formal languages - Z into Isabelle -

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i trying input , prove z specifications in isabelle.

say have vending machine specification written in latex format: 

\begin{zed}     price:\nat     \end{zed}  \begin{schema}{vmstate}     stock, takings: \nat     \end{schema}  \begin{schema}{vm\_operation}     \delta vmstate \\     cash\_tendered?, cash\_refunded!: \nat \\     bars\_delivered! : \nat     \end{schema}  \begin{schema}{exact\_cash}     cash\_tendered?: \nat     \where     cash\_tendered? = price     \end{schema}

i don't know if should put schema's lemmas or functions?

this have far:

theory vendingmachine imports main fact "~~/src/hol/hoare/hoare_logic"  begin type_synonym price = nat  type_synonym stock = nat  type_synonym takings = nat  type_synonym cash_tendered = nat  function exact_cash "(cash_tendered:nat)" cash_tendered ≡ price; end

the type synonyms work fine when exact cash schema have translated exact_cash functions keep getting errors.

so in summary know how input schema's isabelle.

some people developed frameworks z-specifications in isabelle/hol (other link) decade ago. (as far know, not maintained anymore – maybe can still of you.)

usually, z-specifications can rewritten tla specifications quite easily. so, try use actively maintained hol-tla-session of isabelle.

but let's first stick common isabelle/hol.

encoding z-specification fragment in plain isabelle/hol like:

theory vendingmachine imports   main begin  --"record datatype state variables" record vmstate =   stock :: nat   takings :: nat  --"a vending machine parameterized on price constant" locale vendingmachine = fixes price :: nat begin  definition vm_operation ::   "vmstate ⇒ vmstate ⇒ nat ⇒ nat ⇒ nat ⇒ bool" "vm_operation vmstate vmstate' cash_tendered cash_refunded bars_delivered ≡   true" --"todo: specify predicate"  definition exact_cash ::   "nat ⇒ bool" "exact_cash cash_tendered ≡   cash_tendered = price"  end  end

notice dropped distinction between in- , output variables. delta-variable vmstate in vm_operation split vmstate , vmstate'.

to work such specification, need more auxiliary definitions. instance, state space of specification defined inductive predicate like, e.g.:

inductive_set state_space :: "vmstate set"    init: "⦇ stock = 10, takings = 0 ⦈ ∈ state_space"     --"some initial state sake of meaningful definition...." | step: "vmstate ∈ state_space ∧ (∃ cash_tendered cash_refunded bars_delivered .    vm_operation vmstate vmstate' cash_tendered cash_refunded bars_delivered) ⟹ vmstate' ∈ state_space"

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