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- Stefan Berghofer, Tobias Nipkow
- Proceedings of the Second International…
- 2004

When developing non-trivial formalizations in a theorem prover, a considerable amount of time is devoted to "debugging" specifications and conjectures by failed proof attempts. To detect such problems early in the proof and save development time, we have extended the Isabelle theorem prover with a tool for testing specifications by evaluating propositions… (More)

- Ulrich Berger, Stefan Berghofer, Pierre Letouzey, Helmut Schwichtenberg
- Studia Logica
- 1993

This paper describes formalizations of Tait’s normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction… (More)

- Makarius Wenzel, Stefan Berghofer, +6 authors Sebastian Skalberg
- 1999

Intelligible semi-automated reasoning (Isar) is a generic approach to readable formal proof documents. It sets out to bridge the semantic gap between any internal notions of proof based on primitive inferences and tactics, and an appropriate level of abstraction for user-level work. The Isar formal proof language has been designed to satisfy quite… (More)

- Stefan Berghofer, Tobias Nipkow
- TYPES
- 2000

We report on the design of a prototyping component for the theorem prover Isabelle/HOL. Specifications consisting of datatypes, recursive functions and inductive definitions are compiled into a functional program. Functions and inductively defined relations can be mixed. Inductive definitions must be such that they can be executed in Prolog style but… (More)

- Stefan Berghofer, Tobias Nipkow
- TPHOLs
- 2000

This paper presents proof terms for simply typed, intuitionistic higher order logic, a popular logical framework. Unification-based algorithms for the compression and reconstruction of proof terms are described and have been implemented in the theorem prover Isabelle. Experimental results confirm the effectiveness of the compression scheme.

- Stefan Berghofer, Markus Wenzel
- TPHOLs
- 1999

Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also support inverted datatype definitions for characterizing existing… (More)

- Christian Urban, Stefan Berghofer
- IJCAR
- 2006

The nominal datatype package implements an infrastructure in Isabelle/HOL for defining languages involving binders and for reasoning conveniently about alpha-equivalence classes. Pitts stated some general conditions under which functions over alpha-equivalence classes can be defined by a form of structural recursion and gave a clever proof for the existence… (More)

- Christian Urban, Stefan Berghofer, Michael Norrish
- CADE
- 2007

Inductive definitions and rule inductions are two fundamental reasoning tools in logic and computer science. When inductive definitions involve binders, then Barendregt’s variable convention is nearly always employed (explicitly or implicitly) in order to obtain simple proofs. Using this convention, one does not consider truly arbitrary bound names, as… (More)

- Christine Röckl, Daniel Hirschkoff, Stefan Berghofer
- FoSSaCS
- 2001

- Stefan Berghofer
- TYPES
- 2003

Higman’s lemma, a specific instance of Kruskal’s theorem, is an interesting result from the area of combinatorics, which has often been used as a test case for theorem provers. We present a constructive proof of Higman’s lemma in the theorem prover Isabelle, based on a paper proof by Coquand and Fridlender. Making use of Isabelle’s newly-introduced… (More)