Mads Sig Ager

Bio: Mads Sig Ager is an academic researcher from Aarhus University. The author has contributed to research in topics: Abstract machine & String (computer science). The author has an hindex of 10, co-authored 16 publications receiving 575 citations.

A Functional Correspondence between Evaluators and Abstract Machines

Abstract: We bridge the gap between functional evaluators and abstract machines for the lambda-calculus, using closure conversion, transformation into continuation-passing style, and defunctionalization of continuations. We illustrate this bridge by deriving Krivine's abstract machine from an ordinary call-by-name evaluator and by deriving an ordinary call-by-value evaluator from Felleisen et al.'s CEK machine. The first derivation is strikingly simpler than what can be found in the literature. The second one is new. Together, they show that Krivine's abstract machine and the CEK machine correspond to the call-by-name and call-by-value facets of an ordinary evaluator for the lambda-calculus. We then reveal the denotational content of Hannan and Miller's CLS machine and of Landin's SECD machine. We formally compare the corresponding evaluators and we illustrate some relative degrees of freedom in the design spaces of evaluators and of abstract machines for the lambda-calculus with computational effects. For the purpose of this work, we distinguish between virtual machines, which have an instruction set, and abstract machines, which do not. The Categorical Abstract Machine, for example, has an instruction set, but Krivine's machine, the CEK machine, the CLS machine, and the SECD machine do not; they directly operate on lambda-terms instead. We present the abstract machine that corresponds to the Categorical Abstract Machine.

A functional correspondence between evaluators and abstract machines

Abstract: We bridge the gap between functional evaluators and abstract machines for the λ-calculus, using closure conversion, transformation into continuation-passing style, and defunctionalization.We illustrate this approach by deriving Krivine's abstract machine from an ordinary call-by-name evaluator and by deriving an ordinary call-by-value evaluator from Felleisen et al.'s CEK machine. The first derivation is strikingly simpler than what can be found in the literature. The second one is new. Together, they show that Krivine's abstract machine and the CEK machine correspond to the call-by-name and call-by-value facets of an ordinary evaluator for the λ-calculus.We then reveal the denotational content of Hannan and Miller's CLS machine and of Landin's SECD machine. We formally compare the corresponding evaluators and we illustrate some degrees of freedom in the design spaces of evaluators and of abstract machines for the λ-calculus with computational effects.Finally, we consider the Categorical Abstract Machine and the extent to which it is more of a virtual machine than an abstract machine.

From Interpreter to Compiler and Virtual Machine: A Functional Derivation

Abstract: We show how to derive a compiler and a virtual machine from a compositional interpreter. We first illustrate the derivation with two evaluation functions and two normalization functions. We obtain Krivine's machine, Felleisen et al.'s CEK machine, and a generalization of these machines performing strong normalization, which is new. We observe that several existing compilers and virtual machines--e.g., the Categorical Abstract Machine (CAM), Schmidt's VEC machine, and Leroy's Zinc abstract machine--are already in derived form and we present the corresponding interpreter for the CAM and the VEC machine. We also consider Hannan and Miller's CLS machine and Landin's SECD machine. We derived Krivine's machine via a call-by-name CPS transformation and the CEK machine via a call-by-value CPS transformation. These two derivations hold both for an evaluation function and for a normalization function. They provide a non-trivial illustration of Reynolds's warning about the evaluation order of a meta-language.

Some logical metatheorems with applications in functional analysis

Abstract: In previous papers we have developed proof-theoretic techniques for extracting effective uniform bounds from large classes of ineffective existence proofs in functional analysis. Here 'uniform' means independence from parameters in compact spaces. A recent case study in fixed point theory systematically yielded uniformity even w.r.t. parameters in metrically bounded (but noncompact) subsets which had been known before only in special cases. In the present paper we prove general logical metatheorems which cover these applications to fixed point theory as special cases but are not restricted to this area at all. Our theorems guarantee under general logical conditions such strong uniform versions of non-uniform existence statements. Moreover, they provide algorithms for actually extracting effective uniform bounds and transforming the original proof into one for the stronger uniformity result. Our metatheorems deal with general classes of spaces like metric spaces, hyperbolic spaces, CAT(0)-spaces, normed linear spaces, uniformly convex spaces, as well as inner product spaces.

FreshML: programming with binders made simple

Abstract: FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving statically scoped binding operations User-declared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming bound variables explicitly This may have the computational effect of swapping bound names with freshly generated ones; previous work on FreshML used a complicated static type system inferring information about the 'freshness' of names for expressions in order to tame this effect The main contribution of this paper is to show (perhaps surprisingly) that a standard type system without freshness inference, coupled with a conventional treatment of fresh name generation, suffices for FreshML's crucial correctness property that values of datatypes involving binders are operationally equivalent if and only if they represent a-equivalent pieces of object-level syntax This is established via a novel denotational semantics FreshML without static freshness inference is no more impure than ML and experience with it shows that it supports a programming style pleasingly close to informal practice when it comes to dealing with object-level syntax modulo a-equivalence

A length-flexible threshold cryptosystem with applications

Abstract: We propose a public-key cryptosystem which is derived from the Paillier cryptosystem. The scheme inherits the attractive homomorphic properties of Paillier encryption. In addition, we achieve two new properties: First, all users can use the same modulus when generating key pairs, this allows more efficient proofs of relations between different encryptions. Second, we can construct a threshold decryption protocol for our scheme that is length-flexible, i.e., it can handle efficiently messages of arbitrary length, even though the public key and the secret key shares held by decryption servers are of fixed size. We show how to apply this cryptosystem to build a self-tallying election scheme with perfect ballot secrecy, and to build a length-flexible mix-net which is universally verifiable, where the size of keys and ciphertexts do not depend on the number of mix servers, and is robust against a corrupt minority.