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Notions of computability at higher types I
 In Logic Colloquium 2000
, 2005
"... We discuss the conceptual problem of identifying the natural notions of computability at higher types (over the natural numbers). We argue for an eclectic approach, in which one considers a wide range of possible approaches to defining higher type computability and then looks for regularities. As a ..."
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Cited by 12 (5 self)
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We discuss the conceptual problem of identifying the natural notions of computability at higher types (over the natural numbers). We argue for an eclectic approach, in which one considers a wide range of possible approaches to defining higher type computability and then looks for regularities. As a first step in this programme, we give an extended survey of the di#erent strands of research on higher type computability to date, bringing together material from recursion theory, constructive logic and computer science. The paper thus serves as a reasonably complete overview of the literature on higher type computability. Two sequel papers will be devoted to developing a more systematic account of the material reviewed here.
DomainTheoretic Methods for Program Synthesis
"... formal proofs. A recent outcome of this analysis is the development of computer systems for automated or interactive theorem proving that can for instance be used for computer aided program verication. An example of such a system is the interactive theorem prover Minlog developed by the logic group ..."
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formal proofs. A recent outcome of this analysis is the development of computer systems for automated or interactive theorem proving that can for instance be used for computer aided program verication. An example of such a system is the interactive theorem prover Minlog developed by the logic group at the University of Munich (7). As a former member of this group I was mainly involved in the theoretical background steering the implementation of the system. The system also exploits the socalled proofsasprograms paradigm as a logical approach to correct software development: from a formal proof that a certain specication has a solution one fully automatically extracts a program that provably meets the specication. We carried out a number of extended case studies extracting programs from proofs in areas such as arithmetic (6), graph theory (7), innitary combinatorics (7), and lambda calculus (1,2). Special emphasis has been put on an ecient implemen