By Ralf Hinze, Johan Jeuring (auth.), Roland Backhouse, Jeremy Gibbons (eds.)

Generic programming makes an attempt to make programming extra effective via making it extra basic. This e-book is dedicated to a unique type of genericity in courses, in line with parameterizing courses through the constitution of the information they manipulate.

The publication provides the subsequent 4 revised and prolonged chapters first given as lectures on the general Programming summer season university held on the college of Oxford, united kingdom in August 2002:

- accepted Haskell: perform and Theory

- customary Haskell: Applications

- universal homes of Datatypes

- uncomplicated classification idea for versions of Syntax

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Extra info for Generic Programming: Advanced Lectures

Example text

Haskell—or rather, extensions of Haskell come quite close to this ideal language. The Glasgow Haskell Compiler, GHC, [45], the Haskell B. Compiler, HBC, [3] and the Haskell interpreter Hugs [29] provide rank-2 type signatures. 04, even supports general rank-n types. There is, however, one fundamental difference between Haskell and (our presentation) of the polymorphic lambda calculus: Haskell’s notion of type equivalence is based on name equivalence while the polymorphic lambda calculus employs structural equivalence.

By contrast, the mapping function for List (which like f has kind → ) takes a1 → a2 to List a1 → List a2 . The definition below demonstrates that the extra generality is vital. :: ∀a1 a2 . (a1 → a2 ) → (List a1 → List a2 ) mapList mapList mapa = mapFix (mapListBase mapa) The argument of mapFix has type ∀b1 b2 . (b1 → b2 ) → (ListBase a1 b1 → ListBase a2 b2 ), that is, f1 is instantiated to ListBase a1 and f2 to ListBase a2 . Now, let us define a generic version of map. What is the type of the generic mapping function?

Like sum, the flatten function is pointless for types but useful for type constructors. fflatten{|t :: → |} :: ∀a . t a → [a] fflatten{|t|} = flatten{|t|} wrap where wrap a = [a ] The definitions of sum and flatten exhibit a common pattern: the elements of a base type are replaced by a constant (0 and [ ], respectively) and the pair constructor is replaced by a binary operator ((+) and (+ +), respectively). The generic function reduce abstracts away from these particularities. Its kind-indexed type is given by type Reduce{[ ]} t x = x → (x → x → x) → t → x type Reduce{[κ → ν]} t x = ∀a .

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