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Conjecture Synthesis for Inductive Theories
 JOURNAL OF AUTOMATED REASONING
, 2010
"... We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexample checkin ..."
Abstract

Cited by 7 (5 self)
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We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexample checking and passed to the automatic inductive prover IsaPlanner. The main technical contribution is the presentation of a constraint mechanism for synthesis. As theorems are discovered, this generates additional constraints on the synthesis process. We evaluate IsaCoSy as a tool for automatically generating the background theories one would expect in a mature proof assistant, such as the Isabelle system. The results show that IsaCoSy produces most, and sometimes all, of the theorems in the Isabelle libraries. The number of additional uninteresting theorems are small enough to be easily pruned by hand.
QuickSpec: Guessing formal specifications using testing
 In Tests and Proofs, Fourth International Conference, TAP
, 2010
"... Abstract. We present QuickSpec, a tool that automatically generates algebraic specifications for sets of pure functions. The tool is based on testing, rather than static analysis or theorem proving. The main challenge QuickSpec faces is to keep the number of generated equations to a minimum while ma ..."
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Cited by 5 (1 self)
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Abstract. We present QuickSpec, a tool that automatically generates algebraic specifications for sets of pure functions. The tool is based on testing, rather than static analysis or theorem proving. The main challenge QuickSpec faces is to keep the number of generated equations to a minimum while maintaining completeness. We demonstrate how QuickSpec can improve one’s understanding of a program module by exploring the laws that are generated using two case studies: a heap library for Haskell and a fixedpoint arithmetic library for Erlang. 1
forthcoming)). Applying lakatosstyle reasoning to ai problems
 Thinking Machines and the philosophy of computer science: Concepts and principles. IGI Global
, 2010
"... One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, nonmonotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning ..."
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Cited by 1 (1 self)
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One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, nonmonotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning styles collaborate to develop mathematical ideas. Lakatos argued that mathematics is a quasiempirical, flexible, fallible, human endeavour, involving negotiations, mistakes, vague concept definitions and disagreements, and he outlined a heuristic approach towards the subject. In this chapter we apply these heuristics to the AI domains of evolving requirement specifications, planning and constraint satisfaction problems. In drawing analogies between Lakatos’s theory and these three domains we identify areas of work which correspond to each heuristic, and suggest extensions and further ways in which Lakatos’s philosophy can inform AI problem solving. Thus, we show how we might begin to produce a philosophicallyinspired AI theory of combined reasoning. 1
IsaCoSy: Synthesis of Inductive Theorems
"... Abstract. We have implemented a program for inductive theory formation, called IsaCoSy, which synthesises conjectures about recursively defined datatypes and functions. Only irreducible terms are generated, which keeps the search space tractably small. The synthesised terms are filtered through coun ..."
Abstract
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Abstract. We have implemented a program for inductive theory formation, called IsaCoSy, which synthesises conjectures about recursively defined datatypes and functions. Only irreducible terms are generated, which keeps the search space tractably small. The synthesised terms are filtered through counterexample checking and then passed on to the automatic inductive prover IsaPlanner. Experiments have given promising results, with high recall of 83 % for natural numbers and 100 % for lists when compared to libraries for the Isabelle theorem prover. However, precision is somewhat lower, 3863%. 1
Journal of Automated Reasoning manuscript No. (will be inserted by the editor) Conjecture Synthesis for Inductive Theories
, 2010
"... Abstract We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup ’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexamp ..."
Abstract
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Abstract We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottomup ’ from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counterexample checking and passed to the automatic inductive prover IsaPlanner. The main technical contribution is the presentation of a constraint mechanism for synthesis. As theorems are discovered, this generates additional constraints on the synthesis process. We evaluate IsaCoSy as a tool for automatically generating the background theories one would expect in a mature proof assistant, such as the Isabelle system. The results show that IsaCoSy produces most, and sometimes all, of the theorems in the Isabelle libraries. The number of additional uninteresting theorems are small enough to be easily pruned by hand.
Seventy four minutes of mathematics: An analysis of the third MiniPolymath project
"... Abstract. Alan Turing proposed to consider the question, “Can machines think? ” in his famous article [40]. We consider the question, “Can machines do mathematics, and how? ” Turing suggested that intelligence be tested by comparing computer behaviour to human behaviour in an online discussion. We h ..."
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Abstract. Alan Turing proposed to consider the question, “Can machines think? ” in his famous article [40]. We consider the question, “Can machines do mathematics, and how? ” Turing suggested that intelligence be tested by comparing computer behaviour to human behaviour in an online discussion. We hold that this approach could be useful for assessing computational logic systems which, despite having produced formal proofs of the Four Colour Theorem, the Robbins Conjecture and the Kepler Conjecture, have not achieved widespread take up by mathematicians. It has been suggested that this is because computer proofs are perceived as ungainly, bruteforce searches which lack elegance, beauty or mathematical insight. One response to this is to build such systems which perform in a more humanlike manner, which raises the question of what a “humanlike manner ” may be. Timothy Gowers recently initiated Polymath [4], a series of experiments in online collaborative mathematics, in which problems are posted online, and an open invitation issued for people to try to solve them collaboratively, documenting every step of the ensuing discussion. The resulting record provides an unusual example of fully documented mathematical activity leading to a proof, in contrast to typical research papers which record proofs, but not how they were obtained. We consider the third MiniPolymath project [3], started by Terence Tao and published online on July