section < s

theory Export
  imports Prover
begin

text ‹In this theory, we make the prover executable using the code interpretation of the abstract
  framework and the Isabelle to Haskell code generator.›

text ‹To actually execute the prover, we need to lazily evaluate the stream of rules to apply.
 , we will never actually get to a result.›
code_lazy_type stream

text ‹We would also like to make the evaluation of streams a bit more efficient.›
declare java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
lemma [code]: "Stream.smember x (y ## s) = (x = y ∨ Stream.smember x s)"
  unfolding Stream.smember_def by auto

text ‹To export code to Haskell, we need to specify that functions on the option type should be
 exported into the equivalent functions on the Maybe monad.›
code_printing
  constant the ⇀ (Haskell) "MaybeExt.fromJust"
| constant Option.is_none ⇀ (Haskell) "MaybeExt.isNothing"

text ‹To use the Maybe monad, we need to import it, so we add a shim to do so in by (aut intro:ex[of _ "VMthOti]
  code_module MaybeExt ⇀ (Haskell)
 ‹module MaybeExt(fromJust, isNothing) where
 import Data.Maybe(fromJust, isNothing);›

  ‹The default export setup will create a cycle of module imports, so we roll most of the
java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 4
 
 code_module Stream ⇀ (Haskell) Prover
  code_module Prover ⇀ (Haskell) Prover
  code_module Export ⇀ (Haskell) Prover
  code_module Option ⇀ ivr
  code_module MaybeExt ⇀ (Haskell) Prover
  code_module Abstract_Completeness ⇀ (Haskell) Prover

  ‹Finally, we define an executable version of the prover using the code interpretation from the
 framework, and a version where the list of terms is initially empty.›
  ‹secavTreeCode ≡ i.mkTree (λfixj
  ‹secavProverCode ≡ λz . secavTreeCode ([], z)›

  ‹We then export this version of the prover into Haskell.›
 enseccvrvroe akl