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An Adequate, Denotational, FunctionalStyle Semantics for Typed FlatCurry
"... Abstract. With the aim of putting typebased reasoning for functional logic languages, as recently explored by Christiansen et al. (2010), on a formal basis, we develop a denotational semantics for a typed core language of Curry. Dealing with the core language FlatCurry rather than with full Curry s ..."
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Abstract. With the aim of putting typebased reasoning for functional logic languages, as recently explored by Christiansen et al. (2010), on a formal basis, we develop a denotational semantics for a typed core language of Curry. Dealing with the core language FlatCurry rather than with full Curry suffices, since there exists a typepreserving translation from the latter into the former. In contrast to existing semantics for functional logic languages, we deliberately approach the problem “from the functional side”. That is, rather than adapting approaches previously known from the study of (resolutionlike) semantics for logic languages, we aim for a semantics in the spirit of standard denotational semantics for the polymorphic lambda calculus. We claim and set out to prove that the presented semantics is adequate with respect to an existing operational semantics. A particularly interesting aspect, we think, is that we give the first denotational treatment of recursive letbindings in combination with calltime choice. 1
A Denotational Semantics for Curry (progress report)
"... Abstract. We aim to build a denotational semantics for the functional logic programming language Curry, to be used for parametricity and logical relation arguments. First, we investigate only a subset of Curry, but include the important features that separate Curry from a just functional language. W ..."
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Abstract. We aim to build a denotational semantics for the functional logic programming language Curry, to be used for parametricity and logical relation arguments. First, we investigate only a subset of Curry, but include the important features that separate Curry from a just functional language. We compare a poweralgebraic and a multialgebraic semantic approach and motivate our decision for the multialgebraic one. Afterwards, we describe how general recursion and lists, as an example for algebraic data types, can be added. 1
der Rheinischen FriedrichWilhelmsUniversität Bonn An Adequate, Denotational, FunctionalStyle Semantics for Typed FlatCurry
"... Forschungsberichte sind erhältlich durch: Technical reports can be requested from: ..."
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Forschungsberichte sind erhältlich durch: Technical reports can be requested from:
Parametricity and Proving Free Theorems for FunctionalLogic Languages
"... The goal of this paper is to provide the required foundations for establishing free theorems – statements about program equivalence, guaranteed by polymorphic types – for the functionallogic programming language Curry. For the sake of presentation we restrict ourselves to a language fragment that ..."
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The goal of this paper is to provide the required foundations for establishing free theorems – statements about program equivalence, guaranteed by polymorphic types – for the functionallogic programming language Curry. For the sake of presentation we restrict ourselves to a language fragment that we call CuMin, and that has the characteristic features of Curry (both functional and logic). We present a new denotational semantics based on partially ordered sets without limits. We then introduce an intermediate language called set type, and again give a denotational semantics. We show that the standard (logical relations) techniques can be applied to obtain a general parametricity theorem for SaLT and derive free theorems from it. Via a translation from CuMin to SaLT that fits the respective semantics, we then derive free theorems for CuMin.