2,526 research outputs found
A Vernacular for Coherent Logic
We propose a simple, yet expressive proof representation from which proofs
for different proof assistants can easily be generated. The representation uses
only a few inference rules and is based on a frag- ment of first-order logic
called coherent logic. Coherent logic has been recognized by a number of
researchers as a suitable logic for many ev- eryday mathematical developments.
The proposed proof representation is accompanied by a corresponding XML format
and by a suite of XSL transformations for generating formal proofs for
Isabelle/Isar and Coq, as well as proofs expressed in a natural language form
(formatted in LATEX or in HTML). Also, our automated theorem prover for
coherent logic exports proofs in the proposed XML format. All tools are
publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
A strategy for automatically generating programs in the lucid programming language
A strategy for automatically generating and verifying simple computer programs is described. The programs are specified by a precondition and a postcondition in predicate calculus. The programs generated are in the Lucid programming language, a high-level, data-flow language known for its attractive mathematical properties and ease of program verification. The Lucid programming is described, and the automatic program generation strategy is described and applied to several example problems
A System for Deduction-based Formal Verification of Workflow-oriented Software Models
The work concerns formal verification of workflow-oriented software models
using deductive approach. The formal correctness of a model's behaviour is
considered. Manually building logical specifications, which are considered as a
set of temporal logic formulas, seems to be the significant obstacle for an
inexperienced user when applying the deductive approach. A system, and its
architecture, for the deduction-based verification of workflow-oriented models
is proposed. The process of inference is based on the semantic tableaux method
which has some advantages when compared to traditional deduction strategies.
The algorithm for an automatic generation of logical specifications is
proposed. The generation procedure is based on the predefined workflow patterns
for BPMN, which is a standard and dominant notation for the modeling of
business processes. The main idea for the approach is to consider patterns,
defined in terms of temporal logic,as a kind of (logical) primitives which
enable the transformation of models to temporal logic formulas constituting a
logical specification. Automation of the generation process is crucial for
bridging the gap between intuitiveness of the deductive reasoning and the
difficulty of its practical application in the case when logical specifications
are built manually. This approach has gone some way towards supporting,
hopefully enhancing our understanding of, the deduction-based formal
verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
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