Does anyone know any examples of the following? Proof developments about regular expressions (possibly extended with backreferences) in proof assistants (such as Coq). Programs in dependently-typed languages (such as Agda) about regular expressions. ...
PA6 : ∀{m n} -> m ≡ n -> n ≡ m is the axiom I am trying to solve and support, I've tried using a cong (from the core library) but am having troubles with the cong constructor PA6 = cong gets me nowhere, I know for cong I am required to supply a refl for equality and a type, but I'm, not sure what type I'm supposed to supply. Ideas? ...
I'm trying to encode some denotational semantics into Agda based on a program I wrote in Haskell. data Value = FunVal (Value -> Value) | PriVal Int | ConVal Id [Value] | Error String In Agda, the direct translation would be; data Value : Set where FunVal : (Value -> Value) -> Value PriVal : ℕ...
I'm trying to prove a simple lemma in Agda, which I think is true. If a vector has more than two elements, taking its head following taking the init is the same as taking its head immediately. I have formulated it as follows: lem-headInit : ∀{l} (xs : Vec ℕ (suc (suc l))) -> head (init xs) ≡ head xs lem-headIn...
On the Agda mailing list, Conor McBride asked: is there any way to get hold of operations like a putative trustFromJust :: Maybe x -> x which doesn't actually check for Just and Goes Wrong (in Milner's sense) if fed Nothing? Agda might prove Maybe a == Just1 a, and the intermediate constructor for the sum type could b...