Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Type-based model checking algorithms for higher-order recursion schemes have recently emerged as a promising approach to the verification of functional programs.  introduce  pattern-matching recursion schemes  (PMRS) as an accurate model of computation for functional programs that manipulate algebraic data-types. PMRS are a natural extension of higher-order recursion schemes that incorporate pattern-matching in the defining rules.    is concerned with the following (undecidable) verification problem: given a correctness property φ, a functional program ℘ ( qua  PMRS) and a regular input set ℑ, does every term that is reachable from ℑ under rewriting by ℘ satisfy φ? To solve the PMRS verification problem,  present a sound  semi-algorithm  which is based on model-checking and counterexample guided abstraction refinement. Given a no-instance of the verification problem, the method is guaranteed to terminate.   From an order- n  PMRS and an input set generated by a regular tree grammar, our method constructs an order- n ak  PMRS which over-approximates  only  the first-order pattern-matching behaviour, whilst remaining completely faithful to the higher-order control flow. Using a variation of Kobayashi's type-based approach,  show that the (trivial automaton) model-checking problem for ak PMRS is decidable. When a violation of the property is detected in the abstraction which does not correspond to a violation in the model, the abstraction is automatically refined by `unfolding' the pattern-matching rules in the program to give successively more and more accurate ak PMRS models.
['C.-H. Luke Ong', 'Steven J. Ramsay']
I am writing a research paper on a idea Verifying higher-order functional programs with pattern-matching algebraic data types
[{"from": "human", "value": "I am writing a research paper on a idea Verifying higher-order functional programs with pattern-matching algebraic data types"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Type-based model checking algorithms for higher-order recursion schemes have recently emerged as a promising approach to the verification of functional programs.  introduce  pattern-matching recursion schemes  (PMRS) as an accurate model of computation for functional programs that manipulate algebraic data-types. PMRS are a natural extension of higher-order recursion schemes that incorporate pattern-matching in the defining rules.    is concerned with the following (undecidable) verification problem: given a correctness property \u03c6, a functional program \u2118 ( qua  PMRS) and a regular input set \u2111, does every term that is reachable from \u2111 under rewriting by \u2118 satisfy \u03c6? To solve the PMRS verification problem,  present a sound  semi-algorithm  which is based on model-checking and counterexample guided abstraction refinement. Given a no-instance of the verification problem, the method is guaranteed to terminate.   From an order- n  PMRS and an input set generated by a regular tree grammar, our method constructs an order- n ak  PMRS which over-approximates  only  the first-order pattern-matching behaviour, whilst remaining completely faithful to the higher-order control flow. Using a variation of Kobayashi's type-based approach,  show that the (trivial automaton) model-checking problem for ak PMRS is decidable. When a violation of the property is detected in the abstraction which does not correspond to a violation in the model, the abstraction is automatically refined by `unfolding' the pattern-matching rules in the program to give successively more and more accurate ak PMRS models."}]