Proof Pearl: The Power of Higher-Order Encodings in the Logical Framework LF
نویسنده
چکیده
In this proof pearl, we demonstrate the power of higherorder encodings in the logical framework Twelf[PS99] by investigating proofs about an algorithmic specification of bounded subtype polymorphism, a problem from the POPLmark challenge [ABF05]. Our encoding and representation of the problem plays to the strengths of the logical framework LF. Higher-order abstract syntax is used to deal with issues of bound variables. More importantly, we exploit the full advantage of parametric and higher-order judgments. As a key benefit we get a tedious narrowing lemma, which must normally be proven separately, for free. Consequently, we obtain an extremely compact and elegant encoding of the admissibility of general transitivity and other meta-theoretic properties.
منابع مشابه
Logical Frameworks--A Brief Introduction
A logical framework is a meta-language for the formalization of deductive systems. We provide a brief introduction to logical frameworks and their methodology, concentrating on LF. We use first-order logic as the running example to illustrate the representations of syntax, natural deductions, and proof transformations. We also sketch a recent formulation of LF centered on the notion of canonica...
متن کاملProject Report Categorical Judgments in a Logical Framework 15-816 Modal Logic
Categorical judgments possess a context-clearing property, making them difficult to express elegantly in the LF logical framework because the context of available LF hypotheses grows monotonically. We describe a connection between categorical judgments and a refinement to open terms of LF’s subordination relation. Leveraging this connection, we propose a logical framework, based on open-terms s...
متن کاملA Temporal-Logic Approach to Functional Calculi for Dependent Types and Higher-Order Encodings
Dependent-types and higher-order encodings lead to concise and elegant representations of complex data structures as evidenced by the success of the logical framework LF [HHP93]. In this work we first design a functional calculus utilizing LF to represent its data objects. To avoid problems commonly associated with using the same function space for both representation (LF objects) and computati...
متن کاملTowards Practical Functional Programming with Logical Frameworks Extended version
In this paper we show that the logical framework LF [6] extended by Σ-types serves as an excellent candidate for the representation of special purpose domains that are best encoded using higher-order abstract syntax and hypothetical judgments. It has an elegant meta-theory and Σ-types prove enormously useful in the design of a functional programming language Delphin that permits programmers to ...
متن کاملAdequate encodings of logical systems in UTT
In this paper we present an existing and formalized type theory UTT Luo Goguen as a logical framework We compare the resulting frame work with LF Harper et al and give the representation of two signi cant type systems in the framework the typed lambda calculus which is closely related to higher order logic and a linear type system which is not possible to encode in LF
متن کامل