src/HOL/Statespace/StateSpaceEx.thy
author wenzelm
Mon, 07 Nov 2011 21:32:59 +0100
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(*  Title:      HOL/Statespace/StateSpaceEx.thy
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    Author:     Norbert Schirmer, TU Muenchen
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*)
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header {* Examples \label{sec:Examples} *}
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theory StateSpaceEx
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imports StateSpaceLocale StateSpaceSyntax
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begin
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(*<*)
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syntax
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 "_statespace_updates" :: "('a \<Rightarrow> 'b) \<Rightarrow> updbinds \<Rightarrow> ('a \<Rightarrow> 'b)" ("_\<langle>_\<rangle>" [900,0] 900)
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(*>*)
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text {* Did you ever dream about records with multiple inheritance?
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Then you should definitely have a look at statespaces. They may be
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what you are dreaming of. Or at least almost \dots  *}
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text {* Isabelle allows to add new top-level commands to the
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system. Building on the locale infrastructure, we provide a command
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\isacommand{statespace} like this:*}
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statespace vars =
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  n::nat
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  b::bool
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print_locale vars_namespace
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print_locale vars_valuetypes
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print_locale vars
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text {* \noindent This resembles a \isacommand{record} definition, 
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but introduces sophisticated locale
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infrastructure instead of HOL type schemes.  The resulting context
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postulates two distinct names @{term "n"} and @{term "b"} and
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projection~/ injection functions that convert from abstract values to
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@{typ "nat"} and @{text "bool"}. The logical content of the locale is: *}
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locale vars' =
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  fixes n::'name and b::'name
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  assumes "distinct [n, b]" 
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  fixes project_nat::"'value \<Rightarrow> nat" and inject_nat::"nat \<Rightarrow> 'value"
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  assumes "\<And>n. project_nat (inject_nat n) = n" 
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  fixes project_bool::"'value \<Rightarrow> bool" and inject_bool::"bool \<Rightarrow> 'value"
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  assumes "\<And>b. project_bool (inject_bool b) = b"
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text {* \noindent The HOL predicate @{const "distinct"} describes
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distinctness of all names in the context.  Locale @{text "vars'"}
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defines the raw logical content that is defined in the state space
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locale. We also maintain non-logical context information to support
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the user:
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\begin{itemize}
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\item Syntax for state lookup and updates that automatically inserts
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the corresponding projection and injection functions.
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\item Setup for the proof tools that exploit the distinctness
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information and the cancellation of projections and injections in
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deductions and simplifications.
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\end{itemize}
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This extra-logical information is added to the locale in form of
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declarations, which associate the name of a variable to the
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corresponding projection and injection functions to handle the syntax
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transformations, and a link from the variable name to the
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corresponding distinctness theorem. As state spaces are merged or
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extended there are multiple distinctness theorems in the context. Our
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declarations take care that the link always points to the strongest
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distinctness assumption.  With these declarations in place, a lookup
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can be written as @{text "s\<cdot>n"}, which is translated to @{text
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"project_nat (s n)"}, and an update as @{text "s\<langle>n := 2\<rangle>"}, which is
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translated to @{text "s(n := inject_nat 2)"}. We can now establish the
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following lemma: *}
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lemma (in vars) foo: "s<n := 2>\<cdot>b = s\<cdot>b" by simp
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text {* \noindent Here the simplifier was able to refer to
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distinctness of @{term "b"} and @{term "n"} to solve the equation.
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The resulting lemma is also recorded in locale @{text "vars"} for
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later use and is automatically propagated to all its interpretations.
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Here is another example: *}
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statespace 'a varsX = vars [n=N, b=B] + vars + x::'a
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text {* \noindent The state space @{text "varsX"} imports two copies
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of the state space @{text "vars"}, where one has the variables renamed
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to upper-case letters, and adds another variable @{term "x"} of type
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@{typ "'a"}. This type is fixed inside the state space but may get
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instantiated later on, analogous to type parameters of an ML-functor.
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The distinctness assumption is now @{text "distinct [N, B, n, b, x]"},
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from this we can derive both @{term "distinct [N,B]"} and @{term
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"distinct [n,b]"}, the distinction assumptions for the two versions of
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locale @{text "vars"} above.  Moreover we have all necessary
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projection and injection assumptions available. These assumptions
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together allow us to establish state space @{term "varsX"} as an
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interpretation of both instances of locale @{term "vars"}. Hence we
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inherit both variants of theorem @{text "foo"}: @{text "s\<langle>N := 2\<rangle>\<cdot>B =
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s\<cdot>B"} as well as @{text "s\<langle>n := 2\<rangle>\<cdot>b = s\<cdot>b"}. These are immediate
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consequences of the locale interpretation action.
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The declarations for syntax and the distinctness theorems also observe
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the morphisms generated by the locale package due to the renaming
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@{term "n = N"}: *}
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lemma (in varsX) foo: "s\<langle>N := 2\<rangle>\<cdot>x = s\<cdot>x" by simp
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text {* To assure scalability towards many distinct names, the
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distinctness predicate is refined to operate on balanced trees. Thus
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we get logarithmic certificates for the distinctness of two names by
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the distinctness of the paths in the tree. Asked for the distinctness
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of two names, our tool produces the paths of the variables in the tree
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(this is implemented in SML, outside the logic) and returns a
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certificate corresponding to the different paths.  Merging state
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spaces requires to prove that the combined distinctness assumption
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implies the distinctness assumptions of the components.  Such a proof
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is of the order $m \cdot \log n$, where $n$ and $m$ are the number of
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nodes in the larger and smaller tree, respectively.*}
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text {* We continue with more examples. *}
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statespace 'a foo = 
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  f::"nat\<Rightarrow>nat"
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  a::int
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  b::nat
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  c::'a
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lemma (in foo) foo1: 
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  shows "s\<langle>a := i\<rangle>\<cdot>a = i"
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  by simp
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lemma (in foo) foo2: 
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  shows "(s\<langle>a:=i\<rangle>)\<cdot>a = i"
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  by simp
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lemma (in foo) foo3: 
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  shows "(s\<langle>a:=i\<rangle>)\<cdot>b = s\<cdot>b"
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  by simp
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lemma (in foo) foo4: 
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  shows "(s\<langle>a:=i,b:=j,c:=k,a:=x\<rangle>) = (s\<langle>b:=j,c:=k,a:=x\<rangle>)"
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  by simp
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statespace bar =
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  b::bool
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  c::string
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lemma (in bar) bar1: 
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  shows "(s\<langle>b:=True\<rangle>)\<cdot>c = s\<cdot>c"
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  by simp
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text {* You can define a derived state space by inheriting existing state spaces, renaming
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of components if you like, and by declaring new components.
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*}
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statespace ('a,'b) loo = 'a foo + bar [b=B,c=C] +
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  X::'b
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lemma (in loo) loo1: 
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  shows "s\<langle>a:=i\<rangle>\<cdot>B = s\<cdot>B"
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proof -
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  thm foo1
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  txt {* The Lemma @{thm [source] foo1} from the parent state space 
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         is also available here: \begin{center}@{thm foo1}\end{center} *}
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  have "s<a:=i>\<cdot>a = i"
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    by (rule foo1)
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  thm bar1
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  txt {* Note the renaming of the parameters in Lemma @{thm [source] bar1}: 
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         \begin{center}@{thm bar1}\end{center} *}
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  have "s<B:=True>\<cdot>C = s\<cdot>C"
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    by (rule bar1)
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  show ?thesis
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    by simp
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qed
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statespace 'a dup = 'a foo [f=F, a=A] + 'a foo +
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  x::int
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lemma (in dup)
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 shows "s<a := i>\<cdot>x = s\<cdot>x"
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  by simp
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lemma (in dup)
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 shows "s<A := i>\<cdot>a = s\<cdot>a"
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  by simp
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lemma (in dup)
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 shows "s<A := i>\<cdot>x = s\<cdot>x"
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  by simp
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(*
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text "Hmm, I hoped this would work now..."
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locale fooX = foo +
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 assumes "s<a:=i>\<cdot>b = k"
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*)
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(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *)
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text {* There are known problems with syntax-declarations. They currently
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only work, when the context is already built. Hopefully this will be 
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implemented correctly in future Isabelle versions. *}
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(*
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lemma 
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  assumes "foo f a b c p1 i1 p2 i2 p3 i3 p4 i4"
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  shows True
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proof
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  interpret foo [f a b c p1 i1 p2 i2 p3 i3 p4 i4] by fact
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  term "s<a := i>\<cdot>a = i"
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qed
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*)
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(*
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lemma 
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  includes foo
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  shows "s<a := i>\<cdot>a = i"
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*)
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text {* It would be nice to have nested state spaces. This is
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logically no problem. From the locale-implementation side this may be
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something like an 'includes' into a locale. When there is a more
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elaborate locale infrastructure in place this may be an easy exercise.
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*} 
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subsection {* Benchmarks *}
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text {* Here are some bigger examples for benchmarking. *}
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ML {*
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  fun make_benchmark n =
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    writeln (Markup.markup Markup.sendback
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      ("statespace benchmark" ^ string_of_int n ^ " =\n" ^
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        (cat_lines (map (fn i => "A" ^ string_of_int i ^ "::nat") (1 upto n)))));
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*}
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text "0.2s"
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statespace benchmark100 = A1::nat A2::nat A3::nat A4::nat A5::nat
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A6::nat A7::nat A8::nat A9::nat A10::nat A11::nat A12::nat A13::nat
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A14::nat A15::nat A16::nat A17::nat A18::nat A19::nat A20::nat
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A21::nat A22::nat A23::nat A24::nat A25::nat A26::nat A27::nat
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A28::nat A29::nat A30::nat A31::nat A32::nat A33::nat A34::nat
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A35::nat A36::nat A37::nat A38::nat A39::nat A40::nat A41::nat
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A42::nat A43::nat A44::nat A45::nat A46::nat A47::nat A48::nat
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A49::nat A50::nat A51::nat A52::nat A53::nat A54::nat A55::nat
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A56::nat A57::nat A58::nat A59::nat A60::nat A61::nat A62::nat
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A63::nat A64::nat A65::nat A66::nat A67::nat A68::nat A69::nat
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A70::nat A71::nat A72::nat A73::nat A74::nat A75::nat A76::nat
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A77::nat A78::nat A79::nat A80::nat A81::nat A82::nat A83::nat
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A84::nat A85::nat A86::nat A87::nat A88::nat A89::nat A90::nat
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A91::nat A92::nat A93::nat A94::nat A95::nat A96::nat A97::nat
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A98::nat A99::nat A100::nat
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text "2.4s"
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statespace benchmark500 = A1::nat A2::nat A3::nat A4::nat A5::nat
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A6::nat A7::nat A8::nat A9::nat A10::nat A11::nat A12::nat A13::nat
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A14::nat A15::nat A16::nat A17::nat A18::nat A19::nat A20::nat
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A21::nat A22::nat A23::nat A24::nat A25::nat A26::nat A27::nat
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A28::nat A29::nat A30::nat A31::nat A32::nat A33::nat A34::nat
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A35::nat A36::nat A37::nat A38::nat A39::nat A40::nat A41::nat
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A42::nat A43::nat A44::nat A45::nat A46::nat A47::nat A48::nat
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A49::nat A50::nat A51::nat A52::nat A53::nat A54::nat A55::nat
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A56::nat A57::nat A58::nat A59::nat A60::nat A61::nat A62::nat
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A63::nat A64::nat A65::nat A66::nat A67::nat A68::nat A69::nat
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A70::nat A71::nat A72::nat A73::nat A74::nat A75::nat A76::nat
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A77::nat A78::nat A79::nat A80::nat A81::nat A82::nat A83::nat
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A84::nat A85::nat A86::nat A87::nat A88::nat A89::nat A90::nat
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A91::nat A92::nat A93::nat A94::nat A95::nat A96::nat A97::nat
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A98::nat A99::nat A100::nat A101::nat A102::nat A103::nat A104::nat
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A105::nat A106::nat A107::nat A108::nat A109::nat A110::nat A111::nat
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A112::nat A113::nat A114::nat A115::nat A116::nat A117::nat A118::nat
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A119::nat A120::nat A121::nat A122::nat A123::nat A124::nat A125::nat
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A126::nat A127::nat A128::nat A129::nat A130::nat A131::nat A132::nat
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A133::nat A134::nat A135::nat A136::nat A137::nat A138::nat A139::nat
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A140::nat A141::nat A142::nat A143::nat A144::nat A145::nat A146::nat
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A147::nat A148::nat A149::nat A150::nat A151::nat A152::nat A153::nat
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A154::nat A155::nat A156::nat A157::nat A158::nat A159::nat A160::nat
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A161::nat A162::nat A163::nat A164::nat A165::nat A166::nat A167::nat
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A168::nat A169::nat A170::nat A171::nat A172::nat A173::nat A174::nat
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A175::nat A176::nat A177::nat A178::nat A179::nat A180::nat A181::nat
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A182::nat A183::nat A184::nat A185::nat A186::nat A187::nat A188::nat
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A189::nat A190::nat A191::nat A192::nat A193::nat A194::nat A195::nat
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A196::nat A197::nat A198::nat A199::nat A200::nat A201::nat A202::nat
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A203::nat A204::nat A205::nat A206::nat A207::nat A208::nat A209::nat
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A210::nat A211::nat A212::nat A213::nat A214::nat A215::nat A216::nat
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A217::nat A218::nat A219::nat A220::nat A221::nat A222::nat A223::nat
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A224::nat A225::nat A226::nat A227::nat A228::nat A229::nat A230::nat
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A231::nat A232::nat A233::nat A234::nat A235::nat A236::nat A237::nat
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A238::nat A239::nat A240::nat A241::nat A242::nat A243::nat A244::nat
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   296
A245::nat A246::nat A247::nat A248::nat A249::nat A250::nat A251::nat
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A252::nat A253::nat A254::nat A255::nat A256::nat A257::nat A258::nat
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A259::nat A260::nat A261::nat A262::nat A263::nat A264::nat A265::nat
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A266::nat A267::nat A268::nat A269::nat A270::nat A271::nat A272::nat
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A273::nat A274::nat A275::nat A276::nat A277::nat A278::nat A279::nat
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A280::nat A281::nat A282::nat A283::nat A284::nat A285::nat A286::nat
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A287::nat A288::nat A289::nat A290::nat A291::nat A292::nat A293::nat
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A294::nat A295::nat A296::nat A297::nat A298::nat A299::nat A300::nat
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A301::nat A302::nat A303::nat A304::nat A305::nat A306::nat A307::nat
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A308::nat A309::nat A310::nat A311::nat A312::nat A313::nat A314::nat
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A315::nat A316::nat A317::nat A318::nat A319::nat A320::nat A321::nat
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A322::nat A323::nat A324::nat A325::nat A326::nat A327::nat A328::nat
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A329::nat A330::nat A331::nat A332::nat A333::nat A334::nat A335::nat
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A336::nat A337::nat A338::nat A339::nat A340::nat A341::nat A342::nat
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A343::nat A344::nat A345::nat A346::nat A347::nat A348::nat A349::nat
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A350::nat A351::nat A352::nat A353::nat A354::nat A355::nat A356::nat
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A357::nat A358::nat A359::nat A360::nat A361::nat A362::nat A363::nat
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A364::nat A365::nat A366::nat A367::nat A368::nat A369::nat A370::nat
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A371::nat A372::nat A373::nat A374::nat A375::nat A376::nat A377::nat
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A378::nat A379::nat A380::nat A381::nat A382::nat A383::nat A384::nat
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A385::nat A386::nat A387::nat A388::nat A389::nat A390::nat A391::nat
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A392::nat A393::nat A394::nat A395::nat A396::nat A397::nat A398::nat
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A399::nat A400::nat A401::nat A402::nat A403::nat A404::nat A405::nat
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A406::nat A407::nat A408::nat A409::nat A410::nat A411::nat A412::nat
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wenzelm
parents: 45358
diff changeset
   320
A413::nat A414::nat A415::nat A416::nat A417::nat A418::nat A419::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   321
A420::nat A421::nat A422::nat A423::nat A424::nat A425::nat A426::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   322
A427::nat A428::nat A429::nat A430::nat A431::nat A432::nat A433::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   323
A434::nat A435::nat A436::nat A437::nat A438::nat A439::nat A440::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   324
A441::nat A442::nat A443::nat A444::nat A445::nat A446::nat A447::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   325
A448::nat A449::nat A450::nat A451::nat A452::nat A453::nat A454::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   326
A455::nat A456::nat A457::nat A458::nat A459::nat A460::nat A461::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   327
A462::nat A463::nat A464::nat A465::nat A466::nat A467::nat A468::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   328
A469::nat A470::nat A471::nat A472::nat A473::nat A474::nat A475::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   329
A476::nat A477::nat A478::nat A479::nat A480::nat A481::nat A482::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   330
A483::nat A484::nat A485::nat A486::nat A487::nat A488::nat A489::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   331
A490::nat A491::nat A492::nat A493::nat A494::nat A495::nat A496::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   332
A497::nat A498::nat A499::nat A500::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   333
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   334
text "9.0s"
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   335
statespace benchmark1000 = A1::nat A2::nat A3::nat A4::nat A5::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   336
A6::nat A7::nat A8::nat A9::nat A10::nat A11::nat A12::nat A13::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   337
A14::nat A15::nat A16::nat A17::nat A18::nat A19::nat A20::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   338
A21::nat A22::nat A23::nat A24::nat A25::nat A26::nat A27::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   339
A28::nat A29::nat A30::nat A31::nat A32::nat A33::nat A34::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   340
A35::nat A36::nat A37::nat A38::nat A39::nat A40::nat A41::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   341
A42::nat A43::nat A44::nat A45::nat A46::nat A47::nat A48::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   342
A49::nat A50::nat A51::nat A52::nat A53::nat A54::nat A55::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   343
A56::nat A57::nat A58::nat A59::nat A60::nat A61::nat A62::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   344
A63::nat A64::nat A65::nat A66::nat A67::nat A68::nat A69::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   345
A70::nat A71::nat A72::nat A73::nat A74::nat A75::nat A76::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   346
A77::nat A78::nat A79::nat A80::nat A81::nat A82::nat A83::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   347
A84::nat A85::nat A86::nat A87::nat A88::nat A89::nat A90::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   348
A91::nat A92::nat A93::nat A94::nat A95::nat A96::nat A97::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   349
A98::nat A99::nat A100::nat A101::nat A102::nat A103::nat A104::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   350
A105::nat A106::nat A107::nat A108::nat A109::nat A110::nat A111::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   351
A112::nat A113::nat A114::nat A115::nat A116::nat A117::nat A118::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   352
A119::nat A120::nat A121::nat A122::nat A123::nat A124::nat A125::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   353
A126::nat A127::nat A128::nat A129::nat A130::nat A131::nat A132::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   354
A133::nat A134::nat A135::nat A136::nat A137::nat A138::nat A139::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   355
A140::nat A141::nat A142::nat A143::nat A144::nat A145::nat A146::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   356
A147::nat A148::nat A149::nat A150::nat A151::nat A152::nat A153::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   357
A154::nat A155::nat A156::nat A157::nat A158::nat A159::nat A160::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   358
A161::nat A162::nat A163::nat A164::nat A165::nat A166::nat A167::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   359
A168::nat A169::nat A170::nat A171::nat A172::nat A173::nat A174::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   360
A175::nat A176::nat A177::nat A178::nat A179::nat A180::nat A181::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   361
A182::nat A183::nat A184::nat A185::nat A186::nat A187::nat A188::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   362
A189::nat A190::nat A191::nat A192::nat A193::nat A194::nat A195::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   363
A196::nat A197::nat A198::nat A199::nat A200::nat A201::nat A202::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   364
A203::nat A204::nat A205::nat A206::nat A207::nat A208::nat A209::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   365
A210::nat A211::nat A212::nat A213::nat A214::nat A215::nat A216::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   366
A217::nat A218::nat A219::nat A220::nat A221::nat A222::nat A223::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   367
A224::nat A225::nat A226::nat A227::nat A228::nat A229::nat A230::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   368
A231::nat A232::nat A233::nat A234::nat A235::nat A236::nat A237::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   369
A238::nat A239::nat A240::nat A241::nat A242::nat A243::nat A244::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   370
A245::nat A246::nat A247::nat A248::nat A249::nat A250::nat A251::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   371
A252::nat A253::nat A254::nat A255::nat A256::nat A257::nat A258::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   372
A259::nat A260::nat A261::nat A262::nat A263::nat A264::nat A265::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   373
A266::nat A267::nat A268::nat A269::nat A270::nat A271::nat A272::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   374
A273::nat A274::nat A275::nat A276::nat A277::nat A278::nat A279::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   375
A280::nat A281::nat A282::nat A283::nat A284::nat A285::nat A286::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   376
A287::nat A288::nat A289::nat A290::nat A291::nat A292::nat A293::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   377
A294::nat A295::nat A296::nat A297::nat A298::nat A299::nat A300::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   378
A301::nat A302::nat A303::nat A304::nat A305::nat A306::nat A307::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   379
A308::nat A309::nat A310::nat A311::nat A312::nat A313::nat A314::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   380
A315::nat A316::nat A317::nat A318::nat A319::nat A320::nat A321::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   381
A322::nat A323::nat A324::nat A325::nat A326::nat A327::nat A328::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   382
A329::nat A330::nat A331::nat A332::nat A333::nat A334::nat A335::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   383
A336::nat A337::nat A338::nat A339::nat A340::nat A341::nat A342::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   384
A343::nat A344::nat A345::nat A346::nat A347::nat A348::nat A349::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   385
A350::nat A351::nat A352::nat A353::nat A354::nat A355::nat A356::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   386
A357::nat A358::nat A359::nat A360::nat A361::nat A362::nat A363::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   387
A364::nat A365::nat A366::nat A367::nat A368::nat A369::nat A370::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   388
A371::nat A372::nat A373::nat A374::nat A375::nat A376::nat A377::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   389
A378::nat A379::nat A380::nat A381::nat A382::nat A383::nat A384::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   390
A385::nat A386::nat A387::nat A388::nat A389::nat A390::nat A391::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   391
A392::nat A393::nat A394::nat A395::nat A396::nat A397::nat A398::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   392
A399::nat A400::nat A401::nat A402::nat A403::nat A404::nat A405::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   393
A406::nat A407::nat A408::nat A409::nat A410::nat A411::nat A412::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   394
A413::nat A414::nat A415::nat A416::nat A417::nat A418::nat A419::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   395
A420::nat A421::nat A422::nat A423::nat A424::nat A425::nat A426::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   396
A427::nat A428::nat A429::nat A430::nat A431::nat A432::nat A433::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   397
A434::nat A435::nat A436::nat A437::nat A438::nat A439::nat A440::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   398
A441::nat A442::nat A443::nat A444::nat A445::nat A446::nat A447::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   399
A448::nat A449::nat A450::nat A451::nat A452::nat A453::nat A454::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   400
A455::nat A456::nat A457::nat A458::nat A459::nat A460::nat A461::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   401
A462::nat A463::nat A464::nat A465::nat A466::nat A467::nat A468::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   402
A469::nat A470::nat A471::nat A472::nat A473::nat A474::nat A475::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   403
A476::nat A477::nat A478::nat A479::nat A480::nat A481::nat A482::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   404
A483::nat A484::nat A485::nat A486::nat A487::nat A488::nat A489::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   405
A490::nat A491::nat A492::nat A493::nat A494::nat A495::nat A496::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   406
A497::nat A498::nat A499::nat A500::nat A501::nat A502::nat A503::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   407
A504::nat A505::nat A506::nat A507::nat A508::nat A509::nat A510::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   408
A511::nat A512::nat A513::nat A514::nat A515::nat A516::nat A517::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   409
A518::nat A519::nat A520::nat A521::nat A522::nat A523::nat A524::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   410
A525::nat A526::nat A527::nat A528::nat A529::nat A530::nat A531::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   411
A532::nat A533::nat A534::nat A535::nat A536::nat A537::nat A538::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   412
A539::nat A540::nat A541::nat A542::nat A543::nat A544::nat A545::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   413
A546::nat A547::nat A548::nat A549::nat A550::nat A551::nat A552::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   414
A553::nat A554::nat A555::nat A556::nat A557::nat A558::nat A559::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   415
A560::nat A561::nat A562::nat A563::nat A564::nat A565::nat A566::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   416
A567::nat A568::nat A569::nat A570::nat A571::nat A572::nat A573::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   417
A574::nat A575::nat A576::nat A577::nat A578::nat A579::nat A580::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   418
A581::nat A582::nat A583::nat A584::nat A585::nat A586::nat A587::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   419
A588::nat A589::nat A590::nat A591::nat A592::nat A593::nat A594::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   420
A595::nat A596::nat A597::nat A598::nat A599::nat A600::nat A601::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   421
A602::nat A603::nat A604::nat A605::nat A606::nat A607::nat A608::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   422
A609::nat A610::nat A611::nat A612::nat A613::nat A614::nat A615::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   423
A616::nat A617::nat A618::nat A619::nat A620::nat A621::nat A622::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   424
A623::nat A624::nat A625::nat A626::nat A627::nat A628::nat A629::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   425
A630::nat A631::nat A632::nat A633::nat A634::nat A635::nat A636::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   426
A637::nat A638::nat A639::nat A640::nat A641::nat A642::nat A643::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   427
A644::nat A645::nat A646::nat A647::nat A648::nat A649::nat A650::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   428
A651::nat A652::nat A653::nat A654::nat A655::nat A656::nat A657::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   429
A658::nat A659::nat A660::nat A661::nat A662::nat A663::nat A664::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   430
A665::nat A666::nat A667::nat A668::nat A669::nat A670::nat A671::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   431
A672::nat A673::nat A674::nat A675::nat A676::nat A677::nat A678::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   432
A679::nat A680::nat A681::nat A682::nat A683::nat A684::nat A685::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   433
A686::nat A687::nat A688::nat A689::nat A690::nat A691::nat A692::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   434
A693::nat A694::nat A695::nat A696::nat A697::nat A698::nat A699::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   435
A700::nat A701::nat A702::nat A703::nat A704::nat A705::nat A706::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   436
A707::nat A708::nat A709::nat A710::nat A711::nat A712::nat A713::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   437
A714::nat A715::nat A716::nat A717::nat A718::nat A719::nat A720::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   438
A721::nat A722::nat A723::nat A724::nat A725::nat A726::nat A727::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   439
A728::nat A729::nat A730::nat A731::nat A732::nat A733::nat A734::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   440
A735::nat A736::nat A737::nat A738::nat A739::nat A740::nat A741::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   441
A742::nat A743::nat A744::nat A745::nat A746::nat A747::nat A748::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   442
A749::nat A750::nat A751::nat A752::nat A753::nat A754::nat A755::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   443
A756::nat A757::nat A758::nat A759::nat A760::nat A761::nat A762::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   444
A763::nat A764::nat A765::nat A766::nat A767::nat A768::nat A769::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   445
A770::nat A771::nat A772::nat A773::nat A774::nat A775::nat A776::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   446
A777::nat A778::nat A779::nat A780::nat A781::nat A782::nat A783::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   447
A784::nat A785::nat A786::nat A787::nat A788::nat A789::nat A790::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   448
A791::nat A792::nat A793::nat A794::nat A795::nat A796::nat A797::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   449
A798::nat A799::nat A800::nat A801::nat A802::nat A803::nat A804::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   450
A805::nat A806::nat A807::nat A808::nat A809::nat A810::nat A811::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   451
A812::nat A813::nat A814::nat A815::nat A816::nat A817::nat A818::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   452
A819::nat A820::nat A821::nat A822::nat A823::nat A824::nat A825::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   453
A826::nat A827::nat A828::nat A829::nat A830::nat A831::nat A832::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   454
A833::nat A834::nat A835::nat A836::nat A837::nat A838::nat A839::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   455
A840::nat A841::nat A842::nat A843::nat A844::nat A845::nat A846::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   456
A847::nat A848::nat A849::nat A850::nat A851::nat A852::nat A853::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   457
A854::nat A855::nat A856::nat A857::nat A858::nat A859::nat A860::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   458
A861::nat A862::nat A863::nat A864::nat A865::nat A866::nat A867::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   459
A868::nat A869::nat A870::nat A871::nat A872::nat A873::nat A874::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   460
A875::nat A876::nat A877::nat A878::nat A879::nat A880::nat A881::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   461
A882::nat A883::nat A884::nat A885::nat A886::nat A887::nat A888::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   462
A889::nat A890::nat A891::nat A892::nat A893::nat A894::nat A895::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   463
A896::nat A897::nat A898::nat A899::nat A900::nat A901::nat A902::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   464
A903::nat A904::nat A905::nat A906::nat A907::nat A908::nat A909::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   465
A910::nat A911::nat A912::nat A913::nat A914::nat A915::nat A916::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   466
A917::nat A918::nat A919::nat A920::nat A921::nat A922::nat A923::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   467
A924::nat A925::nat A926::nat A927::nat A928::nat A929::nat A930::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   468
A931::nat A932::nat A933::nat A934::nat A935::nat A936::nat A937::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   469
A938::nat A939::nat A940::nat A941::nat A942::nat A943::nat A944::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   470
A945::nat A946::nat A947::nat A948::nat A949::nat A950::nat A951::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   471
A952::nat A953::nat A954::nat A955::nat A956::nat A957::nat A958::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   472
A959::nat A960::nat A961::nat A962::nat A963::nat A964::nat A965::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   473
A966::nat A967::nat A968::nat A969::nat A970::nat A971::nat A972::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   474
A973::nat A974::nat A975::nat A976::nat A977::nat A978::nat A979::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   475
A980::nat A981::nat A982::nat A983::nat A984::nat A985::nat A986::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   476
A987::nat A988::nat A989::nat A990::nat A991::nat A992::nat A993::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   477
A994::nat A995::nat A996::nat A997::nat A998::nat A999::nat A1000::nat
09bef4e1cc55 some statespace benchmarks;
wenzelm
parents: 45358
diff changeset
   478
45394
94b5016c05c3 more benchmarks;
wenzelm
parents: 45360
diff changeset
   479
lemma (in benchmark100) test: "s<A1 := a>\<cdot>A100 = s\<cdot>A100" by simp
94b5016c05c3 more benchmarks;
wenzelm
parents: 45360
diff changeset
   480
lemma (in benchmark500) test: "s<A1 := a>\<cdot>A100 = s\<cdot>A100" by simp
94b5016c05c3 more benchmarks;
wenzelm
parents: 45360
diff changeset
   481
lemma (in benchmark1000) test: "s<A1 := a>\<cdot>A100 = s\<cdot>A100" by simp
94b5016c05c3 more benchmarks;
wenzelm
parents: 45360
diff changeset
   482
25171
4a9c25bffc9b added Statespace library
schirmer
parents:
diff changeset
   483
end