isabelle-cookbook: comparison CookBook/FirstSteps.thy

equal deleted inserted replaced

-:d3fcc1a0272c
+:90bee31628dc
 \isacommand{imports} Main\\
 \isacommand{begin}\\
 \ldots
 \end{tabular}
 \end{center}
+We also generally assume you are working with HOL. The given examples might
+need to be adapted slightly if you work in a different logic.
 *}
 section {* Including ML-Code *}
 Like normal Isabelle proof scripts, \isacommand{ML}-commands can be
 evaluated by using the advance and undo buttons of your Isabelle
 environment. The code inside the \isacommand{ML}-command can also contain
 value and function bindings, and even those can be undone when the proof
-script is retracted. As mentioned earlier, we will drop the
+script is retracted. As mentioned in the Introduction, we will drop the
 \isacommand{ML}~@{text "\<verbopen> \<dots> \<verbclose>"} scaffolding whenever we
 show code. The lines prefixed with @{text [quotes] ">"} are not part of the
 code, rather they indicate what the response is when the code is evaluated.
 Once a portion of code is relatively stable, you usually want to export it
 ML{*fun str_of_cterms ctxt ts =
 commas (map (str_of_cterm ctxt) ts)*}
 text {*
 The easiest way to get the string of a theorem is to transform it
-into a @{ML_type cterm} using the function @{ML crep_thm}.
+into a @{ML_type cterm} using the function @{ML crep_thm}. Theorems
-*}
+also include schematic variables, such as @{text "?P"}, @{text "?Q"}
+and so on. In order to improve the readability of theorems we convert
-ML{*fun str_of_thm ctxt thm =
+these schematic variables into free variables using the
-let
+function @{ML Variable.import_thms}.
-val {prop, ...} = crep_thm thm
+*}
-in
-str_of_cterm ctxt prop
+ML{*fun no_vars ctxt thm =
-end*}
+let
+val ((_, [thm']), _) = Variable.import_thms true [thm] ctxt
+in
+thm'
+end
+fun str_of_thm ctxt thm =
+let
+val {prop, ...} = crep_thm (no_vars ctxt thm)
+in
+str_of_cterm ctxt prop
+end*}
 text {*
 Again the function @{ML commas} helps with printing more than one theorem.
 *}
 ML{*fun str_of_thms ctxt thms =
 commas (map (str_of_thm ctxt) thms)*}
 section {* Combinators\label{sec:combinators} *}
 text {*
 For beginners perhaps the most puzzling parts in the existing code of Isabelle are
 function that extracts the theorem names stored in a simpset.
 *}
 ML{*fun get_thm_names_from_ss simpset =
 let
-val ({rules,...}, _) = MetaSimplifier.rep_ss simpset
+val {simps,...} = MetaSimplifier.dest_ss simpset
 in
-map #name (Net.entries rules)
+map #1 simps
 end*}
 text {*
-The function @{ML rep_ss in MetaSimplifier} returns a record containing all
+The function @{ML dest_ss in MetaSimplifier} returns a record containing all
-information about the simpset. The rules of a simpset are stored in a
+information stored in the simpset. We are only interested in the You can now use @{ML get_thm_names_from_ss} to obtain all names of theorems stored
-\emph{discrimination net} (a data structure for fast indexing). From this
+in the current simpset. This simpset can be referred to using the antiquotation
-net you can extract the entries using the function @{ML Net.entries}.
-You can now use @{ML get_thm_names_from_ss} to obtain all names of theorems stored
-in the current simpset---this simpset can be referred to using the antiquotation
 @{text "@{simpset}"}.
 @{ML_response_fake [display,gray]
 "get_thm_names_from_ss @{simpset}"
 "[\"Nat.of_nat_eq_id\", \"Int.of_int_eq_id\", \"Nat.One_nat_def\", \<dots>]"}
-\begin{readmore}
+Again, this way or referencing simpsets makes you independent from additions
-The infrastructure for simpsets is implemented in @{ML_file "Pure/meta_simplifier.ML"}
+of lemmas to the simpset by the user that potentially cause loops.
-and @{ML_file "Pure/simplifier.ML"}. Discrimination nets are implemented
-in @{ML_file "Pure/net.ML"}.
-\end{readmore}
 While antiquotations have many applications, they were originally introduced in order
 to avoid explicit bindings for theorems such as:
 *}
 ML{*val allI = thm "allI" *}
 text {*
 These bindings are difficult to maintain and also can be accidentally
-overwritten by the user. This often breakes Isabelle
+overwritten by the user. This often broke Isabelle
 packages. Antiquotations solve this problem, since they are ``linked''
 statically at compile-time.  However, this static linkage also limits their
 usefulness in cases where data needs to be build up dynamically. In the
 course of this chapter you will learn more about these antiquotations:
 they can simplify Isabelle programming since one can directly access all
 kinds of logical elements from th ML-level.
 *}
 section {* Terms and Types *}
 text {*
 Terms are described in detail in \isccite{sec:terms}. Their
 definition and many useful operations are implemented in @{ML_file "Pure/term.ML"}.
 \end{readmore}
 Sometimes the internal representation of terms can be surprisingly different
-from what you see at the user level, because the layers of
+from what you see at the user-level, because the layers of
 parsing/type-checking/pretty printing can be quite elaborate.
 \begin{exercise}
 Look at the internal term representation of the following terms, and
 find out why they are represented like this:
 in @{ML_file "Pure/type.ML"}.
 \end{readmore}
 *}
-section {* Constructing Terms and Types Manually *}
+section {* Constructing Terms and Types Manually\label{sec:terms_types_manually} *}
 text {*
 While antiquotations are very convenient for constructing terms, they can
 only construct fixed terms (remember they are ``linked'' at compile-time).
 However, you often need to construct terms dynamically. For example, a
 To see this apply @{text "@{term S}"}, @{text "@{term T}"} and @{text "@{typ nat}"}
 to both functions. With @{ML make_imp} we obtain the intended term involving
 the given arguments
 @{ML_response [display,gray] "make_imp @{term S} @{term T} @{typ nat}"
 "Const \<dots> $
 Abs (\"x\", Type (\"nat\",[]),
-Const \<dots> $ (Free (\"S\",\<dots>) $ \<dots>) $
+Const \<dots> $ (Free (\"S\",\<dots>) $ \<dots>) $ (Free (\"T\",\<dots>) $ \<dots>))"}
-(Free (\"T\",\<dots>) $ \<dots>))"}
 whereas with @{ML make_wrong_imp} we obtain a term involving the @{term "P"}
 and @{text "Q"} from the antiquotation.
 @{ML_response [display,gray] "make_wrong_imp @{term S} @{term T} @{typ nat}"
 "Const \<dots> $
 Abs (\"x\", \<dots>,
 Const \<dots> $ (Const \<dots> $ (Free (\"P\",\<dots>) $ \<dots>)) $
 (Const \<dots> $ (Free (\"Q\",\<dots>) $ \<dots>)))"}
 Although types of terms can often be inferred, there are many
 situations where you need to construct types manually, especially
 when defining constants. For example the function returning a function
 type is as follows:
 *}
-ML{*fun make_fun_type tau1 tau2 = Type ("fun",[tau1,tau2]) *}
+ML{*fun make_fun_type tau1 tau2 = Type ("fun", [tau1, tau2]) *}
-text {* This can be equally written as: *}
+text {* This can be equally written with the combinator @{ML "-->"} as: *}
 ML{*fun make_fun_type tau1 tau2 = tau1 --> tau2 *}
 text {*
 A handy function for manipulating terms is @{ML map_types}: it takes a
-function and applies it to every type in the term. You can, for example,
+function and applies it to every type in a term. You can, for example,
 change every @{typ nat} in a term into an @{typ int} using the function:
 *}
 ML{*fun nat_to_int t =
 (case t of
 | is_nil_or_all _ = false *}
 text {*
 Occasional you have to calculate what the ``base'' name of a given
 constant is. For this you can use the function @{ML Sign.extern_const} or
-@{ML Sign.base_name}. For example:
+@{ML Long_Name.base_name}. For example:
 @{ML_response [display,gray] "Sign.extern_const @{theory} \"List.list.Nil\"" "\"Nil\""}
 The difference between both functions is that @{ML extern_const in Sign} returns
-the smallest name that is still unique, whereas @{ML base_name in Sign} always
+the smallest name that is still unique, whereas @{ML base_name in Long_Name} always
 strips off all qualifiers.
 \begin{readmore}
-FIXME
+Functions about naming are implemented in @{ML_file "Pure/General/name_space.ML"};
+functions about signatures in @{ML_file "Pure/sign.ML"}.
 \end{readmore}
 *}
 section {* Type-Checking *}
 in
 cterm_of @{theory}
 (Const (@{const_name plus}, natT --> natT --> natT) $ zero $ zero)
 end" "0 + 0"}
+In Isabelle also types need can be certified. For example, you obtain
+the certified type for the Isablle type @{typ "nat \<Rightarrow> bool"} on the ML-level
+as follows:
+@{ML_response_fake [display,gray]
+"ctyp_of @{theory} (@{typ nat} --> @{typ bool})"
+"nat \<Rightarrow> bool"}
+\begin{readmore}
+For functions related to @{ML_type cterm}s and @{ML_type ctyp}s see
+the file @{ML_file "Pure/thm.ML"}.
+\end{readmore}
 \begin{exercise}
 Check that the function defined in Exercise~\ref{fun:revsum} returns a
 result that type-checks.
 \end{exercise}
 Instead of giving explicitly the type for the constant @{text "plus"} and the free
 variable @{text "x"}, the type-inference filles in the missing information.
 \begin{readmore}
 See @{ML_file "Pure/Syntax/syntax.ML"} where more functions about reading,
-checking and pretty-printing of terms are defined.
+checking and pretty-printing of terms are defined. Fuctions related to the
+type inference are implemented in @{ML_file "Pure/type.ML"} and
+@{ML_file "Pure/type_infer.ML"}.
 \end{readmore}
+(FIXME: say something about sorts)
 *}
 section {* Theorems *}
 "[symmetric]"} and so on. Such attributes are \emph{neither} tags \emph{nor} flags
 annotated to theorems, but functions that do further processing once a
 theorem is proven. In particular, it is not possible to find out
 what are all theorems that have a given attribute in common, unless of course
 the function behind the attribute stores the theorems in a retrivable
-datastructure. This can be easily done by the recipe described in
+datastructure.
-\ref{rec:named}.
 If you want to print out all currently known attributes a theorem
 can have, you can use the function:
 @{ML_response_fake [display,gray] "Attrib.print_attributes @{theory}"
 text {*
 where the function @{ML "Thm.rule_attribute"} expects a function taking a
 context (which we ignore in the code above) and a theorem (@{text thm}), and
 returns another theorem (namely @{text thm} resolved with the lemma
 @{thm [source] sym}: @{thm sym[no_vars]}). The function @{ML "Thm.rule_attribute"} then returns
-an attribute (of type @{ML_type "attribute"}).
+an attribute.
 Before we can use the attribute, we need to set it up. This can be done
 using the function @{ML Attrib.add_attributes} as follows.
 *}
 setup {*
 Attrib.add_attributes
-[("my_sym", Attrib.no_args my_symmetric, "applying the sym rule")]
+[("my_sym", Attrib.no_args my_symmetric, "applying the sym rule")] *}
-*}
 text {*
 The attribute does not expect any further arguments (unlike @{text "[OF
 \<dots>]"}, for example, which can take a list of theorems as argument). Therefore
 we use the function @{ML Attrib.no_args}. Later on we will also consider
 \begin{isabelle}
 \isacommand{thm}~@{text "test[my_sym]"}\\
 @{text "> "}~@{thm test[my_sym]}
 \end{isabelle}
-*}
+The purpose of @{ML Thm.rule_attribute} is to directly manipulate theorems.
+Another usage of attributes is to add and delete theorems from stored data.
-text {*
+For example the attribute @{text "[simp]"} adds or deletes a theorem from the
-What are:
+current simpset. For these applications, you can use @{ML Thm.declaration_attribute}.
+To illustrate this function, let us introduce a reference containing a list
+of theorems.
-@{text "declaration_attribute"}
+*}
-@{text "theory_attributes"}
+ML{*val my_thms = ref ([]:thm list)*}
-@{text "proof_attributes"}
+text {*
+A word of warning: such references must not be used in any code that
+is meant to be more than just for testing purposes! Here it is only used
+to illustrate matters. We will show later how to store data properly without
+using references. The function @{ML Thm.declaration_attribute} expects us to
+provide two functions that add and delete theorems from this list.
+For this we use the two functions:
+*}
+ML{*fun my_thms_add thm ctxt =
+(my_thms := Thm.add_thm thm (!my_thms); ctxt)
+fun my_thms_del thm ctxt =
+(my_thms := Thm.del_thm thm (!my_thms); ctxt)*}
+text {*
+These functions take a theorem and a context and, for what we are explaining
+here it is sufficient that they just return the context unchanged. They change
+however the reference @{ML my_thms}, whereby the function @{ML Thm.add_thm}
+adds a theorem if it is not already included in the list, and @{ML
+Thm.del_thm} deletes one. Both functions use the predicate @{ML
+Thm.eq_thm_prop} which compares theorems according to their proved
+propositions (modulo alpha-equivalence).
+You can turn both functions into attributes using
+*}
+ML{*val my_add = Thm.declaration_attribute my_thms_add
+val my_del = Thm.declaration_attribute my_thms_del *}
+text {*
+and set up the attributes as follows
+*}
+setup {*
+Attrib.add_attributes
+[("my_thms", Attrib.add_del_args my_add my_del,
+"maintaining a list of my_thms")] *}
+text {*
+Now if you prove the lemma attaching the attribute @{text "[my_thms]"}
+*}
+lemma trueI_2[my_thms]: "True" by simp
+text {*
+then you can see the lemma is added to the initially empty list.
+@{ML_response_fake [display,gray]
+"!my_thms" "[\"True\"]"}
+You can also add theorems using the command \isacommand{declare}.
+*}
+declare test[my_thms] trueI_2[my_thms add]
+text {*
+The @{text "add"} is the default operation and does not need
+to be given. This declaration will cause the theorem list to be
+updated as follows.
+@{ML_response_fake [display,gray]
+"!my_thms"
+"[\"True\", \"Suc (Suc 0) = 2\"]"}
+The theorem @{thm [source] trueI_2} only appears once, since the
+function @{ML Thm.add_thm} tests for duplicates, before extending
+the list. Deletion from the list works as follows:
+*}
+declare test[my_thms del]
+text {* After this, the theorem list is again:
+@{ML_response_fake [display,gray]
+"!my_thms"
+"[\"True\"]"}
+We used in this example two functions declared as @{ML Thm.declaration_attribute},
+but there can be any number of them. We just have to change the parser for reading
+the arguments accordingly.
+However, as said at the beginning of this example, using references for storing theorems is
+\emph{not} the received way of doing such things. The received way is to
+start a ``data slot'' in a context by using the functor @{text GenericDataFun}:
+*}
+ML {*structure Data = GenericDataFun
+(type T = thm list
+val empty = []
+val extend = I
+fun merge _ = Thm.merge_thms) *}
+text {*
+To use this data slot, you only have to change @{ML my_thms_add} and
+@{ML my_thms_del} to:
+*}
+ML{*val thm_add = Data.map o Thm.add_thm
+val thm_del = Data.map o Thm.del_thm*}
+text {*
+where @{ML Data.map} updates the data appropriately in the context. Since storing
+theorems in a special list is such a common task, there is the functor @{text NamedThmsFun},
+which does most of the work for you. To obtain such a named theorem lists, you just
+declare
+*}
+ML{*structure FooRules = NamedThmsFun
+(val name = "foo"
+val description = "Rules for foo"); *}
+text {*
+and set up the @{ML_struct FooRules} with the command
+*}
+setup {* FooRules.setup *}
+text {*
+This code declares a data slot where the theorems are stored,
+an attribute @{text foo} (with the @{text add} and @{text del} options
+for adding and deleting theorems) and an internal ML interface to retrieve and
+modify the theorems.
+Furthermore, the facts are made available on the user-level under the dynamic
+fact name @{text foo}. For example you can declare three lemmas to be of the kind
+@{text foo} by:
+*}
+lemma rule1[foo]: "A" sorry
+lemma rule2[foo]: "B" sorry
+lemma rule3[foo]: "C" sorry
+text {* and undeclare the first one by: *}
+declare rule1[foo del]
+text {* and query the remaining ones with:
+\begin{isabelle}
+\isacommand{thm}~@{text "foo"}\\
+@{text "> ?C"}\\
+@{text "> ?B"}
+\end{isabelle}
+On the ML-level the rules marked with @{text "foo"} can be retrieved
+using the function @{ML FooRules.get}:
+@{ML_response_fake [display,gray] "FooRules.get @{context}" "[\"?C\",\"?B\"]"}
+\begin{readmore}
+For more information see @{ML_file "Pure/Tools/named_thms.ML"} and also
+the recipe in Section~\ref{recipe:storingdata} about storing arbitrary
+data.
+\end{readmore}
+(FIXME What are: @{text "theory_attributes"}, @{text "proof_attributes"}?)
 \begin{readmore}
 FIXME: @{ML_file "Pure/more_thm.ML"} @{ML_file "Pure/Isar/attrib.ML"}
 \end{readmore}
+*}
-*}
+section {* Theories, Contexts and Local Theories (TBD) *}
-section {* Theories and Local Theories *}
 text {*
 (FIXME: expand)
 (FIXME: explain \isacommand{setup})
 *}
-section {* Storing Theorems\label{sec:storing} *}
+section {* Storing Theorems\label{sec:storing} (TBD) *}
 text {* @{ML PureThy.add_thms_dynamic} *}
 (* FIXME: some code below *)
 (*<*)
+(*
 setup {*
-Sign.add_consts_i [("bar", @{typ "nat"},NoSyn)]
+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.name "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 {* Misc *}
+section {* Pretty-Printing (TBD) *}
+text {*
+@{ML Pretty.big_list},
+@{ML Pretty.brk},
+@{ML Pretty.block},
+@{ML Pretty.chunks}
+*}
+section {* Misc (TBD) *}
 ML {*DatatypePackage.get_datatype @{theory} "List.list"*}
 end

changeset 170	90bee31628dc
parent 163	2319cff107f0
child 171	18f90044c777