Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The confluence of untyped @l-calculus with unconditional rewriting is now ll un- derstood. ,  investigate the confluence of @l-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Muller and Dougherty for unconditional rewriting. Two cases are considered, whether @b-reduction is allod or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing @b-reduction to akly normalizing @b-reduction.  also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second,  go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules.
['Frédéric Blanqui', 'Claude Kirchner', 'Colin Riba']
I am writing a research paper on a idea On the confluence of lambda-calculus with conditional rewriting
[{"from": "human", "value": "I am writing a research paper on a idea On the confluence of lambda-calculus with conditional rewriting"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The confluence of untyped @l-calculus with unconditional rewriting is now ll un- derstood. ,  investigate the confluence of @l-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Muller and Dougherty for unconditional rewriting. Two cases are considered, whether @b-reduction is allod or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing @b-reduction to akly normalizing @b-reduction.  also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second,  go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules."}]