Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Consider the following problem: given a simply typed lambda term of Boolean type and of order r, does it normalize to "true"? A related problem is: given a term M of word type and of order r together with#R##N#a finite automaton D, does D accept the word represented by the normal form of M?  prove that these problems are n-EXPTIME complete for r=2n+2, and n-EXPSPACE complete for r=2n+3.#R##N##R##N#While the hardness part is relatively easy, the membership part is not so obvious; in particular, simply applying beta reduction does not work. Some preceding works employ semantic evaluation in the category of sets and functions, but it is not efficient enough for our purpose.#R##N##R##N# present an algorithm for the above type of problem that is a fine blend of beta reduction, Krivine abstract machine and semantic evaluation in a category based on preorders and order ideals, also known as the Scott model of linear logic. The semantic evaluation can also be presented as intersection type checking.
['Kazushige Terui']
I am writing a research paper on a idea Semantic Evaluation, Intersection Types and Complexity of Simply Typed Lambda Calculus
[{"from": "human", "value": "I am writing a research paper on a idea Semantic Evaluation, Intersection Types and Complexity of Simply Typed Lambda Calculus"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Consider the following problem: given a simply typed lambda term of Boolean type and of order r, does it normalize to \"true\"? A related problem is: given a term M of word type and of order r together with#R##N#a finite automaton D, does D accept the word represented by the normal form of M?  prove that these problems are n-EXPTIME complete for r=2n+2, and n-EXPSPACE complete for r=2n+3.#R##N##R##N#While the hardness part is relatively easy, the membership part is not so obvious; in particular, simply applying beta reduction does not work. Some preceding works employ semantic evaluation in the category of sets and functions, but it is not efficient enough for our purpose.#R##N##R##N# present an algorithm for the above type of problem that is a fine blend of beta reduction, Krivine abstract machine and semantic evaluation in a category based on preorders and order ideals, also known as the Scott model of linear logic. The semantic evaluation can also be presented as intersection type checking."}]