theory Advanced
imports Base First_Steps
begin
chapter \<open>Advanced Isabelle\label{chp:advanced}\<close>
text \<open>
\begin{flushright}
{\em All things are difficult before they are easy.} \\[1ex]
proverb\\[2ex]
{\em Programming is not just an act of telling a computer what
to do: it is also an act of telling other programmers what you
wished the computer to do. Both are important, and the latter
deserves care.}\\[1ex]
---Andrew Morton, Linux Kernel mailinglist, 13 March 2012
\end{flushright}
\medskip
While terms, types and theorems are the most basic data structures in
Isabelle, there are a number of layers built on top of them. Most of these
layers are concerned with storing and manipulating data. Handling them
properly is an essential skill for programming on the ML-level of Isabelle.
The most basic layer are theories. They contain global data and
can be seen as the ``long-term memory'' of Isabelle. There is usually only
one theory active at each moment. Proof contexts and local theories, on the
other hand, store local data for a task at hand. They act like the
``short-term memory'' and there can be many of them that are active in
parallel.
\<close>
section \<open>Theories\label{sec:theories}\<close>
text \<open>
Theories, as said above, are the most basic layer of abstraction in
Isabelle. They record information about definitions, syntax declarations, axioms,
theorems and much more. For example, if a definition is made, 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 theory can be queried with the
Isabelle command \isacommand{print\_theory}.
\begin{isabelle}
\isacommand{print\_theory}\\
\<open>> names: Pure Code_Generator HOL \<dots>\<close>\\
\<open>> classes: Inf < type \<dots>\<close>\\
\<open>> default sort: type\<close>\\
\<open>> syntactic types: #prop \<dots>\<close>\\
\<open>> logical types: 'a \<times> 'b \<dots>\<close>\\
\<open>> type arities: * :: (random, random) random \<dots>\<close>\\
\<open>> logical constants: == :: 'a \<Rightarrow> 'a \<Rightarrow> prop \<dots>\<close>\\
\<open>> abbreviations: \<dots>\<close>\\
\<open>> axioms: \<dots>\<close>\\
\<open>> oracles: \<dots>\<close>\\
\<open>> definitions: \<dots>\<close>\\
\<open>> theorems: \<dots>\<close>
\end{isabelle}
Functions acting on theories often end with the suffix \<open>_global\<close>,
for example the function @{ML read_term_global in Syntax} in the structure
@{ML_structure Syntax}. The reason is to set them syntactically apart from
functions acting on contexts or local theories, which will be discussed in
the next sections. There is a tendency amongst Isabelle developers to prefer
``non-global'' operations, because they have some advantages, as we will also
discuss later. However, some basic understanding of theories is still necessary
for effective Isabelle programming.
An important Isabelle command with theories is \isacommand{setup}. In the
previous chapters we used it already to make a theorem attribute known
to Isabelle and to register a theorem under a name. 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 attribute has been registered or the theorem has been
stored. This is a fundamental principle in Isabelle. A similar situation
arises with declaring a constant, which can be done on the ML-level with
function @{ML_ind declare_const in Sign} from the structure @{ML_structure
Sign}. To see how \isacommand{setup} works, consider the following code:
\<close>
ML %grayML\<open>let
val thy = @{theory}
val bar_const = ((@{binding "BAR"}, @{typ "nat"}), NoSyn)
in
Sign.declare_const @{context} bar_const thy
end\<close>
text \<open>
If you simply run this code\footnote{Recall that ML-code needs to be enclosed in
\isacommand{ML}~\<open>\<verbopen> \<dots> \<verbclose>\<close>.} with the
intention of declaring a constant \<open>BAR\<close> having type @{typ nat}, then
indeed you obtain a theory as result. But if you query the
constant on the Isabelle level using the command \isacommand{term}
\begin{isabelle}
\isacommand{term}~\<open>BAR\<close>\\
\<open>> "BAR" :: "'a"\<close>
\end{isabelle}
you can see that you do \emph{not} obtain the expected 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
\<close>
setup %gray \<open>fn thy =>
let
val bar_const = ((@{binding "BAR"}, @{typ "nat"}), NoSyn)
val (_, thy') = Sign.declare_const @{context} bar_const thy
in
thy'
end\<close>
text \<open>
where the declaration is actually applied to the current theory and
\begin{isabelle}
\isacommand{term}~@{text [quotes] "BAR"}\\
\<open>> "BAR" :: "nat"\<close>
\end{isabelle}
now returns a (black) constant with the type @{typ nat}, as expected.
In a sense, \isacommand{setup} can be seen as a transaction that
takes the current theory \<open>thy\<close>, applies an operation, and
produces a new current theory \<open>thy'\<close>. This means that we have
to be careful to apply operations always to the most current theory,
not to a \emph{stale} one. Consider again the function inside the
\isacommand{setup}-command:
\begin{isabelle}
\begin{graybox}
\isacommand{setup}~\<open>\<verbopen>\<close> @{ML \<open>fn thy =>
let
val bar_const = ((@{binding "BAR"}, @{typ "nat"}), NoSyn)
val (_, thy') = Sign.declare_const @{context} bar_const thy
in
thy
end\<close>}~\<open>\<verbclose>\<close>\isanewline
\<open>> ERROR: "Stale theory encountered"\<close>
\end{graybox}
\end{isabelle}
This time we erroneously return the original theory \<open>thy\<close>, instead of
the modified one \<open>thy'\<close>. Such buggy code will always result into
a runtime error message about stale theories.
\begin{readmore}
Most of the functions about theories are implemented in
@{ML_file "Pure/theory.ML"} and @{ML_file "Pure/global_theory.ML"}.
\end{readmore}
\<close>
section \<open>Contexts\<close>
text \<open>
Contexts are arguably more important than theories, even though they only
contain ``short-term memory data''. The reason is that a vast number of
functions in Isabelle depend in one way or another on contexts. Even such
mundane operations like printing out a term make essential use of contexts.
For this consider the following contrived proof-snippet whose purpose is to
fix two variables:
\<close>
lemma "True"
proof -
ML_prf \<open>Variable.dest_fixes @{context}\<close>
fix x y
ML_prf \<open>Variable.dest_fixes @{context}\<close>(*<*)oops(*>*)
text \<open>
The interesting point is that we injected ML-code before and after
the variables are fixed. For this remember that ML-code inside a proof
needs to be enclosed inside \isacommand{ML\_prf}~\<open>\<verbopen> \<dots> \<verbclose>\<close>,
not \isacommand{ML}~\<open>\<verbopen> \<dots> \<verbclose>\<close>. The function
@{ML_ind dest_fixes in Variable} from the structure @{ML_structure Variable} takes
a context and returns all its currently fixed variable (names). That
means a context has a dataslot containing information about fixed variables.
The ML-antiquotation \<open>@{context}\<close> points to the context that is
active at that point of the theory. Consequently, in the first call to
@{ML dest_fixes in Variable} this dataslot is empty; in the second it is
filled with \<open>x\<close> and \<open>y\<close>. What is interesting is that contexts
can be stacked. For this consider the following proof fragment:
\<close>
lemma "True"
proof -
fix x y
{ fix z w
ML_prf \<open>Variable.dest_fixes @{context}\<close>
}
ML_prf \<open>Variable.dest_fixes @{context}\<close>(*<*)oops(*>*)
text \<open>
Here the first time we call @{ML dest_fixes in Variable} we have four fixes variables;
the second time we get only the fixes variables \<open>x\<close> and \<open>y\<close> as answer, since
\<open>z\<close> and \<open>w\<close> are not anymore in the scope of the context.
This means the curly-braces act on the Isabelle level as opening and closing statements
for a context. The above proof fragment corresponds roughly to the following ML-code
\<close>
ML %grayML\<open>val ctxt0 = @{context};
val ([x, y], ctxt1) = Variable.add_fixes ["x", "y"] ctxt0;
val ([z, w], ctxt2) = Variable.add_fixes ["z", "w"] ctxt1\<close>
text \<open>
where the function @{ML_ind add_fixes in Variable} fixes a list of variables
specified by strings. Let us come back to the point about printing terms. Consider
printing out the term \mbox{\<open>(x, y, z, w)\<close>} using our function @{ML_ind pretty_term}.
This function takes a term and a context as argument. Notice how the printing
of the term changes according to which context is used.
\begin{isabelle}
\begin{graybox}
@{ML \<open>let
val trm = @{term "(x, y, z, w)"}
in
pwriteln (Pretty.chunks
[ pretty_term ctxt0 trm,
pretty_term ctxt1 trm,
pretty_term ctxt2 trm ])
end\<close>}\\
\setlength{\fboxsep}{0mm}
\<open>>\<close>~\<open>(\<close>\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>x\<close>}}\<open>,\<close>~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>y\<close>}}\<open>,\<close>~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>z\<close>}}\<open>,\<close>~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>w\<close>}}\<open>)\<close>\\
\<open>>\<close>~\<open>(\<close>\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>x\<close>}}\<open>,\<close>~%
\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>y\<close>}}\<open>,\<close>~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>z\<close>}}\<open>,\<close>~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>w\<close>}}\<open>)\<close>\\
\<open>>\<close>~\<open>(\<close>\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>x\<close>}}\<open>,\<close>~%
\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>y\<close>}}\<open>,\<close>~%
\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>z\<close>}}\<open>,\<close>~%
\colorbox{gray!20}{\raisebox{0mm}[3mm][1mm]{\<open>w\<close>}}\<open>)\<close>
\end{graybox}
\end{isabelle}
The term we are printing is in all three cases the same---a tuple containing
four free variables. As you can see, however, in case of @{ML \<open>ctxt0\<close>} all
variables are highlighted indicating a problem, while in case of @{ML \<open>ctxt1\<close>} \<open>x\<close> and \<open>y\<close> are printed as normal (blue) free
variables, but not \<open>z\<close> and \<open>w\<close>. In the last case all variables
are printed as expected. The point of this example is that the context
contains the information which variables are fixed, and designates all other
free variables as being alien or faulty. Therefore the highlighting.
While this seems like a minor detail, the concept of making the context aware
of fixed variables is actually quite useful. For example it prevents us from
fixing a variable twice
@{ML_response [gray, display]
\<open>@{context}
|> Variable.add_fixes ["x", "x"]\<close>
\<open>Duplicate fixed variable(s): "x"\<close>}
More importantly it also allows us to easily create fresh names for
fixed variables. For this you have to use the function @{ML_ind
variant_fixes in Variable} from the structure @{ML_structure Variable}.
@{ML_response [gray, display]
\<open>@{context}
|> Variable.variant_fixes ["y", "y", "z"]\<close>
\<open>(["y", "ya", "z"],\<dots>\<close>}
Now a fresh variant for the second occurence of \<open>y\<close> is created
avoiding any clash. In this way we can also create fresh free variables
that avoid any clashes with fixed variables. In Line~3 below we fix
the variable \<open>x\<close> in the context \<open>ctxt1\<close>. Next we want to
create two fresh variables of type @{typ nat} as variants of the
string @{text [quotes] "x"} (Lines 6 and 7).
@{ML_matchresult [display, gray, linenos]
\<open>let
val ctxt0 = @{context}
val (_, ctxt1) = Variable.add_fixes ["x"] ctxt0
val frees = replicate 2 ("x", @{typ nat})
in
(Variable.variant_frees ctxt0 [] frees,
Variable.variant_frees ctxt1 [] frees)
end\<close>
\<open>([("x", _), ("xa", _)],
[("xa", _), ("xb", _)])\<close>}
As you can see, if we create the fresh variables with the context \<open>ctxt0\<close>,
then we obtain \<open>x\<close> and \<open>xa\<close>; but in \<open>ctxt1\<close> we obtain \<open>xa\<close>
and \<open>xb\<close> avoiding \<open>x\<close>, which was fixed in this context.
Often one has the problem that given some terms, create fresh variables
avoiding any variable occurring in those terms. For this you can use the
function @{ML_ind declare_term in Variable} from the structure @{ML_structure Variable}.
@{ML_matchresult [gray, display]
\<open>let
val ctxt1 = Variable.declare_term @{term "(x, xa)"} @{context}
val frees = replicate 2 ("x", @{typ nat})
in
Variable.variant_frees ctxt1 [] frees
end\<close>
\<open>[("xb", _), ("xc", _)]\<close>}
The result is \<open>xb\<close> and \<open>xc\<close> for the names of the fresh
variables, since \<open>x\<close> and \<open>xa\<close> occur in the term we declared.
Note that @{ML_ind declare_term in Variable} does not fix the
variables; it just makes them ``known'' to the context. You can see
that if you print out a declared term.
\begin{isabelle}
\begin{graybox}
@{ML \<open>let
val trm = @{term "P x y z"}
val ctxt1 = Variable.declare_term trm @{context}
in
pwriteln (pretty_term ctxt1 trm)
end\<close>}\\
\setlength{\fboxsep}{0mm}
\<open>>\<close>~\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>P\<close>}}~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>x\<close>}}~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>y\<close>}}~%
\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>z\<close>}}
\end{graybox}
\end{isabelle}
All variables are highligted, indicating that they are not
fixed. However, declaring a term is helpful when parsing terms using
the function @{ML_ind read_term in Syntax} from the structure
@{ML_structure Syntax}. Consider the following code:
@{ML_response [gray, display]
\<open>let
val ctxt0 = @{context}
val ctxt1 = Variable.declare_term @{term "x::nat"} ctxt0
in
(Syntax.read_term ctxt0 "x",
Syntax.read_term ctxt1 "x")
end\<close>
\<open>(Free ("x", "'a"), Free ("x", "nat"))\<close>}
Parsing the string in the context \<open>ctxt0\<close> results in a free variable
with a default polymorphic type, but in case of \<open>ctxt1\<close> we obtain a
free variable of type @{typ nat} as previously declared. Which
type the parsed term receives depends upon the last declaration that
is made, as the next example illustrates.
@{ML_response [gray, display]
\<open>let
val ctxt1 = Variable.declare_term @{term "x::nat"} @{context}
val ctxt2 = Variable.declare_term @{term "x::int"} ctxt1
in
(Syntax.read_term ctxt1 "x",
Syntax.read_term ctxt2 "x")
end\<close>
\<open>(Free ("x", "nat"), Free ("x", "int"))\<close>}
The most useful feature of contexts is that one can export, or transfer,
terms and theorems between them. We show this first for terms.
\begin{isabelle}
\begin{graybox}
\begin{linenos}
@{ML \<open>let
val ctxt0 = @{context}
val (_, ctxt1) = Variable.add_fixes ["x", "y", "z"] ctxt0
val foo_trm = @{term "P x y z"}
in
singleton (Variable.export_terms ctxt1 ctxt0) foo_trm
|> pretty_term ctxt0
|> pwriteln
end\<close>}
\end{linenos}
\setlength{\fboxsep}{0mm}
\<open>>\<close>~\colorbox{gray!5}{\raisebox{0mm}[3mm][1mm]{\<open>P\<close>}}~%
\<open>?x ?y ?z\<close>
\end{graybox}
\end{isabelle}
In Line 3 we fix the variables @{term x}, @{term y} and @{term z} in
context \<open>ctxt1\<close>. The function @{ML_ind export_terms in
Variable} from the structure @{ML_structure Variable} can be used to transfer
terms between contexts. Transferring means to turn all (free)
variables that are fixed in one context, but not in the other, into
schematic variables. In our example, we are transferring the term
\<open>P x y z\<close> from context \<open>ctxt1\<close> to \<open>ctxt0\<close>,
which means @{term x}, @{term y} and @{term z} become schematic
variables (as can be seen by the leading question marks in the result).
Note that the variable \<open>P\<close> stays a free variable, since it not fixed in
\<open>ctxt1\<close>; it is even highlighed, because \<open>ctxt0\<close> does
not know about it. Note also that in Line 6 we had to use the
function @{ML_ind singleton}, because the function @{ML_ind
export_terms in Variable} normally works over lists of terms.
The case of transferring theorems is even more useful. The reason is
that the generalisation of fixed variables to schematic variables is
not trivial if done manually. For illustration purposes we use in the
following code the function @{ML_ind make_thm in Skip_Proof} from the
structure @{ML_structure Skip_Proof}. This function will turn an arbitray
term, in our case @{term "P x y z x y z"}, into a theorem (disregarding
whether it is actually provable).
@{ML_response [display, gray]
\<open>let
val thy = @{theory}
val ctxt0 = @{context}
val (_, ctxt1) = Variable.add_fixes ["P", "x", "y", "z"] ctxt0
val foo_thm = Skip_Proof.make_thm thy @{prop "P x y z x y z"}
in
singleton (Proof_Context.export ctxt1 ctxt0) foo_thm
end\<close>
\<open>?P ?x ?y ?z ?x ?y ?z\<close>}
Since we fixed all variables in \<open>ctxt1\<close>, in the exported
result all of them are schematic. The great point of contexts is
that exporting from one to another is not just restricted to
variables, but also works with assumptions. For this we can use the
function @{ML_ind export in Assumption} from the structure
@{ML_structure Assumption}. Consider the following code.
@{ML_response [display, gray, linenos]
\<open>let
val ctxt0 = @{context}
val ([eq], ctxt1) = Assumption.add_assumes [@{cprop "x \<equiv> y"}] ctxt0
val eq' = Thm.symmetric eq
in
Assumption.export false ctxt1 ctxt0 eq'
end\<close>
\<open>x \<equiv> y \<Longrightarrow> y \<equiv> x\<close>}
The function @{ML_ind add_assumes in Assumption} from the structure
@{ML_structure Assumption} adds the assumption \mbox{\<open>x \<equiv> y\<close>}
to the context \<open>ctxt1\<close> (Line 3). This function expects a list
of @{ML_type cterm}s and returns them as theorems, together with the
new context in which they are ``assumed''. In Line 4 we use the
function @{ML_ind symmetric in Thm} from the structure @{ML_structure
Thm} in order to obtain the symmetric version of the assumed
meta-equality. Now exporting the theorem \<open>eq'\<close> from \<open>ctxt1\<close> to \<open>ctxt0\<close> means @{term "y \<equiv> x"} will be prefixed with
the assumed theorem. The boolean flag in @{ML_ind export in
Assumption} indicates whether the assumptions should be marked with
the goal marker (see Section~\ref{sec:basictactics}). In normal
circumstances this is not necessary and so should be set to @{ML
false}. The result of the export is then the theorem \mbox{@{term
"x \<equiv> y \<Longrightarrow> y \<equiv> x"}}. As can be seen this is an easy way for obtaing
simple theorems. We will explain this in more detail in
Section~\ref{sec:structured}.
The function @{ML_ind export in Proof_Context} from the structure
@{ML_structure Proof_Context} combines both export functions from
@{ML_structure Variable} and @{ML_structure Assumption}. This can be seen
in the following example.
@{ML_response [display, gray]
\<open>let
val ctxt0 = @{context}
val ((fvs, [eq]), ctxt1) = ctxt0
|> Variable.add_fixes ["x", "y"]
||>> Assumption.add_assumes [@{cprop "x \<equiv> y"}]
val eq' = Thm.symmetric eq
in
Proof_Context.export ctxt1 ctxt0 [eq']
end\<close>
\<open>["?x \<equiv> ?y \<Longrightarrow> ?y \<equiv> ?x"]\<close>}
\<close>
text \<open>
\<close>
(*
ML %grayML{*Proof_Context.debug := true*}
ML %grayML{*Proof_Context.verbose := true*}
*)
(*
lemma "True"
proof -
{ -- "\<And>x. _"
fix x
have "B x" sorry
thm this
}
thm this
{ -- "A \<Longrightarrow> _"
assume A
have B sorry
thm this
}
thm this
{ -- "\<And>x. x = _ \<Longrightarrow> _"
def x \<equiv> a
have "B x" sorry
}
thm this
oops
*)
section \<open>Local Theories and Local Setups\label{sec:local} (TBD)\<close>
text \<open>
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 \<open>Context.>> o Context.map_theory\<close>}
@{ML_ind "Local_Theory.declaration"}
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.
\<close>
section \<open>Morphisms (TBD)\<close>
text \<open>
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}
\<open>binding:\<close> & \<open>binding -> binding\<close>\\
\<open>typ:\<close> & \<open>typ -> typ\<close>\\
\<open>term:\<close> & \<open>term -> term\<close>\\
\<open>fact:\<close> & \<open>thm list -> thm list\<close>
\end{tabular}
\end{isabelle}
The simplest morphism is the @{ML_ind identity in Morphism}-morphism defined as
\<close>
ML %grayML\<open>val identity = Morphism.morphism "" {binding = [], typ = [], term = [], fact = []}\<close>
text \<open>
Morphisms can be composed with the function @{ML_ind "$>" in Morphism}
\<close>
ML %grayML\<open>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\<close>
ML %grayML\<open>val phi = Morphism.term_morphism "foo" trm_phi\<close>
ML %grayML\<open>Morphism.term phi @{term "P x y"}\<close>
text \<open>
@{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}
\<close>
section \<open>Misc (TBD)\<close>
text \<open>
FIXME: association lists:
@{ML_file "Pure/General/alist.ML"}
FIXME: calling the ML-compiler
\<close>
section \<open>What Is In an Isabelle Name? (TBD)\<close>
text \<open>
On the ML-level of Isabelle, you often have to work with qualified names.
These are strings with some additional information, such as positional
information and qualifiers. Such qualified names can be generated with the
antiquotation \<open>@{binding \<dots>}\<close>. For example
@{ML_matchresult [display,gray]
\<open>@{binding "name"}\<close>
\<open>name\<close>}
An example where a qualified name is needed is the function
@{ML_ind define in Local_Theory}. This function is used below to define
the constant @{term "TrueConj"} as the conjunction @{term "True \<and> True"}.
\<close>
local_setup %gray \<open>
Local_Theory.define ((@{binding "TrueConj"}, NoSyn),
((@{binding "TrueConj_def"}, []), @{term "True \<and> True"})) #> snd\<close>
text \<open>
Now querying the definition you obtain:
\begin{isabelle}
\isacommand{thm}~\<open>TrueConj_def\<close>\\
\<open>> \<close>~@{thm TrueConj_def}
\end{isabelle}
\begin{readmore}
The basic operations on bindings are implemented in
@{ML_file "Pure/General/binding.ML"}.
\end{readmore}
\footnote{\bf FIXME give a better example why bindings are important}
\footnote{\bf FIXME give a pointer to \isacommand{local\_setup}; if not, then explain
why @{ML snd} is needed.}
\footnote{\bf FIXME: There should probably a separate section on binding, long-names
and sign.}
\<close>
ML \<open>Sign.intern_type @{theory} "list"\<close>
ML \<open>Sign.intern_const @{theory} "prod_fun"\<close>
text \<open>
\footnote{\bf FIXME: Explain the following better; maybe put in a separate
section and link with the comment in the antiquotation section.}
Occasionally you have to calculate what the ``base'' name of a given
constant is. For this you can use the function @{ML_ind Long_Name.base_name}. For example:
@{ML_matchresult [display,gray] \<open>Long_Name.base_name "List.list.Nil"\<close> \<open>"Nil"\<close>}
\begin{readmore}
Functions about naming are implemented in @{ML_file "Pure/General/name_space.ML"};
functions about signatures in @{ML_file "Pure/sign.ML"}.
\end{readmore}
\<close>
text \<open>
@{ML_ind "Binding.name_of"} returns the string without markup
@{ML_ind "Binding.concealed"}
\<close>
section \<open>Concurrency (TBD)\<close>
text \<open>
@{ML_ind prove_future in Goal}
@{ML_ind future_result in Goal}
\<close>
section \<open>Parse and Print Translations (TBD)\<close>
section \<open>Summary\<close>
text \<open>
TBD
\<close>
end