The Mathematical Style of Haskell

 

 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
functional programming is just one of several major programming paradigms

(see diagram here)

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 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
bullet History of functional programming
functional proramming properly begins with LISP and APL in the 1950's and 1960's
(but it got a big boost in the late 70's with Backus' Turing Award)

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 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
bullet History of functional programming
bullet History of Haskell
Haskell was a community effort (open source) in reaction to proprietary Miranda ("Miranda" is a trademark of Research Software, Ltd.")

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 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
bullet History of functional programming
bullet History of Haskell
bullet Haskell fits well with mathematical style and usage
many features collaborate to support this fit based on mathematical concepts (functions, algebra)

• higher-order functions, algebra = structure + operations concise, high-level descriptions

• whole-structure manipulation referential transparency (allows equational reasoning)

• no aliasing, no time-bound effects well-behaved numeric types

• big integers and exact rationals

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 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
bullet History of functional programming
bullet History of Haskell
bullet Haskell fits well with mathematical style and usage
bullet an uncluttered, math-compatible syntax
infix operators, ZF-expressions, guards, let declarations 
2+3*4

[ x^2 | x <- [1..10] ]

abs x | (x < 0 )  = -x
      | otherwise =  x

let x = 3*y+7 in x^2-k

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 Functional Programming in Haskell
Willamette Mathematics Colloquium • Fall 2002

The Mathematical Style of Haskell
bullet Programming paradigms
bullet History of functional programming
bullet History of Haskell
bullet Haskell fits well with mathematical style and usage
bullet an uncluttered, math-compatible syntax
bullet Haskell has been guided by a consistent, persistent design philosophy
the community has held its ground against encroachment by "impure" features this discipline has actually led to major innovations (e.g., monads)

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