Lambda Usefull outside functional programming, functions nowadays - - PowerPoint PPT Presentation

61

Lambda functions

• Nameless functions, "functions as values"
• r "function literals"
• Usefull outside functional programming,

nowadays also in Java, C++, Python, C#, ...

• Compare "int i = 3;" and "3" with

"void f(int i){...}" and "[](int i){...}" (C++ syntax), named function = "variable containing a

lambda"

• Used heavily in functional programming,

since functions are 1st class citizens

• Uses: passing short functions as parameters,

storing them...

62

Named and nameless functions

<func_name> <formal_params> = <expr> ) \ <formal_param> -> <expr> square x = x * x square 5 \x -> x * x square = \x -> x * x ( \x -> x * x ) 5 square 5

Named function: Nameless function (lambda):

63

Higher order functions

• Functions are 1st class citizens
• Higher order functions: functions that

take functions as parameters and/or return them

• A little bit like function pointers in

C/C++/...

• Store functionality in data structures,

create new functionality based on that, call later

64

Functions as 1st class citizens

• Functions as variable/parameter values:

next x = x + 1 make = next; make 4 5 ➜ 6 use3 f = f 3 use3 next 4 ➜ 6 map next [1, 2, 3] [2, 3, 4] ➜ 6 frac3 n = foldl (*) 1 [1..n]

• Lambda-functions:

use (\x -> x*x) 9 ➜ 6 filter (\x -> x*x<10) [1..] [1, 2, 3] ➜ 6

• (C++11:)

for_each(v.begin(), v.end(), [](int x){cout<<x});

65

Currying

• In Haskell all functions have just one

parameter: plus x y = x + y t: plus plus :: a -> a -> a ➜ 6

• plus takes a parameter x and returns

another function, that takes y and calculates the result

• ("Values" can be thought of as

functions with no parameters)

66

Currying

• Currying makes it possible to use only some
• f the parameters:

plus = x + y plus3 = plus 3 :t plus3 plus3 :: a -> a ➜ 6 plus3 8 11 ➜ 6 map plus3 [2, 4, 6] [5, 7, 9] ➜ 6

67

I/O in Haskell

• I/O is a side-effect and demands strictly
• rdered execution, which contradicts

functional paradigm

• Haskell uses monads
• Complicated, not discussed here in

detail

• Idea: I/O-functions have their own

"category", I/O-functions are chained with invisible parameters, forcing sequential execution

• Monads have many other uses too...

68

Logic

programming

• Logic programming paradigm

– "Logic programming can be viewed as

controlled deduction."

• Logic program

– expressing facts and rules about some problem domain

• Execution of a program

– Searching for a result that fulfills the rules

69

Features of Logic programming

• Declarative semantics

– Simpler than for imperative languages – (Functional programming also declarative)

• Programmer describes the result,

not how it is achieved

– e.g., how to sort vs. what does "sorted" mean – Sometimes solving strategy can be given

sort ( old_list, new_list )  permutation ( old_list, new_list )  sorted ( new_list ) sorted ( list )  j: 1  j < n, list ( j )  list ( j + 1 ) ”The challenge of imperative programming is that all details

• f computation

must be expressed.”

70

Curry - functional logic language

• "Modern" research language
• Combines functional and logic

paradigms

• Several implementations exist
• Syntax (almost) from Haskell
• Adds features for logic programming:

– Free variables – Non-deterministic functions – Logical constraints, built-in search

(with several search strategies)

71

New in Curry (vs Haskell)

Non-deterministic functions

• f x = x

f x = x+1 f 3

– Haskell: first match is chosen, 3

returned

– Curry: both matches chosen, two

execution branches, both 3 and 4 returned

• Builtin choice-operator ?:

0 ? 1 returns both 0 and 1

72

New in Curry (vs Haskell)

Partial functions

• empty [] = []

empty [3]

– Haskell: Run-time error – Curry: "No solution" (continue search

for other solutions)

73

New in Curry (vs Haskell)

Constraints

• equality =:=, constraint combinator & (and

&>), anything returning success

• Unlike booleans (==), requires constraint to

hold

• Can be used to limit function definitions

(other major uses too) f x y | x =:= reverse y = x++y function defined only for some lists

• "Functional patterns" do this implicitly:

last (_++[e]) = e

74

New in Curry (vs Haskell)

Free variables

• Value not known beforehand
• Curry tries to deduce (search for) the

value based on constraints (unification)

• [1]++x =:= [1,2,3] where x

free returns binding x=[2,3]

75

Curry examples

• take 3 x =:= [1,2,3] & reverse x

=:= x where x free

• insert x ys = x:ys

insert x (y:ys) = y : insert x ys permutate [] = [] permutate (x:xs) = insert x (permutate xs)

• permutate [1,2,3,1] =:= a++[1,2]++b

where a,b free

76

Problems with logic paradigm

• Controlling the order of resolution

– efficiency – Infinite loops possible

• Closed-world assumption

– A goal can be proven but not disproven

• Natural limits

– No need to describe computation – However, different solution strategies differ in efficiency

77

Applications for logic programming

• Relational databases

– Input (facts) – Database relations (rules) – Queries

• AI
• Expert systems

– Fact-based deduction

• Language processing

– top-down –resolution resembles natural language

• Teaching