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Atze Dijkstra, S. Doaitse Swierstra (auth.), Varmo Vene,'s Advanced Functional Programming: 5th International School, PDF

By Atze Dijkstra, S. Doaitse Swierstra (auth.), Varmo Vene, Tarmo Uustalu (eds.)

ISBN-10: 3540285407

ISBN-13: 9783540285403

ISBN-10: 3540318720

ISBN-13: 9783540318729

This educational publication offers 9 rigorously revised lectures given on the fifth foreign tuition on practical Programming, AFP 2004, in Tartu, Estonia in August 2004.

The publication offers the next 9, rigorously cross-reviewed chapters, written through major experts within the box: Typing Haskell with an characteristic Grammar, Programming with Arrows, Epigram: sensible Programming with based kinds, Combining Datatypes and results, GEC: a toolkit for known quick Prototyping, A sensible Shell that Operates on Typed and Compiled purposes, Declarative Debugging with Buddha, Server-Side internet Programming in WASH, and Refactoring sensible Programs.

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Extra resources for Advanced Functional Programming: 5th International School, AFP 2004, Tartu, Estonia, August 14 – 21, 2004, Revised Lectures

Sample text

KnTy = Ty Any The rule f-arrow1 in Fig. 8 for comparing function types compares the types for arguments in the opposite direction. Only in later versions of EH when really behaves asymmetrically we will discuss this aspect of the rules which is named contravariance. In the rules in Fig. 8 the direction makes no difference; the correct use of the direction for now only anticipates issues yet to come. The Haskell counterpart of f it σ1 σ2 : σ is implemented by fitsIn: fitsIn :: Ty → Ty → FIOut fitsIn ty1 ty2 = f ty1 ty2 where res t = emptyFO{foTy = t } f Ty Any t2 = res t2 f t1 Ty Any = res t1 f t1 @(Ty Con s1) t2 @(Ty Con s2) | s1 ≡ s2 = res t2 f t1 @(Ty App (Ty App (Ty Con c1) ta1 ) tr1 ) t2 @(Ty App (Ty App (Ty Con c2) ta2 ) tr2 ) | hsnIsArrow c1 ∧ c1 ≡ c2 = comp ta2 tr1 ta1 tr2 (λa r → [a] ‘mkTyArrow‘ r) 34 A.

The definition of Ty will be used in both the Haskell world and the AG world. InHaskell we use the corresponding data type generated by the AG compiler, for example in the derived type TyL: type TyL = [Ty] The data type is used to construct type representations. In the AG world we define computations over the type structure in terms of attributes. The corresponding semantic functions generated by the AG system can then be applied to Haskell values. 3 Checking Types The type system of a programming language is described by typing rules.

D. ty which uses some additional functions for creating type variables mkNewTyVar :: UID → Ty mkNewTyVar u = let ( , v) = mkNewUID u in mkTyVar v mkNewUIDTyVarL :: Int → UID → ([UID], TyL) mkNewUIDTyVarL sz u = let vs = mkNewUIDL sz u in (vs, map mkTyVar vs) mkNewTyVarL :: Int → UID → TyL mkNewTyVarL sz u = snd (mkNewUIDTyVarL sz u) Some observations are in place: – The main difference with the previous implementation is the use of type variables to represent unknown knowledge. Previously was used for that purpose, for example, the rule e-lam2 and its implementation show that fresh type variables vi in ν1 → ν2 are used instead of → to enforce a .

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Advanced Functional Programming: 5th International School, AFP 2004, Tartu, Estonia, August 14 – 21, 2004, Revised Lectures by Atze Dijkstra, S. Doaitse Swierstra (auth.), Varmo Vene, Tarmo Uustalu (eds.)


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