Functional Programming

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1 The Meta Language (ML) and Functional Programming Daniel S. Fava Department of informatics University of Oslo, Norway

2 Motivation ML Demo

3 Which programming languages are functional?

4 Which programming languages are functional? Lambda calculus 1930 (a model of computation)

5 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 ML 1973

6 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 dynamically typed ML 1973 statically typed

7 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 dynamically typed Scheme 1970 Racket 1995 ML 1973 statically typed

8 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 dynamically typed Scheme 1970 Racket 1995 ML 1973 statically typed Standard ML or SML Caml 1985 OCaml 1996

9 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 dynamically typed Scheme 1970 Racket 1995 ML 1973 statically typed Standard ML or SML Caml 1985 OCaml 1996 Haskell 1990

10 Which programming languages are functional? Lambda calculus 1930 (a model of computation) Lisp 1950 dynamically typed Scheme 1970 Racket 1995 ML 1973 statically typed Standard ML or SML Caml 1985 OCaml 1996 Haskell 1990 Erlang 1986, Scala 2004, Clojure 2007 (multi-paradigm)

11 Why another programming paradigm?

12 Why another programming paradigm? A different way of thinking

13 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs

14 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#...

15 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce

16 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce Debatable

17 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce Debatable easier to reason about and to prove properties of

18 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce Debatable easier to reason about and to prove properties of more compact, simpler code

19 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce Debatable easier to reason about and to prove properties of in the eye of the beholder more compact, simpler code

20 Why another programming paradigm? A different way of thinking Non-functional PLs borrowing functional constructs JavaScript, Python, Lua, PHP, C++11, C#... MapReduce Debatable easier to reason about and to prove properties of in the eye of the beholder more compact, simpler code problems can be easier to express given certain idioms match the language to the problem

21 What is functional programming? [100]a [100]a [100]a [100]a

22 What is functional programming? It is programming with: [100]a [100]a [100]a [100]a

23 What is functional programming? It is programming with: first-class and higher-order functions [100]a [100]a [100]a

24 What is functional programming? It is programming with: first-class and higher-order functions purity [100]a [100]a

25 What is functional programming? It is programming with: first-class and higher-order functions purity pattern matching [100]a

26 What is functional programming? It is programming with: first-class and higher-order functions purity pattern matching recursion

27 first-class and higher-order functions purity pattern matching recursion

28 first-class and higher-order functions Currying Closures purity pattern matching recursion

29 first-class and higher-order functions Currying Closures purity Statements versus Expressions and Declarations Side effects versus Effect free Immutability Referential transparency pattern matching recursion

30 first-class and higher-order functions Currying Closures purity Statements versus Expressions and Declarations Side effects versus Effect free Immutability Referential transparency pattern matching constructors and pattern matching data structures Nat, Lists, Trees, etc recursion

31 first-class and higher-order functions Currying Closures purity Statements versus Expressions and Declarations Side effects versus Effect free Immutability Referential transparency pattern matching constructors and pattern matching data structures Nat, Lists, Trees, etc recursion tail recursion termination and total functions continuations and continuation passing style (CPS)

32 The Meta Language (ML) ML is a functional programming language with imperative features,

33 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover.

34 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF)

35 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF) Project headed by Robin Milner in 1972.

36 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF) Project headed by Robin Milner in notation for programs

37 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF) Project headed by Robin Milner in notation for programs notation for proofs (eg. proof that quicksort returns a sorted array)

38 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF) Project headed by Robin Milner in notation for programs notation for proofs (eg. proof that quicksort returns a sorted array) write programs that search for proofs

39 The Meta Language (ML) ML is a functional programming language with imperative features, it was part of project to create an interactive theorem prover. Logic for Computable Functions (LCF) Project headed by Robin Milner in notation for programs notation for proofs (eg. proof that quicksort returns a sorted array) write programs that search for proofs have a program that checks a proof

40 tactic : formula proof

41 Composition of tactics tactic : formula proof

42 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic

43 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking

44 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type

45 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem

46 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem calling tactic on a formula can either:

47 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or

48 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or diverge, which means run forever, or

49 tactic : formula proof Composition of tactics Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or diverge, which means run forever, or raise an exception

50 tactic : formula proof Composition of tactics Higher-order functions Take tactics as input and return a more complex tactic Proof checking theorem abstract data type theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or diverge, which means run forever, or raise an exception

51 tactic : formula proof Composition of tactics Higher-order functions Take tactics as input and return a more complex tactic Proof checking theorem abstract data type Expressive and sound type system theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or diverge, which means run forever, or raise an exception

52 tactic : formula proof Composition of tactics Higher-order functions Take tactics as input and return a more complex tactic Proof checking theorem abstract data type Expressive and sound type system theorems derivable only via inference rules given by theorem calling tactic on a formula can either: terminate and return a proof, or diverge, which means run forever, or raise an exception First language with type-safe exceptions

53 Read-Evaluate-Print Loop (REPL)

54 Read-Evaluate-Print Loop (REPL) In ML, expressions are type-checked after R and before E

CMSC 330: Organization of Programming Languages. Functional Programming with OCaml

CMSC 330: Organization of Programming Languages Functional Programming with OCaml 1 What is a functional language? A functional language: defines computations as mathematical functions discourages use