 + (1 + 0))))

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natSum 0 = 0 natSum n = n + natSum (n - 1) natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))        㱺 5 + (4 + (3 + (2 + (1 + natSum (1 - 1)))))        㱺 5 + (4 + (3 + (2 + (1 + natSum 0))))        㱺 5 + (4 + (3 + (2 + (1 + 0))))        㱺 15 natSum 5  㱺 5 + natSum (5 - 1)        㱺 5 + natSum 4        㱺 5 + (4 + natSum (4 - 1))        㱺 5 + (4 + natSum 3)        㱺 5 + (4 + (3 + natSum (3 - 1)))        㱺 5 + (4 + (3 + natSum 2))        㱺 5 + (4 + (3 + (2 + natSum (2 - 1))))        㱺 5 + (4 + (3 + (2 + natSum 1)))        㱺 5 + (4 + (3 + (2 + (1 + natSum (1 - 1)))))        㱺 5 + (4 + (3 + (2 + (1 + natSum 0))))        㱺 5 + (4 + (3 + (2 + (1 + 0))))        㱺 15

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Example-Driven Development Illustrates the concept (here recursion)

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code)

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion Higher-order functions

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion Higher-order functions Parametric polymorphism

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion Higher-order functions Parametric polymorphism Type classes

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion Higher-order functions Parametric polymorphism Type classes Categorial structures

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Example-Driven Development Illustrates the concept (here recursion) Provides a concrete problem solving strategy (to get students started on their own code) Recursion Higher-order functions Parametric polymorphism Type classes Categorial structures and more

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Teach design patterns FP abstractions are used in various idiomatic ways

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allSquares :: Num a => [a] -> [a] allSquares [] = [] allSquares (x : xs) = x * x : allSquares xs

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allSquares :: Num a => [a] -> [a] allSquares [] = [] allSquares (x : xs) = x * x : allSquares xs allToUpper :: String -> String allToUpper [] = [] allToUpper (chr : restString) = toUpper chr : allToUpper restString

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allSquares :: Num a => [a] -> [a] allSquares [] = [] allSquares (x : xs) = x * x : allSquares xs allToUpper :: String -> String allToUpper [] = [] allToUpper (chr : restString) = toUpper chr : allToUpper restString

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allSquares :: Num a => [a] -> [a] allSquares [] = [] allSquares (x : xs) = x * x : allSquares xs allToUpper :: String -> String allToUpper [] = [] allToUpper (chr : restString) = toUpper chr : allToUpper restString recursiveFunction [] = [] recursiveFunction (x : xs) = doSomethingWith x : recursiveFunction xs

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Computational Design Patterns Illustrates a computational idiom (here map-like recursion)

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Computational Design Patterns Illustrates a computational idiom (here map-like recursion) Provides learners with concrete guidance on how to get started

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Tight feedback loop Examples, stepwise evaluation, playgrounds

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Examples first Generalise & abstract only after demonstrating a need Teach design patterns FP abstractions are used in various idiomatic ways Tight feedback loop Examples, stepwise evaluation, playgrounds Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Visualisation can be an effective tool Pure computations lend themselves to visualisation

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Pythagorean Trees

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Pythagorean Trees

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Pythagorean Trees

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Pythagorean Trees

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Pythagorean Trees

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Pythagorean Trees

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Pythagorean Trees

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Properties Type Systems

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Are types restraints?

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Types are a design tool!

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https://speakerdeck.com/mchakravarty/a-type-is-worth-a-thousand-tests YOW! Connected 2016, Melbourne

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“Doesn’t static typing hinder experimentation as you have to get everything right, before you can run it?”

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Improving Our Tools

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Is this the best we can do?

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http://worrydream.com

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Haskell for Mac

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Haskell for Mac

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Swift Playgrounds (iPad)

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mchakravarty TacticalGrace justtesting.org haskellformac.com

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natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 ⋮ Examples first mchakravarty TacticalGrace justtesting.org haskellformac.com

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natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 ⋮ Examples first recursiveFunction [] = [] recursiveFunction (x : xs) = doSomethingWith x : recursiveFunction xs Teach design patterns mchakravarty TacticalGrace justtesting.org haskellformac.com

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natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 ⋮ Examples first recursiveFunction [] = [] recursiveFunction (x : xs) = doSomethingWith x : recursiveFunction xs Teach design patterns Tight feedback loop & visualisation mchakravarty TacticalGrace justtesting.org haskellformac.com

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natSum 0 = 0 natSum 1 = 1 + 0 natSum 2 = 2 + 1 + 0 ⋮ Examples first recursiveFunction [] = [] recursiveFunction (x : xs) = doSomethingWith x : recursiveFunction xs Teach design patterns Tight feedback loop & visualisation http://learninghaskell.com mchakravarty TacticalGrace justtesting.org haskellformac.com

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Thank you!

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