theory Advanced
imports Base FirstSteps
begin

(*<*)
setup{*
open_file_with_prelude 
  "Advanced_Code.thy"
  ["theory General", "imports Base FirstSteps", "begin"]
*}
(*>*)


chapter {* Advanced Isabelle *}

text {*
  TBD
*}

section {* Theories\label{sec:theories} (TBD) *}

text {*
  Theories are the most fundamental building blocks in Isabelle. They 
  contain definitions, syntax declarations, axioms, proofs etc. If a definition
  is stated, it must be stored in a theory in order to be usable later
  on. Similar with proofs: once a proof is finished, the proved theorem
  needs to be stored in the theorem database of the theory in order to
  be usable. All relevant data of a theort can be querried as follows.

  \begin{isabelle}
  \isacommand{print\_theory}\\
  @{text "> names: Pure Code_Generator HOL \<dots>"}\\
  @{text "> classes: Inf < type \<dots>"}\\
  @{text "> default sort: type"}\\
  @{text "> syntactic types: #prop \<dots>"}\\
  @{text "> logical types: 'a \<times> 'b \<dots>"}\\
  @{text "> type arities: * :: (random, random) random \<dots>"}\\
  @{text "> logical constants: == :: 'a \<Rightarrow> 'a \<Rightarrow> prop \<dots>"}\\
  @{text "> abbreviations: \<dots>"}\\
  @{text "> axioms: \<dots>"}\\
  @{text "> oracles: \<dots>"}\\
  @{text "> definitions: \<dots>"}\\
  @{text "> theorems: \<dots>"}
  \end{isabelle}

  \begin{center}
  \begin{tikzpicture}
  \node[top color=white, bottom color=gray!30, draw=black!100, drop shadow] {A};
  \end{tikzpicture}
  \end{center}


  In contrast to an ordinary theory, which simply consists of a type
  signature, as well as tables for constants, axioms and theorems, a local
  theory contains additional context information, such as locally fixed
  variables and local assumptions that may be used by the package. The type
  @{ML_type local_theory} is identical to the type of \emph{proof contexts}
  @{ML_type "Proof.context"}, although not every proof context constitutes a
  valid local theory.

  @{ML "Context.>> o Context.map_theory"}

  \footnote{\bf FIXME: list append in merge operations can cause 
  exponential blowups.}
*}

section {* Setups (TBD) *}

text {*
  @{ML Sign.declare_const}

  In the previous section we used \isacommand{setup} in order to make
  a theorem attribute known to Isabelle. What happens behind the scenes
  is that \isacommand{setup} expects a function of type 
  @{ML_type "theory -> theory"}: the input theory is the current theory and the 
  output the theory where the theory attribute has been stored.
  
  This is a fundamental principle in Isabelle. A similar situation occurs 
  for example with declaring constants. The function that declares a 
  constant on the ML-level is @{ML_ind  add_consts_i in Sign}. 
  If you write\footnote{Recall that ML-code  needs to be 
  enclosed in \isacommand{ML}~@{text "\<verbopen> \<dots> \<verbclose>"}.} 
*}  

ML{*Sign.add_consts_i [(@{binding "BAR"}, @{typ "nat"}, NoSyn)] @{theory} *}

text {*
  for declaring the constant @{text "BAR"} with type @{typ nat} and 
  run the code, then you indeed obtain a theory as result. But if you 
  query the constant on the Isabelle level using the command \isacommand{term}

  \begin{isabelle}
  \isacommand{term}~@{text [quotes] "BAR"}\\
  @{text "> \"BAR\" :: \"'a\""}
  \end{isabelle}

  you do not obtain a constant of type @{typ nat}, but a free variable (printed in 
  blue) of polymorphic type. The problem is that the ML-expression above did 
  not register the declaration with the current theory. This is what the command
  \isacommand{setup} is for. The constant is properly declared with
*}

setup %gray {* Sign.add_consts_i [(@{binding "BAR"}, @{typ "nat"}, NoSyn)] *}

text {* 
  Now 
  
  \begin{isabelle}
  \isacommand{term}~@{text [quotes] "BAR"}\\
  @{text "> \"BAR\" :: \"nat\""}
  \end{isabelle}

  returns a (black) constant with the type @{typ nat}.

  A similar command is \isacommand{local\_setup}, which expects a function
  of type @{ML_type "local_theory -> local_theory"}. Later on we will also
  use the commands \isacommand{method\_setup} for installing methods in the
  current theory and \isacommand{simproc\_setup} for adding new simprocs to
  the current simpset.
*}

section {* Contexts (TBD) *}

section {* Local Theories (TBD) *}

text {*
  @{ML_ind "Local_Theory.declaration"}
*}

(*
setup {*
 Sign.add_consts_i [(Binding"bar", @{typ "nat"},NoSyn)] 
*}
lemma "bar = (1::nat)"
  oops

setup {*   
  Sign.add_consts_i [("foo", @{typ "nat"},NoSyn)] 
 #> PureThy.add_defs false [((@{binding "foo_def"}, 
       Logic.mk_equals (Const ("FirstSteps.foo", @{typ "nat"}), @{term "1::nat"})), [])] 
 #> snd
*}
*)
(*
lemma "foo = (1::nat)"
  apply(simp add: foo_def)
  done

thm foo_def
*)

section {* Morphisms (TBD) *}

text {*
  Morphisms are arbitrary transformations over terms, types, theorems and bindings.
  They can be constructed using the function @{ML_ind morphism in Morphism},
  which expects a record with functions of type

  \begin{isabelle}
  \begin{tabular}{rl}
  @{text "binding:"} & @{text "binding -> binding"}\\
  @{text "typ:"}     & @{text "typ -> typ"}\\
  @{text "term:"}    & @{text "term -> term"}\\
  @{text "fact:"}    & @{text "thm list -> thm list"}
  \end{tabular}
  \end{isabelle}

  The simplest morphism is the  @{ML_ind identity in Morphism}-morphism defined as
*}

ML{*val identity = Morphism.morphism {binding = I, typ = I, term = I, fact = I}*}
  
text {*
  Morphisms can be composed with the function @{ML_ind "$>" in Morphism}
*}

ML{*fun trm_phi (Free (x, T)) = Var ((x, 0), T) 
  | trm_phi (Abs (x, T, t)) = Abs (x, T, trm_phi t)
  | trm_phi (t $ s) = (trm_phi t) $ (trm_phi s)
  | trm_phi t = t*}

ML{*val phi = Morphism.term_morphism trm_phi*}

ML{*Morphism.term phi @{term "P x y"}*}

text {*
  @{ML_ind term_morphism in Morphism}

  @{ML_ind term in Morphism},
  @{ML_ind thm in Morphism}

  \begin{readmore}
  Morphisms are implemented in the file @{ML_file "Pure/morphism.ML"}.
  \end{readmore}
*}

section {* Misc (TBD) *}

ML {*Datatype.get_info @{theory} "List.list"*}

text {* 
FIXME: association lists:
@{ML_file "Pure/General/alist.ML"}

FIXME: calling the ML-compiler

*}

section {* Managing Name Spaces (TBD) *}

ML {* Sign.intern_type @{theory} "list" *}
ML {* Sign.intern_const @{theory} "prod_fun" *}


text {* 
  @{ML_ind "Binding.str_of"} returns the string with markup;
  @{ML_ind "Binding.name_of"} returns the string without markup

  @{ML_ind "Binding.conceal"} 
*}

section {* Concurrency (TBD) *}

text {*
  @{ML_ind prove_future in Goal}
  @{ML_ind future_result in Goal}
  @{ML_ind fork_pri in Future}
*}

section {* Summary *}

text {*
  TBD
*}

end