Re: [isabelle] HOLCF equality

On 07/09/2012 05:45 PM, Brian Huffman wrote:
On Sat, Jul 7, 2012 at 6:04 AM, Christian Sternagel
<c-sterna at> wrote:
Dear all,

is there already something like Haskell's "Eq" typeclass for HOLCF (which
seems to be neccessariy/convenient to formalize typical Haskell functions).
If not, are there any other reasons than lack of time?

A library with class "Eq" and other classes from Haskell would
certainly be useful, and I don't think it would take much time to

I think the main reason I never implemented it is I could never decide
on the details: what to name the functions, what syntax to provide,
what axioms to use, which classes to provide, etc.

- Brian

I am currently using

class eq =
  fixes eq :: "'a::pcpo → 'a → tr"
  assumes equals_strict [simp]:
    "eq⋅x⋅⊥ = ⊥" "eq⋅⊥⋅y = ⊥"
    and eq_iff [iff]:
    "eq⋅x⋅y = TT ⟷ x ≠ ⊥ ∧ y ≠ ⊥ ∧ x = y"
    "eq⋅x⋅y = FF ⟷ x ≠ ⊥ ∧ y ≠ ⊥ ∧ x ≠ y"
    "eq⋅x⋅y = ⊥ ⟷ x = ⊥ ∨ y = ⊥"

but did not think much about the details ;).

Maybe something like a theory for standard Haskell functions could be placed where everybody can browse and contribute? (I am currently mainly defining very basic list functions and proving basic properties about them.)



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