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Over the last few years, the Haskell community has risen to the task of building the library infrastructure necessary for Haskell to succeed as a programming language. Programming languages can succeed or fail based on the breadth and quality of their library collection. The quality of a programming language itself is only one component in the ability of application writers to get the job done.
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We also show some of the techniques that we have used for the implementation including meta programming and generic programming. Nevertheless, in practice this kind of translation has proven to be adequate and powerful. To this end we had to sacrifice soundness and completeness of the translation. This approach is pragmatic, since its focus is to produce theories that are easily readable and minimise the effort to construct proofs. We present an implementation - written in Haskell - which enables to translate Haskell programs into Isabelle/HOL theories. On the other hand, the theorem prover Isabelle allows specifying functional programs in its logic HOL.
#Haskell curry verification#
Yet, a comparable success for the verification of Haskell programs has not been achieved, so far. Haskell is one of the rare purely functional programming languages that is also of practical relevance. This facilitates reasoning over programs considerably. View full-textĪmong other things the functional programming paradigm - in its pure form - offers the advantage of referential transparency. It is based on the idea that if we have certain defining rules for some α, e. The idea of inverting logical rules can be found in a well-known remark by Gentzen: "The introductions are so to say the 'definitions' of the sym-bols concerned, and the eliminations are ultimately only consequences hereof, what can approximately be expressed as follows: In eliminating a symbol, the formula concerned – of which the outermost symbol is in question – may only 'be used as that what it means on the ground of the introduction of that symbol'." 1 The inversion principle itself was formulated by Lorenzen (1955) in the general context of rule-based systems and is thus not restricted to logical rules.
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This generalises the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. Using the framework of definitional reflection and its admis-sibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are admissible when the right introduction rules are taken as the definitions of the logical constants and vice versa. For the context of admissibility statements, this has been further elaborated by. Hallnäs and Schroeder-Heister (1990/91) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants.