doc-src/Ref/theories.tex
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%% $Id$
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\chapter{Theories, Terms and Types} \label{theories}
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\index{theories|(}\index{signatures|bold}
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\index{reading!axioms|see{\texttt{assume_ax}}} Theories organize the
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syntax, declarations and axioms of a mathematical development.  They
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are built, starting from the {\Pure} or {\CPure} theory, by extending
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and merging existing theories.  They have the \ML\ type
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\mltydx{theory}.  Theory operations signal errors by raising exception
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\xdx{THEORY}, returning a message and a list of theories.
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Signatures, which contain information about sorts, types, constants and
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syntax, have the \ML\ type~\mltydx{Sign.sg}.  For identification, each
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signature carries a unique list of \bfindex{stamps}, which are \ML\
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references to strings.  The strings serve as human-readable names; the
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references serve as unique identifiers.  Each primitive signature has a
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single stamp.  When two signatures are merged, their lists of stamps are
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also merged.  Every theory carries a unique signature.
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Terms and types are the underlying representation of logical syntax.  Their
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\ML\ definitions are irrelevant to naive Isabelle users.  Programmers who
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wish to extend Isabelle may need to know such details, say to code a tactic
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that looks for subgoals of a particular form.  Terms and types may be
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`certified' to be well-formed with respect to a given signature.
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\section{Defining theories}\label{sec:ref-defining-theories}
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Theories are defined via theory files $name$\texttt{.thy} (there are also
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\ML-level interfaces which are only intended for people building advanced
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theory definition packages).  Appendix~\ref{app:TheorySyntax} presents the
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concrete syntax for theory files; here follows an explanation of the
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constituent parts.
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\begin{description}
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\item[{\it theoryDef}] is the full definition.  The new theory is called $id$.
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  It is the union of the named {\bf parent
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    theories}\indexbold{theories!parent}, possibly extended with new
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  components.  \thydx{Pure} and \thydx{CPure} are the basic theories, which
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  contain only the meta-logic.  They differ just in their concrete syntax for
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  function applications.
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  The new theory begins as a merge of its parents.
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  \begin{ttbox}
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    Attempt to merge different versions of theories: "\(T@1\)", \(\ldots\), "\(T@n\)"
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  \end{ttbox}
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  This error may especially occur when a theory is redeclared --- say to
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  change an inappropriate definition --- and bindings to old versions persist.
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  Isabelle ensures that old and new theories of the same name are not involved
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  in a proof.
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\item[$classes$]
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  is a series of class declarations.  Declaring {\tt$id$ < $id@1$ \dots\
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    $id@n$} makes $id$ a subclass of the existing classes $id@1\dots
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  id@n$.  This rules out cyclic class structures.  Isabelle automatically
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  computes the transitive closure of subclass hierarchies; it is not
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  necessary to declare \texttt{c < e} in addition to \texttt{c < d} and \texttt{d <
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    e}.
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\item[$default$]
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  introduces $sort$ as the new default sort for type variables.  This applies
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  to unconstrained type variables in an input string but not to type
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  variables created internally.  If omitted, the default sort is the listwise
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  union of the default sorts of the parent theories (i.e.\ their logical
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  intersection).
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\item[$sort$] is a finite set of classes.  A single class $id$ abbreviates the
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  sort $\{id\}$.
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\item[$types$]
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  is a series of type declarations.  Each declares a new type constructor
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  or type synonym.  An $n$-place type constructor is specified by
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  $(\alpha@1,\dots,\alpha@n)name$, where the type variables serve only to
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  indicate the number~$n$.
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  A {\bf type synonym}\indexbold{type synonyms} is an abbreviation
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  $(\alpha@1,\dots,\alpha@n)name = \tau$, where $name$ and $\tau$ can
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  be strings.
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\item[$infix$]
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  declares a type or constant to be an infix operator of priority $nat$
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  associating to the left (\texttt{infixl}) or right (\texttt{infixr}).  Only
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  2-place type constructors can have infix status; an example is {\tt
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  ('a,'b)~"*"~(infixr~20)}, which may express binary product types.
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\item[$arities$] is a series of type arity declarations.  Each assigns
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  arities to type constructors.  The $name$ must be an existing type
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  constructor, which is given the additional arity $arity$.
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\item[$nonterminals$]\index{*nonterminal symbols} declares purely
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  syntactic types to be used as nonterminal symbols of the context
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  free grammar.
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\item[$consts$] is a series of constant declarations.  Each new
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  constant $name$ is given the specified type.  The optional $mixfix$
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  annotations may attach concrete syntax to the constant.
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\item[$syntax$] \index{*syntax section}\index{print mode} is a variant
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  of $consts$ which adds just syntax without actually declaring
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  logical constants.  This gives full control over a theory's context
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  free grammar.  The optional $mode$ specifies the print mode where the
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  mixfix productions should be added.  If there is no \texttt{output}
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  option given, all productions are also added to the input syntax
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  (regardless of the print mode).
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\item[$mixfix$] \index{mixfix declarations}
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  annotations can take three forms:
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  \begin{itemize}
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  \item A mixfix template given as a $string$ of the form
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    {\tt"}\dots{\tt\_}\dots{\tt\_}\dots{\tt"} where the $i$-th underscore
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    indicates the position where the $i$-th argument should go.  The list
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    of numbers gives the priority of each argument.  The final number gives
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    the priority of the whole construct.
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  \item A constant $f$ of type $\tau@1\To(\tau@2\To\tau)$ can be given {\bf
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    infix} status.
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  \item A constant $f$ of type $(\tau@1\To\tau@2)\To\tau$ can be given {\bf
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    binder} status.  The declaration \texttt{binder} $\cal Q$ $p$ causes
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  ${\cal Q}\,x.F(x)$ to be treated
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  like $f(F)$, where $p$ is the priority.
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  \end{itemize}
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\item[$trans$]
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  specifies syntactic translation rules (macros).  There are three forms:
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  parse rules (\texttt{=>}), print rules (\texttt{<=}), and parse/print rules ({\tt
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  ==}).
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\item[$rules$]
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  is a series of rule declarations.  Each has a name $id$ and the formula is
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  given by the $string$.  Rule names must be distinct within any single
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  theory.
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\item[$defs$] is a series of definitions.  They are just like $rules$, except
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  that every $string$ must be a definition (see below for details).
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\item[$constdefs$] combines the declaration of constants and their
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  definition.  The first $string$ is the type, the second the definition.
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\item[$axclass$] \index{*axclass section} defines an \rmindex{axiomatic type
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    class} \cite{Wenzel:1997:TPHOL} as the intersection of existing classes,
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  with additional axioms holding.  Class axioms may not contain more than one
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  type variable.  The class axioms (with implicit sort constraints added) are
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  bound to the given names.  Furthermore a class introduction rule is
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  generated, which is automatically employed by $instance$ to prove
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  instantiations of this class.
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\item[$instance$] \index{*instance section} proves class inclusions or
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  type arities at the logical level and then transfers these to the
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  type signature.  The instantiation is proven and checked properly.
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  The user has to supply sufficient witness information: theorems
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  ($longident$), axioms ($string$), or even arbitrary \ML{} tactic
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  code $verbatim$.
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\item[$oracle$] links the theory to a trusted external reasoner.  It is
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  allowed to create theorems, but each theorem carries a proof object
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  describing the oracle invocation.  See \S\ref{sec:oracles} for details.
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\item[$local$, $global$] change the current name declaration mode.
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  Initially, theories start in $local$ mode, causing all names of
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  types, constants, axioms etc.\ to be automatically qualified by the
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  theory name.  Changing this to $global$ causes all names to be
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  declared as short base names only.
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  The $local$ and $global$ declarations act like switches, affecting
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  all following theory sections until changed again explicitly.  Also
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  note that the final state at the end of the theory will persist.  In
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  particular, this determines how the names of theorems stored later
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  on are handled.
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\item[$setup$]\index{*setup!theory} applies a list of ML functions to
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  the theory.  The argument should denote a value of type
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  \texttt{(theory -> theory) list}.  Typically, ML packages are
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  initialized in this way.
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\item[$ml$] \index{*ML section}
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  consists of \ML\ code, typically for parse and print translation functions.
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\end{description}
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%
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Chapters~\ref{Defining-Logics} and \ref{chap:syntax} explain mixfix
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declarations, translation rules and the \texttt{ML} section in more detail.
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\subsection{Definitions}\indexbold{definitions}
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{\bf Definitions} are intended to express abbreviations.  The simplest
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form of a definition is $f \equiv t$, where $f$ is a constant.
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Isabelle also allows a derived forms where the arguments of~$f$ appear
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on the left, abbreviating a string of $\lambda$-abstractions.
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Isabelle makes the following checks on definitions:
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\begin{itemize}
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\item Arguments (on the left-hand side) must be distinct variables.
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\item All variables on the right-hand side must also appear on the left-hand
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  side. 
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\item All type variables on the right-hand side must also appear on
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  the left-hand side; this prohibits definitions such as {\tt
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    (zero::nat) == length ([]::'a list)}.
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\item The definition must not be recursive.  Most object-logics provide
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  definitional principles that can be used to express recursion safely.
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\end{itemize}
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These checks are intended to catch the sort of errors that might be made
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accidentally.  Misspellings, for instance, might result in additional
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variables appearing on the right-hand side.  More elaborate checks could be
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made, but the cost might be overly strict rules on declaration order, etc.
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\subsection{*Classes and arities}
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\index{classes!context conditions}\index{arities!context conditions}
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In order to guarantee principal types~\cite{nipkow-prehofer},
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arity declarations must obey two conditions:
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\begin{itemize}
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\item There must not be any two declarations $ty :: (\vec{r})c$ and
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  $ty :: (\vec{s})c$ with $\vec{r} \neq \vec{s}$.  For example, this
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  excludes the following:
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\begin{ttbox}
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arities
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  foo :: ({\ttlbrace}logic{\ttrbrace}) logic
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  foo :: ({\ttlbrace}{\ttrbrace})logic
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\end{ttbox}
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\item If there are two declarations $ty :: (s@1,\dots,s@n)c$ and $ty ::
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  (s@1',\dots,s@n')c'$ such that $c' < c$ then $s@i' \preceq s@i$ must hold
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  for $i=1,\dots,n$.  The relationship $\preceq$, defined as
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\[ s' \preceq s \iff \forall c\in s. \exists c'\in s'.~ c'\le c, \]
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expresses that the set of types represented by $s'$ is a subset of the
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set of types represented by $s$.  Assuming $term \preceq logic$, the
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following is forbidden:
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\begin{ttbox}
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arities
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  foo :: ({\ttlbrace}logic{\ttrbrace})logic
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  foo :: ({\ttlbrace}{\ttrbrace})term
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\end{ttbox}
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\end{itemize}
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\section{The theory loader}\label{sec:more-theories}
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\index{theories!reading}\index{files!reading}
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Isabelle's theory loader manages dependencies of the internal graph of theory
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nodes (the \emph{theory database}) and the external view of the file system.
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See \S\ref{sec:intro-theories} for its most basic commands, such as
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\texttt{use_thy}.  There are a few more operations available.
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\begin{ttbox}
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use_thy_only    : string -> unit
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update_thy_only : string -> unit
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touch_thy       : string -> unit
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remove_thy      : string -> unit
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delete_tmpfiles : bool ref \hfill{\bf initially true}
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\end{ttbox}
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\begin{ttdescription}
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\item[\ttindexbold{use_thy_only} "$name$";] is similar to \texttt{use_thy},
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  but processes the actual theory file $name$\texttt{.thy} only, ignoring
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  $name$\texttt{.ML}.  This might be useful in replaying proof scripts by hand
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  from the very beginning, starting with the fresh theory.
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\item[\ttindexbold{update_thy_only} "$name$";] is similar to
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  \texttt{update_thy}, but processes the actual theory file
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  $name$\texttt{.thy} only, ignoring $name$\texttt{.ML}.
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\item[\ttindexbold{touch_thy} "$name$";] marks theory node $name$ of the
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  internal graph as outdated.  While the theory remains usable, subsequent
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  operations such as \texttt{use_thy} may cause a reload.
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\item[\ttindexbold{remove_thy} "$name$";] deletes theory node $name$,
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  including \emph{all} of its descendants.  Beware!  This is a quick way to
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  dispose a large number of theories at once.  Note that {\ML} bindings to
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  theorems etc.\ of removed theories may still persist.
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\item[reset \ttindexbold{delete_tmpfiles};] processing theory files usually
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  involves temporary {\ML} files to be created.  By default, these are deleted
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  afterwards.  Resetting the \texttt{delete_tmpfiles} flag inhibits this,
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  leaving the generated code for debugging purposes.  The basic location for
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  temporary files is determined by the \texttt{ISABELLE_TMP} environment
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  variable (which is private to the running Isabelle process and may be
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  retrieved by \ttindex{getenv} from {\ML}).
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\end{ttdescription}
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\medskip Theory and {\ML} files are located by skimming through the
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directories listed in Isabelle's internal load path, which merely contains the
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current directory ``\texttt{.}'' by default.  The load path may be accessed by
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the following operations.
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\begin{ttbox}
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show_path: unit -> string list
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add_path: string -> unit
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del_path: string -> unit
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reset_path: unit -> unit
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\end{ttbox}
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\begin{ttdescription}
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\item[\ttindexbold{show_path}();] displays the load path components in
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  canonical string representation (which is always according to Unix rules).
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\item[\ttindexbold{add_path} "$dir$";] adds component $dir$ to the beginning
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  of the load path.
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\item[\ttindexbold{del_path} "$dir$";] removes any occurrences of component
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  $dir$ from the load path.
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\item[\ttindexbold{reset_path}();] resets the load path to ``\texttt{.}''
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  (current directory) only.
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\end{ttdescription}
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In operations referring indirectly to some file, the argument may be prefixed
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by a directory that will be temporarily appended to the load path, e.g.\ 
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\texttt{use_thy~"$dir/name$"}.  Note that, depending on which parts of the
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ancestry of $name$ are already loaded, the dynamic change of paths might be
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hard to predict.  Use this feature with great care only.
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\section{Locales}
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\label{Locales}
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Locales \cite{kammueller-locales} are a concept of local proof contexts.  They
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are introduced as named syntactic objects within theories and can be
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opened in any descendant theory.
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\subsection{Declaring Locales}
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A locale is declared in a theory section that starts with the
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keyword \texttt{locale}.  It consists typically of three parts, the
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\texttt{fixes} part, the \texttt{assumes} part, and the \texttt{defines} part.
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Appendix \ref{app:TheorySyntax} presents the full syntax.
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\subsubsection{Parts of Locales}
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   331
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The subsection introduced by the keyword \texttt{fixes} declares the locale
5f1ce866c497 locale documentation (from Florian)
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   333
constants in a way that closely resembles a global \texttt{consts}
5f1ce866c497 locale documentation (from Florian)
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   334
declaration.  In particular, there may be an optional pretty printing syntax
5f1ce866c497 locale documentation (from Florian)
paulson
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   335
for the locale constants.
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   336
5f1ce866c497 locale documentation (from Florian)
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   337
The subsequent \texttt{assumes} part specifies the locale rules.  They are
5f1ce866c497 locale documentation (from Florian)
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   338
defined like \texttt{rules}: by an identifier followed by the rule
5f1ce866c497 locale documentation (from Florian)
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   339
given as a string.  Locale rules admit the statement of local assumptions
5f1ce866c497 locale documentation (from Florian)
paulson
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   340
about the locale constants.  The \texttt{assumes} part is optional.  Non-fixed
5f1ce866c497 locale documentation (from Florian)
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   341
variables in locale rules are automatically bound by the universal quantifier
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   342
\texttt{!!} of the meta-logic.
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diff changeset
   343
5f1ce866c497 locale documentation (from Florian)
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   344
Finally, the \texttt{defines} part introduces the definitions that are
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   345
available in the locale.  Locale constants declared in the \texttt{fixes}
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   346
section are defined using the meta-equality \texttt{==}.  If the
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paulson
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   347
locale constant is a functiond then its definition can (as usual) have
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   348
variables on the left-hand side acting as formal parameters; they are
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   349
considered as schematic variables and are automatically generalized by
5f1ce866c497 locale documentation (from Florian)
paulson
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   350
universal quantification of the meta-logic.  The right hand side of a
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paulson
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   351
definition must not contain variables that are not already on the left hand
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paulson
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   352
side.  In so far locale definitions behave like theory level definitions.
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paulson
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diff changeset
   353
However, the locale concept realizes \emph{dependent definitions}: any variable
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   354
that is fixed as a locale constant can occur on the right hand side of
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paulson
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   355
definitions.  For an illustration of these dependent definitions see the
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paulson
parents: 6658
diff changeset
   356
occurrence of the locale constant \texttt{G} on the right hand side of the
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paulson
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diff changeset
   357
definitions of the locale \texttt{group} below.  Naturally, definitions can
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paulson
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   358
already use the syntax of the locale constants in the \texttt{fixes}
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paulson
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   359
subsection.  The \texttt{defines} part is, as the \texttt{assumes} part,
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paulson
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   360
optional.
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paulson
parents: 6658
diff changeset
   361
5f1ce866c497 locale documentation (from Florian)
paulson
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diff changeset
   362
\subsubsection{Example for Definition}
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diff changeset
   363
The concrete syntax of locale definitions is demonstrated by example below.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   364
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   365
Locale \texttt{group} assumes the definition of groups in a theory
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   366
file\footnote{This and other examples are from \texttt{HOL/ex}.}.  A locale
5f1ce866c497 locale documentation (from Florian)
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   367
defining a convenient proof environment for group related proofs may be
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paulson
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   368
added to the theory as follows:
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   369
\begin{ttbox}
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  locale group =
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   371
    fixes 
5f1ce866c497 locale documentation (from Florian)
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   372
      G         :: "'a grouptype"
5f1ce866c497 locale documentation (from Florian)
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   373
      e         :: "'a"
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   374
      binop     :: "'a => 'a => 'a"        (infixr "#" 80)
5f1ce866c497 locale documentation (from Florian)
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   375
      inv       :: "'a => 'a"              ("i(_)" [90] 91)
5f1ce866c497 locale documentation (from Florian)
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   376
    assumes
5f1ce866c497 locale documentation (from Florian)
paulson
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   377
      Group_G   "G: Group"
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
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   378
    defines
5f1ce866c497 locale documentation (from Florian)
paulson
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   379
      e_def     "e == unit G"
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   380
      binop_def "x # y == bin_op G x y"
5f1ce866c497 locale documentation (from Florian)
paulson
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   381
      inv_def   "i(x) == inverse G x"
5f1ce866c497 locale documentation (from Florian)
paulson
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   382
\end{ttbox}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   383
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   384
\subsubsection{Polymorphism}
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paulson
parents: 6658
diff changeset
   385
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   386
In contrast to polymorphic definitions in theories, the use of the
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paulson
parents: 6658
diff changeset
   387
same type variable for the declaration of different locale constants in the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   388
fixes part means \emph{the same} type.  In other words, the scope of the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   389
polymorphic variables is extended over all constant declarations of a locale.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   390
In the above example \texttt{'a} refers to the same type which is fixed inside
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   391
the locale.  In an exported theorem (see \S\ref{sec:locale-export}) the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   392
constructors of locale \texttt{group} are polymorphic, yet only simultaneously
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   393
instantiatable.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   394
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   395
\subsubsection{Nested Locales}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   396
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   397
A locale can be defined as the extension of a previously defined
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   398
locale.  This operation of extension is optional and is syntactically
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   399
expressed as 
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   400
\begin{ttbox}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   401
locale foo = bar + ...
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   402
\end{ttbox}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   403
The locale \texttt{foo} builds on the constants and syntax of the locale {\tt
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   404
bar}.  That is, all contents of the locale \texttt{bar} can be used in
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   405
definitions and rules of the corresponding parts of the locale {\tt
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   406
foo}.  Although locale \texttt{foo} assumes the \texttt{fixes} part of \texttt{bar} it
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   407
does not automatically subsume its rules and definitions.  Normally, one
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   408
expects to use locale \texttt{foo} only if locale \texttt{bar} is already
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   409
active.  These aspects of use and activation of locales are considered in the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   410
subsequent section.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   411
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   412
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   413
\subsection{Locale Scope}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   414
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   415
Locales are by default inactive, but they can be invoked.  The list of
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   416
currently active locales is called \emph{scope}.  The process of activating
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   417
them is called \emph{opening}; the reverse is \emph{closing}.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   418
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   419
\subsubsection{Scope}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   420
The locale scope is part of each theory.  It is a dynamic stack containing
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   421
all active locales at a certain point in an interactive session.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   422
The scope lives until all locales are explicitly closed.  At one time there
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   423
can be more than one locale open.  The contents of these various active
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   424
locales are all visible in the scope.  In case of nested locales for example,
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   425
the nesting is actually reflected to the scope, which contains the nested
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   426
locales as layers.  To check the state of the scope during a development the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   427
function \texttt{Print\_scope} may be used.  It displays the names of all open
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   428
locales on the scope.  The function \texttt{print\_locales} applied to a theory
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   429
displays all locales contained in that theory and in addition also the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   430
current scope.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   431
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   432
The scope is manipulated by the commands for opening and closing of locales. 
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   433
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   434
\subsubsection{Opening}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   435
Locales can be \emph{opened} at any point during a session where
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   436
we want to prove theorems concerning the locale.  Opening a locale means
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   437
making its contents visible by pushing it onto the scope of the current
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   438
theory.  Inside a scope of opened locales, theorems can use all definitions and
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   439
rules contained in the locales on the scope.  The rules and definitions may
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   440
be accessed individually using the function \ttindex{thm}.  This function is
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   441
applied to the names assigned to locale rules and definitions as
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   442
strings.  The opening command is called \texttt{Open\_locale} and takes the 
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   443
name of the locale to be opened as its argument.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   444
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   445
If one opens a locale \texttt{foo} that is defined by extension from locale
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   446
\texttt{bar}, the function \texttt{Open\_locale} checks if locale \texttt{bar}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   447
is open.  If so, then it just opens \texttt{foo}, if not, then it prints a
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   448
message and opens \texttt{bar} before opening \texttt{foo}.  Naturally, this
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   449
carries on, if \texttt{bar} is again an extension.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   450
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   451
\subsubsection{Closing}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   452
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   453
\emph{Closing} means to cancel the last opened locale, pushing it out of the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   454
scope.  Theorems proved during the life cycle of this locale will be disabled,
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   455
unless they have been explicitly exported, as described below.  However, when
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   456
the same locale is opened again these theorems may be used again as well,
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   457
provided that they were saved as theorems in the first place, using
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   458
\texttt{qed} or ML assignment.  The command \texttt{Close\_locale} takes a
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   459
locale name as a string and checks if this locale is actually the topmost
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   460
locale on the scope.  If this is the case, it removes this locale, otherwise
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   461
it prints a warning message and does not change the scope.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   462
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   463
\subsubsection{Export of Theorems}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   464
\label{sec:locale-export}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   465
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   466
Export of theorems transports theorems out of the scope of locales.  Locale
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   467
rules that have been used in the proof of an exported theorem inside the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   468
locale are carried by the exported form of the theorem as its individual
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   469
meta-assumptions.  The locale constants are universally quantified variables
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   470
in these theorems, hence such theorems can be instantiated individually.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   471
Definitions become unfolded; locale constants that were merely used for
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   472
definitions vanish.  Logically, exporting corresponds to a combined
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   473
application of introduction rules for implication and universal
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   474
quantification.  Exporting forms a kind of normalization of theorems in a
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   475
locale scope.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   476
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   477
According to the possibility of nested locales there are two different forms
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   478
of export.  The first one is realized by the function \texttt{export} that
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   479
exports theorems through all layers of opened locales of the scope.  Hence,
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   480
the application of export to a theorem yields a theorem of the global level,
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   481
that is, the current theory context without any local assumptions or
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   482
definitions.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   483
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   484
When locales are nested we might want to export a theorem, not to the global
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   485
level of the current theory but just to the previous level.  The other export
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   486
function, \texttt{Export}, transports theorems one level up in the scope; the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   487
theorem still uses locale constants, definitions and rules of the locales
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   488
underneath.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   489
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   490
\subsection{Functions for Locales}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   491
\label{Syntax}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   492
\index{locales!functions}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   493
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   494
Here is a quick reference list of locale functions.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   495
\begin{ttbox}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   496
  Open_locale  : xstring -> unit 
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   497
  Close_locale : xstring -> unit
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   498
  export       :     thm -> thm
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   499
  Export       :     thm -> thm
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   500
  thm          : xstring -> thm
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   501
  Print_scope  :    unit -> unit
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   502
  print_locales:  theory -> unit
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   503
\end{ttbox}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   504
\begin{ttdescription}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   505
\item[\ttindexbold{Open_locale} $xstring$] 
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   506
    opens the locale {\it xstring}, adding it to the scope of the theory of the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   507
  current context.  If the opened locale is built by extension, the ancestors
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   508
  are opened automatically.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   509
  
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   510
\item[\ttindexbold{Close_locale} $xstring$] eliminates the locale {\it
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   511
    xstring} from the scope if it is the topmost item on it, otherwise it does
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   512
  not change the scope and produces a warning.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   513
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   514
\item[\ttindexbold{export} $thm$] locale definitions become expanded in {\it
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   515
    thm} and locale rules that were used in the proof of {\it thm} become part
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   516
  of its individual assumptions.  This normalization happens with respect to
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   517
  \emph{all open locales} on the scope.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   518
  
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   519
\item[\ttindexbold{Export} $thm$] works like \texttt{export} but normalizes
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   520
  theorems only up to the previous level of locales on the scope.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   521
  
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   522
\item[\ttindexbold{thm} $xstring$] applied to the name of a locale definition
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   523
  or rule it returns the definition as a theorem.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   524
  
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   525
\item[\ttindexbold{Print_scope}()] prints the names of the locales in the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   526
  current scope of the current theory context.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   527
  
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   528
\item[\ttindexbold{print_locale} $theory$] prints all locales that are
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   529
  contained in {\it theory} directly or indirectly.  It also displays the
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   530
  current scope similar to \texttt{Print\_scope}.
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   531
\end{ttdescription}
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   532
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   533
866
2d3d020eef11 added documentation of bind_thm, qed, qed_goal, get_thm, thms_of
clasohm
parents: 864
diff changeset
   534
\section{Basic operations on theories}\label{BasicOperationsOnTheories}
4384
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   535
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   536
\subsection{*Theory inclusion}
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   537
\begin{ttbox}
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   538
subthy      : theory * theory -> bool
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   539
eq_thy      : theory * theory -> bool
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   540
transfer    : theory -> thm -> thm
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   541
transfer_sg : Sign.sg -> thm -> thm
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   542
\end{ttbox}
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   543
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   544
Inclusion and equality of theories is determined by unique
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   545
identification stamps that are created when declaring new components.
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   546
Theorems contain a reference to the theory (actually to its signature)
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   547
they have been derived in.  Transferring theorems to super theories
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   548
has no logical significance, but may affect some operations in subtle
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   549
ways (e.g.\ implicit merges of signatures when applying rules, or
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   550
pretty printing of theorems).
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   551
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   552
\begin{ttdescription}
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   553
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   554
\item[\ttindexbold{subthy} ($thy@1$, $thy@2$)] determines if $thy@1$
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   555
  is included in $thy@2$ wrt.\ identification stamps.
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   556
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   557
\item[\ttindexbold{eq_thy} ($thy@1$, $thy@2$)] determines if $thy@1$
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   558
  is exactly the same as $thy@2$.
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   559
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   560
\item[\ttindexbold{transfer} $thy$ $thm$] transfers theorem $thm$ to
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   561
  theory $thy$, provided the latter includes the theory of $thm$.
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   562
  
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   563
\item[\ttindexbold{transfer_sg} $sign$ $thm$] is similar to
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   564
  \texttt{transfer}, but identifies the super theory via its
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   565
  signature.
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   566
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   567
\end{ttdescription}
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   568
429cba89b4c8 \subsection{*Theory inclusion};
wenzelm
parents: 4374
diff changeset
   569
6571
wenzelm
parents: 6569
diff changeset
   570
\subsection{*Primitive theories}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   571
\begin{ttbox}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   572
ProtoPure.thy  : theory
3108
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   573
Pure.thy       : theory
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   574
CPure.thy      : theory
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   575
\end{ttbox}
3108
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   576
\begin{description}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   577
\item[\ttindexbold{ProtoPure.thy}, \ttindexbold{Pure.thy},
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   578
  \ttindexbold{CPure.thy}] contain the syntax and signature of the
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   579
  meta-logic.  There are basically no axioms: meta-level inferences
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   580
  are carried out by \ML\ functions.  \texttt{Pure} and \texttt{CPure}
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   581
  just differ in their concrete syntax of prefix function application:
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   582
  $t(u@1, \ldots, u@n)$ in \texttt{Pure} vs.\ $t\,u@1,\ldots\,u@n$ in
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   583
  \texttt{CPure}.  \texttt{ProtoPure} is their common parent,
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   584
  containing no syntax for printing prefix applications at all!
6571
wenzelm
parents: 6569
diff changeset
   585
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   586
%% FIXME
478
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   587
%\item [\ttindexbold{extend_theory} $thy$ {\tt"}$T${\tt"} $\cdots$] extends
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   588
%  the theory $thy$ with new types, constants, etc.  $T$ identifies the theory
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   589
%  internally.  When a theory is redeclared, say to change an incorrect axiom,
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   590
%  bindings to the old axiom may persist.  Isabelle ensures that the old and
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   591
%  new theories are not involved in the same proof.  Attempting to combine
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   592
%  different theories having the same name $T$ yields the fatal error
838bd766d536 added init_thy_reader and removed extend_theory
nipkow
parents: 332
diff changeset
   593
%extend_theory  : theory -> string -> \(\cdots\) -> theory
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   594
%\begin{ttbox}
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   595
%Attempt to merge different versions of theory: \(T\)
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   596
%\end{ttbox}
3108
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   597
\end{description}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   598
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   599
%% FIXME
275
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   600
%\item [\ttindexbold{extend_theory} $thy$ {\tt"}$T${\tt"}
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   601
%      ($classes$, $default$, $types$, $arities$, $consts$, $sextopt$) $rules$]
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   602
%\hfill\break   %%% include if line is just too short
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   603
%is the \ML{} equivalent of the following theory definition:
275
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   604
%\begin{ttbox}
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   605
%\(T\) = \(thy\) +
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   606
%classes \(c\) < \(c@1\),\(\dots\),\(c@m\)
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   607
%        \dots
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   608
%default {\(d@1,\dots,d@r\)}
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   609
%types   \(tycon@1\),\dots,\(tycon@i\) \(n\)
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   610
%        \dots
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   611
%arities \(tycon@1'\),\dots,\(tycon@j'\) :: (\(s@1\),\dots,\(s@n\))\(c\)
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   612
%        \dots
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   613
%consts  \(b@1\),\dots,\(b@k\) :: \(\tau\)
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   614
%        \dots
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   615
%rules   \(name\) \(rule\)
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   616
%        \dots
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   617
%end
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   618
%\end{ttbox}
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   619
%where
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   620
%\begin{tabular}[t]{l@{~=~}l}
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   621
%$classes$ & \tt[("$c$",["$c@1$",\dots,"$c@m$"]),\dots] \\
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   622
%$default$ & \tt["$d@1$",\dots,"$d@r$"]\\
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   623
%$types$   & \tt[([$tycon@1$,\dots,$tycon@i$], $n$),\dots] \\
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   624
%$arities$ & \tt[([$tycon'@1$,\dots,$tycon'@j$], ([$s@1$,\dots,$s@n$],$c$)),\dots]
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   625
%\\
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   626
%$consts$  & \tt[([$b@1$,\dots,$b@k$],$\tau$),\dots] \\
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   627
%$rules$   & \tt[("$name$",$rule$),\dots]
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   628
%\end{tabular}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   629
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   630
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   631
\subsection{Inspecting a theory}\label{sec:inspct-thy}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   632
\index{theories!inspecting|bold}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   633
\begin{ttbox}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   634
print_syntax        : theory -> unit
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   635
print_theory        : theory -> unit
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   636
parents_of          : theory -> theory list
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   637
ancestors_of        : theory -> theory list
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   638
sign_of             : theory -> Sign.sg
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   639
Sign.stamp_names_of : Sign.sg -> string list
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   640
\end{ttbox}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   641
These provide means of viewing a theory's components.
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   642
\begin{ttdescription}
3108
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   643
\item[\ttindexbold{print_syntax} $thy$] prints the syntax of $thy$
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   644
  (grammar, macros, translation functions etc., see
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   645
  page~\pageref{pg:print_syn} for more details).
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   646
  
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   647
\item[\ttindexbold{print_theory} $thy$] prints the logical parts of
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   648
  $thy$, excluding the syntax.
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   649
  
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   650
\item[\ttindexbold{parents_of} $thy$] returns the direct ancestors
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   651
  of~$thy$.
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   652
  
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   653
\item[\ttindexbold{ancestors_of} $thy$] returns all ancestors of~$thy$
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   654
  (not including $thy$ itself).
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   655
  
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   656
\item[\ttindexbold{sign_of} $thy$] returns the signature associated
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   657
  with~$thy$.  It is useful with functions like {\tt
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   658
    read_instantiate_sg}, which take a signature as an argument.
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   659
  
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   660
\item[\ttindexbold{Sign.stamp_names_of} $sg$]\index{signatures}
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   661
  returns the names of the identification \rmindex{stamps} of ax
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   662
  signature.  These coincide with the names of its full ancestry
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   663
  including that of $sg$ itself.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   664
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   665
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   666
1369
b82815e61b30 corrected documentation of pseudo theories;
clasohm
parents: 866
diff changeset
   667
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   668
\section{Terms}
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   669
\index{terms|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   670
Terms belong to the \ML\ type \mltydx{term}, which is a concrete datatype
3108
335efc3f5632 misc updates, tuning, cleanup;
wenzelm
parents: 1905
diff changeset
   671
with six constructors:
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   672
\begin{ttbox}
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   673
type indexname = string * int;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   674
infix 9 $;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   675
datatype term = Const of string * typ
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   676
              | Free  of string * typ
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   677
              | Var   of indexname * typ
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   678
              | Bound of int
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   679
              | Abs   of string * typ * term
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   680
              | op $  of term * term;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   681
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   682
\begin{ttdescription}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   683
\item[\ttindexbold{Const} ($a$, $T$)] \index{constants|bold}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   684
  is the {\bf constant} with name~$a$ and type~$T$.  Constants include
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   685
  connectives like $\land$ and $\forall$ as well as constants like~0
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   686
  and~$Suc$.  Other constants may be required to define a logic's concrete
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   687
  syntax.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   688
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   689
\item[\ttindexbold{Free} ($a$, $T$)] \index{variables!free|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   690
  is the {\bf free variable} with name~$a$ and type~$T$.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   691
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   692
\item[\ttindexbold{Var} ($v$, $T$)] \index{unknowns|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   693
  is the {\bf scheme variable} with indexname~$v$ and type~$T$.  An
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   694
  \mltydx{indexname} is a string paired with a non-negative index, or
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   695
  subscript; a term's scheme variables can be systematically renamed by
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   696
  incrementing their subscripts.  Scheme variables are essentially free
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   697
  variables, but may be instantiated during unification.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   698
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   699
\item[\ttindexbold{Bound} $i$] \index{variables!bound|bold}
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   700
  is the {\bf bound variable} with de Bruijn index~$i$, which counts the
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   701
  number of lambdas, starting from zero, between a variable's occurrence
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   702
  and its binding.  The representation prevents capture of variables.  For
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   703
  more information see de Bruijn \cite{debruijn72} or
6592
c120262044b6 Now uses manual.bib; some references updated
paulson
parents: 6571
diff changeset
   704
  Paulson~\cite[page~376]{paulson-ml2}.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   705
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   706
\item[\ttindexbold{Abs} ($a$, $T$, $u$)]
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   707
  \index{lambda abs@$\lambda$-abstractions|bold}
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   708
  is the $\lambda$-{\bf abstraction} with body~$u$, and whose bound
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   709
  variable has name~$a$ and type~$T$.  The name is used only for parsing
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   710
  and printing; it has no logical significance.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   711
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   712
\item[$t$ \$ $u$] \index{$@{\tt\$}|bold} \index{function applications|bold}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   713
is the {\bf application} of~$t$ to~$u$.
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   714
\end{ttdescription}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   715
Application is written as an infix operator to aid readability.
332
01b87a921967 final Springer copy
lcp
parents: 324
diff changeset
   716
Here is an \ML\ pattern to recognize \FOL{} formulae of
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   717
the form~$A\imp B$, binding the subformulae to~$A$ and~$B$:
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   718
\begin{ttbox}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   719
Const("Trueprop",_) $ (Const("op -->",_) $ A $ B)
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   720
\end{ttbox}
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   721
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   722
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   723
\section{*Variable binding}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   724
\begin{ttbox}
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   725
loose_bnos     : term -> int list
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   726
incr_boundvars : int -> term -> term
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   727
abstract_over  : term*term -> term
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   728
variant_abs    : string * typ * term -> string * term
4374
wenzelm
parents: 4317
diff changeset
   729
aconv          : term * term -> bool\hfill{\bf infix}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   730
\end{ttbox}
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   731
These functions are all concerned with the de Bruijn representation of
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   732
bound variables.
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   733
\begin{ttdescription}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   734
\item[\ttindexbold{loose_bnos} $t$]
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   735
  returns the list of all dangling bound variable references.  In
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   736
  particular, \texttt{Bound~0} is loose unless it is enclosed in an
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   737
  abstraction.  Similarly \texttt{Bound~1} is loose unless it is enclosed in
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   738
  at least two abstractions; if enclosed in just one, the list will contain
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   739
  the number 0.  A well-formed term does not contain any loose variables.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   740
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   741
\item[\ttindexbold{incr_boundvars} $j$]
332
01b87a921967 final Springer copy
lcp
parents: 324
diff changeset
   742
  increases a term's dangling bound variables by the offset~$j$.  This is
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   743
  required when moving a subterm into a context where it is enclosed by a
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   744
  different number of abstractions.  Bound variables with a matching
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   745
  abstraction are unaffected.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   746
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   747
\item[\ttindexbold{abstract_over} $(v,t)$]
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   748
  forms the abstraction of~$t$ over~$v$, which may be any well-formed term.
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   749
  It replaces every occurrence of \(v\) by a \texttt{Bound} variable with the
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   750
  correct index.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   751
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   752
\item[\ttindexbold{variant_abs} $(a,T,u)$]
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   753
  substitutes into $u$, which should be the body of an abstraction.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   754
  It replaces each occurrence of the outermost bound variable by a free
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   755
  variable.  The free variable has type~$T$ and its name is a variant
332
01b87a921967 final Springer copy
lcp
parents: 324
diff changeset
   756
  of~$a$ chosen to be distinct from all constants and from all variables
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   757
  free in~$u$.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   758
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   759
\item[$t$ \ttindexbold{aconv} $u$]
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   760
  tests whether terms~$t$ and~$u$ are \(\alpha\)-convertible: identical up
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   761
  to renaming of bound variables.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   762
\begin{itemize}
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   763
  \item
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   764
    Two constants, \texttt{Free}s, or \texttt{Var}s are \(\alpha\)-convertible
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   765
    if their names and types are equal.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   766
    (Variables having the same name but different types are thus distinct.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   767
    This confusing situation should be avoided!)
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   768
  \item
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   769
    Two bound variables are \(\alpha\)-convertible
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   770
    if they have the same number.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   771
  \item
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   772
    Two abstractions are \(\alpha\)-convertible
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   773
    if their bodies are, and their bound variables have the same type.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   774
  \item
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   775
    Two applications are \(\alpha\)-convertible
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   776
    if the corresponding subterms are.
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   777
\end{itemize}
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   778
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   779
\end{ttdescription}
286
e7efbf03562b first draft of Springer book
lcp
parents: 275
diff changeset
   780
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   781
\section{Certified terms}\index{terms!certified|bold}\index{signatures}
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   782
A term $t$ can be {\bf certified} under a signature to ensure that every type
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   783
in~$t$ is well-formed and every constant in~$t$ is a type instance of a
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   784
constant declared in the signature.  The term must be well-typed and its use
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   785
of bound variables must be well-formed.  Meta-rules such as \texttt{forall_elim}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   786
take certified terms as arguments.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   787
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   788
Certified terms belong to the abstract type \mltydx{cterm}.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   789
Elements of the type can only be created through the certification process.
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   790
In case of error, Isabelle raises exception~\ttindex{TERM}\@.
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   791
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   792
\subsection{Printing terms}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   793
\index{terms!printing of}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   794
\begin{ttbox}
275
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   795
     string_of_cterm :           cterm -> string
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   796
Sign.string_of_term  : Sign.sg -> term -> string
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   797
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   798
\begin{ttdescription}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   799
\item[\ttindexbold{string_of_cterm} $ct$]
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   800
displays $ct$ as a string.
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   801
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   802
\item[\ttindexbold{Sign.string_of_term} $sign$ $t$]
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   803
displays $t$ as a string, using the syntax of~$sign$.
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   804
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   805
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   806
\subsection{Making and inspecting certified terms}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   807
\begin{ttbox}
4543
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   808
cterm_of          : Sign.sg -> term -> cterm
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   809
read_cterm        : Sign.sg -> string * typ -> cterm
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   810
cert_axm          : Sign.sg -> string * term -> string * term
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   811
read_axm          : Sign.sg -> string * string -> string * term
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   812
rep_cterm         : cterm -> {\ttlbrace}T:typ, t:term, sign:Sign.sg, maxidx:int\ttrbrace
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   813
Sign.certify_term : Sign.sg -> term -> term * typ * int
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   814
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   815
\begin{ttdescription}
4543
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   816
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   817
\item[\ttindexbold{cterm_of} $sign$ $t$] \index{signatures} certifies
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   818
  $t$ with respect to signature~$sign$.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   819
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   820
\item[\ttindexbold{read_cterm} $sign$ ($s$, $T$)] reads the string~$s$
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   821
  using the syntax of~$sign$, creating a certified term.  The term is
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   822
  checked to have type~$T$; this type also tells the parser what kind
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   823
  of phrase to parse.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   824
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   825
\item[\ttindexbold{cert_axm} $sign$ ($name$, $t$)] certifies $t$ with
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   826
  respect to $sign$ as a meta-proposition and converts all exceptions
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   827
  to an error, including the final message
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   828
\begin{ttbox}
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   829
The error(s) above occurred in axiom "\(name\)"
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   830
\end{ttbox}
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   831
4543
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   832
\item[\ttindexbold{read_axm} $sign$ ($name$, $s$)] similar to {\tt
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   833
    cert_axm}, but first reads the string $s$ using the syntax of
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   834
  $sign$.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   835
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   836
\item[\ttindexbold{rep_cterm} $ct$] decomposes $ct$ as a record
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   837
  containing its type, the term itself, its signature, and the maximum
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   838
  subscript of its unknowns.  The type and maximum subscript are
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   839
  computed during certification.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   840
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   841
\item[\ttindexbold{Sign.certify_term}] is a more primitive version of
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   842
  \texttt{cterm_of}, returning the internal representation instead of
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   843
  an abstract \texttt{cterm}.
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   844
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   845
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   846
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   847
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   848
\section{Types}\index{types|bold}
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   849
Types belong to the \ML\ type \mltydx{typ}, which is a concrete datatype with
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   850
three constructor functions.  These correspond to type constructors, free
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   851
type variables and schematic type variables.  Types are classified by sorts,
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   852
which are lists of classes (representing an intersection).  A class is
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   853
represented by a string.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   854
\begin{ttbox}
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   855
type class = string;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   856
type sort  = class list;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   857
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   858
datatype typ = Type  of string * typ list
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   859
             | TFree of string * sort
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   860
             | TVar  of indexname * sort;
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   861
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   862
infixr 5 -->;
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   863
fun S --> T = Type ("fun", [S, T]);
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   864
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   865
\begin{ttdescription}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   866
\item[\ttindexbold{Type} ($a$, $Ts$)] \index{type constructors|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   867
  applies the {\bf type constructor} named~$a$ to the type operands~$Ts$.
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   868
  Type constructors include~\tydx{fun}, the binary function space
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   869
  constructor, as well as nullary type constructors such as~\tydx{prop}.
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   870
  Other type constructors may be introduced.  In expressions, but not in
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   871
  patterns, \hbox{\tt$S$-->$T$} is a convenient shorthand for function
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   872
  types.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   873
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   874
\item[\ttindexbold{TFree} ($a$, $s$)] \index{type variables|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   875
  is the {\bf type variable} with name~$a$ and sort~$s$.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   876
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   877
\item[\ttindexbold{TVar} ($v$, $s$)] \index{type unknowns|bold}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   878
  is the {\bf type unknown} with indexname~$v$ and sort~$s$.
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   879
  Type unknowns are essentially free type variables, but may be
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   880
  instantiated during unification.
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   881
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   882
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   883
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   884
\section{Certified types}
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   885
\index{types!certified|bold}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   886
Certified types, which are analogous to certified terms, have type
275
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   887
\ttindexbold{ctyp}.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   888
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   889
\subsection{Printing types}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   890
\index{types!printing of}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   891
\begin{ttbox}
275
933ec96c522e update towards LNCS
nipkow
parents: 273
diff changeset
   892
     string_of_ctyp :           ctyp -> string
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   893
Sign.string_of_typ  : Sign.sg -> typ -> string
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   894
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   895
\begin{ttdescription}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   896
\item[\ttindexbold{string_of_ctyp} $cT$]
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   897
displays $cT$ as a string.
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   898
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   899
\item[\ttindexbold{Sign.string_of_typ} $sign$ $T$]
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   900
displays $T$ as a string, using the syntax of~$sign$.
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   901
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   902
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   903
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   904
\subsection{Making and inspecting certified types}
864
d63b111b917a quite a lot of minor and major revisions (inspecting theories, read_axm,
wenzelm
parents: 478
diff changeset
   905
\begin{ttbox}
4543
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   906
ctyp_of          : Sign.sg -> typ -> ctyp
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   907
rep_ctyp         : ctyp -> {\ttlbrace}T: typ, sign: Sign.sg\ttrbrace
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   908
Sign.certify_typ : Sign.sg -> typ -> typ
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   909
\end{ttbox}
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   910
\begin{ttdescription}
4543
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   911
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   912
\item[\ttindexbold{ctyp_of} $sign$ $T$] \index{signatures} certifies
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   913
  $T$ with respect to signature~$sign$.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   914
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   915
\item[\ttindexbold{rep_ctyp} $cT$] decomposes $cT$ as a record
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   916
  containing the type itself and its signature.
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   917
  
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   918
\item[\ttindexbold{Sign.certify_typ}] is a more primitive version of
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   919
  \texttt{ctyp_of}, returning the internal representation instead of
82a45bdd0e80 several minor updates;
wenzelm
parents: 4384
diff changeset
   920
  an abstract \texttt{ctyp}.
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   921
324
34bc15b546e6 penultimate Springer draft
lcp
parents: 286
diff changeset
   922
\end{ttdescription}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
   923
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   924
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   925
\section{Oracles: calling trusted external reasoners}
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   926
\label{sec:oracles}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   927
\index{oracles|(}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   928
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   929
Oracles allow Isabelle to take advantage of external reasoners such as
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   930
arithmetic decision procedures, model checkers, fast tautology checkers or
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   931
computer algebra systems.  Invoked as an oracle, an external reasoner can
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   932
create arbitrary Isabelle theorems.  It is your responsibility to ensure that
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   933
the external reasoner is as trustworthy as your application requires.
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   934
Isabelle's proof objects~(\S\ref{sec:proofObjects}) record how each theorem
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   935
depends upon oracle calls.
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   936
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   937
\begin{ttbox}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   938
invoke_oracle     : theory -> xstring -> Sign.sg * object -> thm
4597
a0bdee64194c Fixed a lot of overfull and underfull lines (hboxes)
paulson
parents: 4543
diff changeset
   939
Theory.add_oracle : bstring * (Sign.sg * object -> term) -> theory 
a0bdee64194c Fixed a lot of overfull and underfull lines (hboxes)
paulson
parents: 4543
diff changeset
   940
                    -> theory
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   941
\end{ttbox}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   942
\begin{ttdescription}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   943
\item[\ttindexbold{invoke_oracle} $thy$ $name$ ($sign$, $data$)]
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   944
  invokes the oracle $name$ of theory $thy$ passing the information
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   945
  contained in the exception value $data$ and creating a theorem
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   946
  having signature $sign$.  Note that type \ttindex{object} is just an
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   947
  abbreviation for \texttt{exn}.  Errors arise if $thy$ does not have
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   948
  an oracle called $name$, if the oracle rejects its arguments or if
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   949
  its result is ill-typed.
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   950
  
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   951
\item[\ttindexbold{Theory.add_oracle} $name$ $fun$ $thy$] extends
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   952
  $thy$ by oracle $fun$ called $name$.  It is seldom called
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   953
  explicitly, as there is concrete syntax for oracles in theory files.
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   954
\end{ttdescription}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   955
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   956
A curious feature of {\ML} exceptions is that they are ordinary constructors.
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   957
The {\ML} type \texttt{exn} is a datatype that can be extended at any time.  (See
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   958
my {\em {ML} for the Working Programmer}~\cite{paulson-ml2}, especially
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   959
page~136.)  The oracle mechanism takes advantage of this to allow an oracle to
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   960
take any information whatever.
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   961
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   962
There must be some way of invoking the external reasoner from \ML, either
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   963
because it is coded in {\ML} or via an operating system interface.  Isabelle
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   964
expects the {\ML} function to take two arguments: a signature and an
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   965
exception object.
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   966
\begin{itemize}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   967
\item The signature will typically be that of a desendant of the theory
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   968
  declaring the oracle.  The oracle will use it to distinguish constants from
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   969
  variables, etc., and it will be attached to the generated theorems.
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   970
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   971
\item The exception is used to pass arbitrary information to the oracle.  This
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   972
  information must contain a full description of the problem to be solved by
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   973
  the external reasoner, including any additional information that might be
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   974
  required.  The oracle may raise the exception to indicate that it cannot
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   975
  solve the specified problem.
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   976
\end{itemize}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   977
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   978
A trivial example is provided in theory \texttt{FOL/ex/IffOracle}.  This
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   979
oracle generates tautologies of the form $P\bimp\cdots\bimp P$, with
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   980
an even number of $P$s.
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   981
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   982
The \texttt{ML} section of \texttt{IffOracle.thy} begins by declaring
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   983
a few auxiliary functions (suppressed below) for creating the
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   984
tautologies.  Then it declares a new exception constructor for the
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   985
information required by the oracle: here, just an integer. It finally
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   986
defines the oracle function itself.
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   987
\begin{ttbox}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   988
exception IffOracleExn of int;\medskip
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   989
fun mk_iff_oracle (sign, IffOracleExn n) =
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   990
  if n > 0 andalso n mod 2 = 0
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   991
  then Trueprop \$ mk_iff n
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   992
  else raise IffOracleExn n;
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
   993
\end{ttbox}
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   994
Observe the function's two arguments, the signature \texttt{sign} and the
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   995
exception given as a pattern.  The function checks its argument for
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   996
validity.  If $n$ is positive and even then it creates a tautology
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   997
containing $n$ occurrences of~$P$.  Otherwise it signals error by
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
   998
raising its own exception (just by happy coincidence).  Errors may be
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
   999
signalled by other means, such as returning the theorem \texttt{True}.
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1000
Please ensure that the oracle's result is correctly typed; Isabelle
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1001
will reject ill-typed theorems by raising a cryptic exception at top
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1002
level.
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1003
6669
5f1ce866c497 locale documentation (from Florian)
paulson
parents: 6658
diff changeset
  1004
The \texttt{oracle} section of \texttt{IffOracle.thy} installs above
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1005
\texttt{ML} function as follows:
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1006
\begin{ttbox}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1007
IffOracle = FOL +\medskip
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1008
oracle
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1009
  iff = mk_iff_oracle\medskip
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1010
end
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1011
\end{ttbox}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1012
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1013
Now in \texttt{IffOracle.ML} we first define a wrapper for invoking
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1014
the oracle:
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1015
\begin{ttbox}
4597
a0bdee64194c Fixed a lot of overfull and underfull lines (hboxes)
paulson
parents: 4543
diff changeset
  1016
fun iff_oracle n = invoke_oracle IffOracle.thy "iff"
a0bdee64194c Fixed a lot of overfull and underfull lines (hboxes)
paulson
parents: 4543
diff changeset
  1017
                      (sign_of IffOracle.thy, IffOracleExn n);
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1018
\end{ttbox}
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1019
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1020
Here are some example applications of the \texttt{iff} oracle.  An
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1021
argument of 10 is allowed, but one of 5 is forbidden:
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1022
\begin{ttbox}
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1023
iff_oracle 10;
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1024
{\out  "P <-> P <-> P <-> P <-> P <-> P <-> P <-> P <-> P <-> P" : thm}
4317
7264fa2ff2ec several minor updates;
wenzelm
parents: 3485
diff changeset
  1025
iff_oracle 5;
1846
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1026
{\out Exception- IffOracleExn 5 raised}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1027
\end{ttbox}
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1028
763f08fb194f Documentation of oracles and their syntax
paulson
parents: 1650
diff changeset
  1029
\index{oracles|)}
104
d8205bb279a7 Initial revision
lcp
parents:
diff changeset
  1030
\index{theories|)}
5369
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1031
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1032
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1033
%%% Local Variables: 
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1034
%%% mode: latex
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1035
%%% TeX-master: "ref"
8384e01b6cf8 added nonterminals, setup;
wenzelm
parents: 4597
diff changeset
  1036
%%% End: