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

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

This instructional booklet provides 9 rigorously revised lectures given on the fifth overseas institution on sensible Programming, AFP 2004, in Tartu, Estonia in August 2004.

The e-book provides the subsequent 9, conscientiously cross-reviewed chapters, written through major experts within the box: Typing Haskell with an characteristic Grammar, Programming with Arrows, Epigram: useful Programming with established forms, Combining Datatypes and results, GEC: a toolkit for general speedy Prototyping, A useful Shell that Operates on Typed and Compiled purposes, Declarative Debugging with Buddha, Server-Side net 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

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The EH programmer) of the type system. 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.

These errors are gathered so they can be incorporated into an annotated pretty printed version of the program. Typing rule e-ident1B uses the environment Γ to retrieve the type of an identifier. This environment valGam for types of identifiers simply is declared as an inherited attribute, initialized at the top of the abstrcat syntax tree. It is only extended with new bindings for identifiers at a declaration of an identifier. valGam = emptyGam f it One may wonder why the judgement σ1 σ2 : σ and its implementation fitsIn returns a type at all; the idea of checking was to only pass explicit type information σk (or knTy) from the top of the abstract syntax tree to the leaf nodes.

N ) → ... 1 C ,n : σ1 → ... , σn ) σk : σ C minint . maxint : σ C (e-int2) Fig. 11. Type inferencing for expressions (using constraints) (e-lam2) C (e-con2) 52 A. D. Swierstra The type rules in Fig. 11 enforcean order in which checking and inferring types has to be done. Actually, the rules in Fig. 11 should be even more specific in how constraints flow around if we want to be closer to the corresponding AG description. tyCnstr @fTy AG: Redefining an attribute value. Normally a value for an attribute may be associated with an attribute only once, using = in a rule.

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