src/HOL/Code_Generator.thy

Added unification case study (using new function package)

(*  ID:         $Id$
    Author:     Florian Haftmann, TU Muenchen
*)

header {* Setup of code generator tools *}

theory Code_Generator
imports HOL
uses "~~/src/HOL/Tools/recfun_codegen.ML"
begin

ML {*
structure HOL =
struct
  val thy = theory "HOL";
end;
*}  -- "belongs to theory HOL"

subsection {* SML code generator setup *}

types_code
  "bool"  ("bool")
attach (term_of) {*
fun term_of_bool b = if b then HOLogic.true_const else HOLogic.false_const;
*}
attach (test) {*
fun gen_bool i = one_of [false, true];
*}
  "prop"  ("bool")
attach (term_of) {*
fun term_of_prop b =
  HOLogic.mk_Trueprop (if b then HOLogic.true_const else HOLogic.false_const);
*}

consts_code
  "Trueprop" ("(_)")
  "True"    ("true")
  "False"   ("false")
  "Not"     ("Bool.not")
  "op |"    ("(_ orelse/ _)")
  "op &"    ("(_ andalso/ _)")
  "If"      ("(if _/ then _/ else _)")

setup {*
let

fun eq_codegen thy defs gr dep thyname b t =
    (case strip_comb t of
       (Const ("op =", Type (_, [Type ("fun", _), _])), _) => NONE
     | (Const ("op =", _), [t, u]) =>
          let
            val (gr', pt) = Codegen.invoke_codegen thy defs dep thyname false (gr, t);
            val (gr'', pu) = Codegen.invoke_codegen thy defs dep thyname false (gr', u);
            val (gr''', _) = Codegen.invoke_tycodegen thy defs dep thyname false (gr'', HOLogic.boolT)
          in
            SOME (gr''', Codegen.parens
              (Pretty.block [pt, Pretty.str " =", Pretty.brk 1, pu]))
          end
     | (t as Const ("op =", _), ts) => SOME (Codegen.invoke_codegen
         thy defs dep thyname b (gr, Codegen.eta_expand t ts 2))
     | _ => NONE);

in

Codegen.add_codegen "eq_codegen" eq_codegen
#> RecfunCodegen.setup

end
*}

text {* Evaluation *}

method_setup evaluation = {*
let

fun evaluation_tac i = Tactical.PRIMITIVE (Conv.fconv_rule
  (Conv.goals_conv (equal i) Codegen.evaluation_conv));

in Method.no_args (Method.SIMPLE_METHOD' (evaluation_tac THEN' rtac TrueI)) end
*} "solve goal by evaluation"


subsection {* Generic code generator setup *}

text {* operational equality for code generation *}

class eq (attach "op =") = type


text {* using built-in Haskell equality *}

code_class eq
  (Haskell "Eq" where "op =" \<equiv> "(==)")

code_const "op ="
  (Haskell infixl 4 "==")


text {* type bool *}

code_datatype True False

lemma [code func]:
  shows "(False \<and> x) = False"
    and "(True \<and> x) = x"
    and "(x \<and> False) = False"
    and "(x \<and> True) = x" by simp_all

lemma [code func]:
  shows "(False \<or> x) = x"
    and "(True \<or> x) = True"
    and "(x \<or> False) = x"
    and "(x \<or> True) = True" by simp_all

lemma [code func]:
  shows "(\<not> True) = False"
    and "(\<not> False) = True" by (rule HOL.simp_thms)+

lemmas [code] = imp_conv_disj

lemmas [code func] = if_True if_False

instance bool :: eq ..

lemma [code func]:
  shows "True = P \<longleftrightarrow> P"
    and "False = P \<longleftrightarrow> \<not> P"
    and "P = True \<longleftrightarrow> P"
    and "P = False \<longleftrightarrow> \<not> P" by simp_all

code_type bool
  (SML "bool")
  (OCaml "bool")
  (Haskell "Bool")

code_instance bool :: eq
  (Haskell -)

code_const "op = \<Colon> bool \<Rightarrow> bool \<Rightarrow> bool"
  (Haskell infixl 4 "==")

code_const True and False and Not and "op &" and "op |" and If
  (SML "true" and "false" and "not"
    and infixl 1 "andalso" and infixl 0 "orelse"
    and "!(if (_)/ then (_)/ else (_))")
  (OCaml "true" and "false" and "not"
    and infixl 4 "&&" and infixl 2 "||"
    and "!(if (_)/ then (_)/ else (_))")
  (Haskell "True" and "False" and "not"
    and infixl 3 "&&" and infixl 2 "||"
    and "!(if (_)/ then (_)/ else (_))")

code_reserved SML
  bool true false not

code_reserved OCaml
  bool true false not


text {* type prop *}

code_datatype Trueprop "prop"


text {* type itself *}

code_datatype "TYPE('a)"


text {* code generation for undefined as exception *}

code_const undefined
  (SML "raise/ Fail/ \"undefined\"")
  (OCaml "failwith/ \"undefined\"")
  (Haskell "error/ \"undefined\"")

code_reserved SML Fail
code_reserved OCaml failwith


subsection {* Evaluation oracle *}

oracle eval_oracle ("term") = {* fn thy => fn t => 
  if CodegenPackage.satisfies thy (HOLogic.dest_Trueprop t) [] 
  then t
  else HOLogic.Trueprop $ HOLogic.true_const (*dummy*)
*}

method_setup eval = {*
let
  fun eval_tac thy = 
    SUBGOAL (fn (t, i) => rtac (eval_oracle thy t) i)
in 
  Method.ctxt_args (fn ctxt => 
    Method.SIMPLE_METHOD' (eval_tac (ProofContext.theory_of ctxt)))
end
*} "solve goal by evaluation"


subsection {* Normalization by evaluation *}

method_setup normalization = {*
let
  fun normalization_tac i = Tactical.PRIMITIVE (Conv.fconv_rule
    (Conv.goals_conv (equal i) (HOLogic.Trueprop_conv
      NBE.normalization_conv)));
in
  Method.no_args (Method.SIMPLE_METHOD' (normalization_tac THEN' resolve_tac [TrueI, refl]))
end
*} "solve goal by normalization"


text {* lazy @{const If} *}

definition
  if_delayed :: "bool \<Rightarrow> (bool \<Rightarrow> 'a) \<Rightarrow> (bool \<Rightarrow> 'a) \<Rightarrow> 'a" where
  [code func del]: "if_delayed b f g = (if b then f True else g False)"

lemma [code func]:
  shows "if_delayed True f g = f True"
    and "if_delayed False f g = g False"
  unfolding if_delayed_def by simp_all

lemma [normal pre, symmetric, normal post]:
  "(if b then x else y) = if_delayed b (\<lambda>_. x) (\<lambda>_. y)"
  unfolding if_delayed_def ..

hide (open) const if_delayed

end