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**1 - 1**of**1**### A Calculus for Conjecture Synthesis

"... Abstract. IsaCoSy is a theory formation system which synthesises and proves conjectures in order to produce a background theory for a new formalisation within a proof assistant. The key idea we employ to make synthesis tractable is to only consider synthesis of terms that are not more complex versio ..."

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Abstract. IsaCoSy is a theory formation system which synthesises and proves conjectures in order to produce a background theory for a new formalisation within a proof assistant. The key idea we employ to make synthesis tractable is to only consider synthesis of terms that are not more complex versions of already known terms. IsaCoSy identifies such undesirable terms as those that match the left-hand sides of rewrite rules. In this paper, we slightly generalise this idea to present a formal language for constraining synthesis such that it does not construct terms that can be matched by a given set of constraint-terms. We give a mathemati-cal account of the algorithms involved, and prove their correctness. In particular, we prove the correctness property for IsaCoSy’s approach to synthesis: when given a set of rewrite rules as input, it only produces irreducible terms. 1