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**1 - 7**of**7**### Relational parametricity and control

- Logical Methods in Computer Science

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"... A call-by-value λ-calculus with lists and control ..."

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### and Reasoning about Programs—Mechanical verification

"... Proof assistants based on dependent type theory are closely related to functional programming languages, and so it is tempting to use them to prove the correctness of functional programs. In this paper, we show how Agda, such a proof assistant, can be used to prove theorems about Haskell programs. H ..."

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Proof assistants based on dependent type theory are closely related to functional programming languages, and so it is tempting to use them to prove the correctness of functional programs. In this paper, we show how Agda, such a proof assistant, can be used to prove theorems about Haskell programs. Haskell programs are translated into an Agda model of their semantics, by translating via GHC’s Core language into a monadic form specially adapted to represent Haskell’s polymorphism in Agda’s predicative type system. The translation can support reasoning about either total values only, or total and partial values, by instantiating the monad appropriately. We claim that, although these Agda models are generated by a relatively complex translation process, proofs about them are simple and natural, and we offer a number of examples to support this claim.

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"... We study the equational theory of Parigot’s secondorder λµ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equiv ..."

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We study the equational theory of Parigot’s secondorder λµ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λµ-terms. On the other hand, the unconstrained relational parametricity on the λµ-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λµ-calculus in a constrained way, which might be called “focal parametricity”. 1.

### Hoare-Style Reasoning with (Algebraic) Continuations

"... Continuations are programming abstractions that allow for manipulating the “future ” of a computation. Amongst their many applications, they enable implementing unstructured program flow through higher-order control operators such as callcc. In this paper we develop a Hoare-style logic for the verif ..."

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Continuations are programming abstractions that allow for manipulating the “future ” of a computation. Amongst their many applications, they enable implementing unstructured program flow through higher-order control operators such as callcc. In this paper we develop a Hoare-style logic for the verification of programs with higher-order control, in the presence of dynamic state. This is done by designing a dependent type theory with first class callcc and abort operators, where pre- and postconditions of programs are tracked through types. Our operators are algebraic in the sense of Plotkin and Power, and Jaskelioff, to reduce the annotation burden and enable verification by symbolic evaluation. We illustrate working with the logic by verifying a number of characteristic examples. 1.