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15
Towards a practical programming language based on dependent type theory
, 2007
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Encoding monomorphic and polymorphic types
, 2012
"... Abstract. Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings ..."
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Cited by 27 (14 self)
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Abstract. Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of “cover”. The new encodings are implemented, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes. 1
Sort it out with monotonicity: translating between manysorted and unsorted firstorder logic
 In Proceedings of the 23rd international conference on Automated deduction, CADE’11
, 2011
"... Abstract. We present a novel analysis for sorted logic, which determines if a given sort is monotone. The domain of a monotone sort can always be extended with an extra element. We use this analysis to significantly improve wellknown translations between unsorted and manysorted logic, making use ..."
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Cited by 12 (1 self)
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Abstract. We present a novel analysis for sorted logic, which determines if a given sort is monotone. The domain of a monotone sort can always be extended with an extra element. We use this analysis to significantly improve wellknown translations between unsorted and manysorted logic, making use of the fact that it is cheaper to translate monotone sorts than nonmonotone sorts. Many interesting problems are more naturally expressed in manysorted firstorder logic than in unsorted logic, but most existing highlyefficient automated theorem provers solve problems only in unsorted logic. Conversely, some reasoning tools, for example model finders, can make good use of sortinformation in a problem, but most problems today are formulated in unsorted logic. This situation motivates translations in both ways between manysorted and unsorted problems. We present the monotonicity analysis and its implementation in our tool Monotonox, and also show experimental results on the TPTP benchmark library. 1
TFF1: The TPTP typed firstorder form with rank1 polymorphism
"... The TPTP World is a wellestablished infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed firstorder form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the ..."
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Cited by 11 (4 self)
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The TPTP World is a wellestablished infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed firstorder form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the TFF1 format, an extension of TFF0 with rank1 polymorphism. It presents its syntax, typing rules, and semantics, as well as a sound and complete translation to TFF0. The format is designed to be easy to process by existing reasoning tools that support MLstyle polymorphism. It opens the door to useful middleware, such as monomorphizers and other translation tools that encode polymorphism in FOF or TFF0. Ultimately, the hope is that TFF1 will be implemented in popular automatic theorem provers.
Two computersupported proofs in metric space topology
 Notices of the American Mathematical Society
, 1991
"... Every mathematician will agree that the discovery, analysis, and communication ..."
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Cited by 8 (3 self)
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Every mathematician will agree that the discovery, analysis, and communication
Connecting a logical framework to a firstorder logic prover
 IN FROCOS’05: PROCEEDINGS OF THE 5TH INTERNATIONAL WORKSHOP ON FRONTIERS OF COMBINING SYSTEMS
, 2005
"... We present one way of combining a logical framework and firstorder logic. The logical framework is used as an interface to a firstorder theorem prover. Its main purpose is to keep track of the structure of the proof and to deal with the high level steps, for instance, induction. The steps that i ..."
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Cited by 6 (0 self)
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We present one way of combining a logical framework and firstorder logic. The logical framework is used as an interface to a firstorder theorem prover. Its main purpose is to keep track of the structure of the proof and to deal with the high level steps, for instance, induction. The steps that involve purely propositional or simple firstorder reasoning are left to a firstorder resolution prover (the system Gandalf in our prototype). The correctness of this interaction is based on a general metatheoretic result. One feature is the simplicity of our translation between the logical framework and firstorder logic, which uses implicit typing. Implementation and case studies are described.
The TPTP Problem Library (TPTP v2.1.0
 Department of Computer Science, James Cook University
, 1997
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Monotonicity or how to encode polymorphic types safely and efficiently
"... Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are either bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonoton ..."
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Cited by 3 (3 self)
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Most automatic theorem provers are restricted to untyped or monomorphic logics, and existing translations from polymorphic logics are either bulky or unsound. Recent research shows how to exploit monotonicity to encode ground types efficiently: monotonic types can be safely erased, while nonmonotonic types must generally be encoded. We extend this work to rank1 polymorphism and show how to eliminate even more clutter by also erasing most occurrences of nonmonotonic types, without sacrificing soundness or completeness. The new encodings are implemented in the Sledgehammer tool for Isabelle/HOL. Our evaluation finds them considerably superior to previous schemes.
Otterlambda, A Theoremprover WITH UNTYPED LAMBDAUNIFICATION
, 2004
"... Support for lambda calculus and an algorithm for untyped lambdaunification has been implemented, starting from the source code for Otter. The result is a new theorem prover called Otterλ. This is the first time that a resolutionbased, clauselanguage prover (that accumulates deduced clauses and u ..."
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Support for lambda calculus and an algorithm for untyped lambdaunification has been implemented, starting from the source code for Otter. The result is a new theorem prover called Otterλ. This is the first time that a resolutionbased, clauselanguage prover (that accumulates deduced clauses and uses strategies to control the deduction and retention of clauses) has been combined with a lambdaunification algorithm to assist in the deductions. The resulting prover combines the advantages of the proofsearch algorithm of Otter and the power of higherorder unification. We describe the untyped lambda unification algorithm used by Otterλ and give several example theorems.