text‹ Isabelle/Isar provides a simple document preparation system based on {PDF-\LaTeX}, with support for hyperlinks and bookmarks within that format. This allows to produce papers, books, theses etc.\ from Isabelle theory sources. {\LaTeX} output is generated while processing a 🪙‹session› i
explained in the 🪙‹The Isabelle System Manual›🍋‹"isabelle-system"›.
The main Isabelle tools to get started with document preparation are
@{tool_ref mkroot} and @{tool_ref build}.
The classic Isabelle/HOL tutorial 🍋‹"isabelle-hol-book"›also explains
some aspects of theory presentation. ›
Markup commands provide a structured way to insert text into the document
generated from a theory. Each markup command takes a single @{syntaxtext}
argument, which is passed as argument to a corresponding {\LaTeX} macro. The
default macros provided by🍋‹~~/lib/texinputs/isabelle.sty› can be
redefined according to the needs of the underlying document and {\LaTeX}
styles.
Note that formal comments (\secref{sec:comments}) are similar to markup
commands, but have a different status within Isabelle/Isar syntax.
🪙 @{command chapter}, @{command section}, @{command subsection} etc.\ mark section headings within the theory source. This works in any context, even
before the initial @{command theory} command. The corresponding {\LaTeX}
macros are 🍋‹\isamarkupchapter›, 🍋‹\isamarkupsection›, 🍋‹\isamarkupsubsection› etc.java.lang.NullPointerException
🪙 @{command text} and @{command txt} specify paragraphs of plain text.
This corresponds to a {\LaTeX} environment 🍋‹\begin{isamarkuptext}›‹…› 🍋‹\end{isamarkuptext}› etc.
🪙 @{command text_raw} is similar to @{command text}, but without any
surrounding markup environment. This allows to inject arbitrary {\LaTeX}
source into the generated document.
All text passed to any of the above markup commands may refer to formal
entities via 🪙‹document antiquotations›, see also\secref{sec:antiq}. These
are interpreted in the present theory or proofcontext.
🪙
The proof markup commands closely resemble those fortheory specifications,
but have a different formal status and produce different {\LaTeX} macros. ›
The overall content of an Isabelle/Isar theory may alternate between formal and informal text. The main body consists of formal specificationandproof
commands, interspersed with markup commands (\secref{sec:markup}) or
document comments (\secref{sec:comments}). The argument of markup commands
quotes informal textto be printed in the resulting document, but may again
refer to formal entities via 🪙‹document antiquotations›.
For example, embedding 🍋‹@{term [show_types] "f x = a + x"}›
within a text block makes \isa{{\isacharparenleft}f{\isasymColon}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharplus}\ x} appear in the final {\LaTeX} document.
Antiquotations usually spare the author tedious typing of logical entities in full detail. Even more importantly, some degree of consistency-checking
between the main body of formal textand its informal explanation is
achieved, since terms andtypes appearing in antiquotations are checked
within the current theory or proofcontext.
🪙
Antiquotations are in general written as 🍋‹@{›\<open>name›~🍋‹[›\<open>options›🍋‹]›~‹arguments›\<^verbatim>‹}›. The short form 🍋‹\\›\<^verbatim>‹🚫close>‹name›\<^verbatim>‹>›\<open>‹argument_content›\<close> (without surrounding 🍋‹@{›\<open>…›🍋‹}›)
works for a single argument that is a cartouche. A cartouche without special
decoration is equivalent to🍋‹🪙›\<open>‹argument_content›\<close>, which is
equivalent to🍋‹@{cartouche›~‹‹argument_content›\🍋‹}›. The special name
@{antiquotation_def cartouche} is defined in the context: Isabelle/Pure
introduces that as an alias to @{antiquotation_ref text} (see below).
Consequently, ‹‹foo_bar + baz ≤ bazar›\text
(unchecked). A control symbol 🍋‹\\›\<^verbatim>‹🚫close>‹name›\🍋‹>› within the body text, but without a subsequent cartouche, is equivalent to 🍋‹@{›\‹name›\🍋‹}›. \begingroup \def\isasymcontrolstart{\isatt{\isacharbackslash\isacharless\isacharcircum}} 🪙‹ @{syntax_def antiquotation}: '@{' antiquotation_body '}' | '🪙' @{syntax_ref name} '>' @{syntax_ref cartouche} | @{syntax_ref cartouche} ; options: '[' (option * ',') ']' ; option: @{syntax name} | @{syntax name} '=' @{syntax name} ; › \endgroup Note that the syntax of antiquotations may 🪙‹not›include source comments \<^verbatim>\<open>(*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*)
🪙‹@{text s}› prints uninterpreted source text‹s›, i.e.\ inner syntax. This is particularly useful to print portions of text according to the Isabelle
document style, without demanding well-formedness, e.g.\ small pieces of
terms that should not be parsed or type-checked yet.
It isalso possible to write this in the short form ‹‹s›\› without any
further decoration.
🪙‹@{theory_text s}› prints uninterpreted theory source text‹s›, i.e.java.lang.NullPointerException
outer syntaxwith command keywords and other tokens.
🪙‹@{theory A}› prints the session-qualified theory name ‹A›, which is
guaranteed to refer to a valid ancestor theoryin the current context.
🪙‹@{thm a🪙1 … a🪙n}› prints theorems‹a🪙1 … a🪙n›. Full fact expressions are
allowed here, including attributes (\secref{sec:syn-att}).
🪙‹@{prop φ}› prints a well-typed proposition ‹φ›.
🪙‹@{lemma φ by m}› proves a well-typed proposition ‹φ›by method ‹m›and
prints the original ‹φ›.
🪙‹@{term t}› prints a well-typed term‹t›.
🪙‹@{value t}› evaluates a term‹t›and prints its result, see also
@{command_ref (HOL) value}.
🪙‹@{term_type t}› prints a well-typed term‹t› annotated with its type.
🪙‹@{typeof t}› prints the type of a well-typed term‹t›.
🪙‹@{const c}› prints a logical or syntactic constant ‹c›.
🪙‹@{abbrev c x🪙1 … x🪙n}› prints a constant abbreviation‹c x🪙1 … x🪙n ≡ rhs›
as defined in the current context.
🪙‹@{typ τ}› prints a well-formed type ‹τ›.
🪙‹@{type κ}› prints a (logical or syntactic) type constructor ‹κ›.
🪙‹@{class c}› prints a class‹c›.
🪙‹@{locale c}› prints a locale‹c›.
🪙‹@{bundle c}› prints a bundle ‹c›.
🪙‹@{command name}›, ‹@{method name}›, ‹@{attribute name}› print checked
entities of the Isar language.
🪙‹@{goals}› prints the current 🪙‹dynamic› goal state. This is mainly for
support of tactic-emulation scripts within Isar. Presentation of goal states
does not conform to the idea of human-readable proof documents!
When explaining proofs in detail it is usually better to spell out the
reasoning via proper Isar proof commands, instead of peeking at the internal
machine configuration.
🪙‹@{subgoals}›is similar to‹@{goals}›, but does not print the main goal.
🪙‹@{prf a🪙1 … a🪙n}› prints the (compact) proof terms corresponding to the theorems‹a🪙1 … a🪙n›. Note that this requires proof terms to be switched on for the current logic session.
🪙‹@{full_prf a🪙1 … a🪙n}›is like ‹@{prf a🪙1 … a🪙n}›, but prints the full proof terms, i.e.\ also displays information omitted in the compact proof term, which is denoted by ``‹_›'' placeholders there.
🪙‹@{ML_text s}› prints ML text verbatim: only the token language is
checked.
🪙‹@{ML s}›, ‹@{ML_infix s}›, ‹@{ML_type s}›, ‹@{ML_structure s}›, and ‹@{ML_functor s}› check text‹s› as ML value, infix operator, type,
exception, structure, and functor respectively. The source is printed
verbatim. The variants ‹@{ML_def s}›and‹@{ML_ref s}› etc. maintain the
document index: ``def'' means to make a bold entry, ``ref'' means to make a
regular entry.
There are two forms for type constructors, with or without separate type
arguments: this impacts only the index entry. For example, ‹@{ML_type_ref ‹'a list›}›
letter ``a''), but ‹@{ML_type_ref 'a ‹list›}› makes an entry for the
constructor name ``‹list›''.
🪙‹@{emph s}› prints document source recursively, with {\LaTeX} markup 🍋‹\emph{›\<open>…›🍋‹}›.
🪙‹@{bold s}› prints document source recursively, with {\LaTeX} markup 🍋‹\textbf{›\<open>…›🍋‹}›.
🪙‹@{verbatim s}› prints uninterpreted source text literally as ASCII
characters, using some type-writer font style.
🪙‹@{bash_function name}› prints the given GNU bash function verbatim. The
name is checked wrt.\ the Isabelle system environment 🍋‹"isabelle-system"›.
🪙‹@{system_option name}› prints the given system option verbatim. The name is checked wrt.\ cumulative 🍋‹etc/options› of all Isabelle components,
notably 🍋‹~~/etc/options›.
🪙‹@{session name}› prints given session name verbatim. The name is checked
wrt.\ the dependencies of the current session.
🪙‹@{path name}› prints the file-system path name verbatim.
🪙‹@{file name}›is like ‹@{path name}›, but ensures that ‹name› refers to a
plain file.
🪙‹@{dir name}›is like ‹@{path name}›, but ensures that ‹name› refers to a
directory.
🪙‹@{url name}› produces markup for the given URL, which results in an
active hyperlink within the text.
🪙‹@{cite arg}› produces the Bib{\TeX} citation macro 🍋‹\cite[...]{...}› with its optional and mandatory argument. The analogous 🍋‹\nocite›, and the 🍋‹\citet›and🍋‹\citep› variants from the 🍋‹natbib›
package🪙‹🪙‹https://ctan.org/pkg/natbib›\
The argument syntaxis uniform for all variants andis usually presented in
control-symbol-cartouche form: ‹🍋‹arg›\syntax of the
nested argument language is defined as follows: 🪙‹arg: (embedded @'in')? (name + @'and') 🍋 (@'using' name)?›
Here the embedded textis free-form {\LaTeX}, which becomes the optional
argument of the 🍋‹\cite› macro. The named items are Bib{\TeX} database
entries and become the mandatory argument (separated by comma). The optional
part ``🪙‹using name›'' specifies an alternative {\LaTeX} macro name.
🪙 @{command "print_antiquotations"} prints all document antiquotations that
are defined in the current context; the ``‹!›'' option indicates extra
verbosity. ›
subsection‹Styled antiquotations›
text‹ The antiquotations ‹thm›, specificationto modify the printed result. A style is specified by a name with a possibly empty number of arguments; multiple styles can be sequenced with commas. The following standard styles are available:
🪙‹lhs› extracts the first argument of any application form with at least
two arguments --- typically meta-level or object-level equality, or any
other binary relation.
🪙‹rhs›is like ‹lhs›, but extracts the second argument.
🪙‹concl› extracts the conclusion ‹C›from a rule in Horn-clause normal form ‹A🪙1 ==>… A🪙n ==> C›.
🪙‹prem›‹n›extract premise number ‹n›fromfrom a rule in Horn-clause
normal form ‹A🪙1 ==>… A🪙n ==> C›. ›
subsection‹General options›
text‹ The following options are available to tune the printed output of antiquotations. Note that many of these coincide with system and configuration options of the same names. 🪙 @{antiquotation_option_def show_types}~‹= bool› a
@{antiquotation_option_def show_sorts}~‹= bool› control printing of
explicit type and sort constraints.
🪙 @{antiquotation_option_def show_structs}~‹= bool› controls printing of
implicit structures.
🪙 @{antiquotation_option_def show_abbrevs}~‹= bool› controls folding of
abbreviations.
🪙 @{antiquotation_option_def names_long}~‹= bool› forces names of types and constants etc.\ to be printed in their fully qualified internal form.
🪙 @{antiquotation_option_def names_short}~‹= bool› forces names of types and constants etc.\ to be printed unqualified. Note that internalizing the output again in the current context may well yield a different result.
🪙 @{antiquotation_option_def names_unique}~‹= bool› determines whether the
printed version of qualified names should be made sufficiently long to
avoid overlap with names declared further back. Set to‹false›for more
concise output.
🪙 @{antiquotation_option_def eta_contract}~‹= bool› prints terms in ‹🪙›-contracted form.
🪙 @{antiquotation_option_def display}~‹= bool› indicates if the textisto
be output as multi-line ``display material'', rather than a small piece of text without line breaks (which is the default).
In this mode the embedded entities are printed in the same style as the
main theorytext.
🪙 @{antiquotation_option_def break}~‹= bool› controls line breaks in
non-display material.
🪙 @{antiquotation_option_def cartouche}~‹= bool› indicates if the output
should be delimited as cartouche.
🪙 @{antiquotation_option_def quotes}~‹= bool› indicates if the output
should be delimited via double quotes (option @{antiquotation_option
cartouche} takes precedence). Note that the Isabelle {\LaTeX} styles may
suppress quotes on their own account.
🪙 @{antiquotation_option_def mode}~‹= name› adds ‹name›to the print mode to be used for presentation. Note that the standard setupfor {\LaTeX} outputis already present by default, with mode ``‹latex›''.
🪙 @{antiquotation_option_def margin}~‹= nat›and
@{antiquotation_option_def indent}~‹= nat› change the margin or
indentation for pretty printing of display material.
🪙 @{antiquotation_option_def goals_limit}~‹= nat› determines the maximum
number of subgoals to be printed (for goal-based antiquotation).
🪙 @{antiquotation_option_def source}~‹= bool› prints the original source text of the antiquotation arguments, rather than its internal
representation. Note that formal checking of @{antiquotation "thm"},
@{antiquotation "term"}, etc. is still enabled; use the @{antiquotation "text"} antiquotation foruncheckedoutput.
Regular ‹term›and‹typ› antiquotations with‹source = false› involve a
full round-trip from the original source to an internalized logical entity backto a source form, according to the syntax of the current context. Thus the printed outputis not under direct control of the author, it may
even fluctuate a bit as the underlying theoryis changed later on.
In contrast, @{antiquotation_option source}~‹= true› admits direct
printing of the given source text, with the desirable well-formedness
check in the background, but without modification of the printed text.
Cartouche delimiters of the argument are stripped for antiquotations that
are internally categorized as ``embedded''.
🪙 @{antiquotation_option_def source_cartouche} is like
@{antiquotation_option source}, but cartouche delimiters are always
preserved in the output.
For Boolean flags, ``‹name = true›'' may be abbreviated as ``‹name›''. All
of the above flags are disabled by default, unless changed specifically for
a logic session in the corresponding 🍋‹ROOT›file. ›
section‹Markdown-like text structure›
text‹ The markup commands @{command_ref text}, @{command_ref txt}, @{command_ref text_raw} (\secref{sec:markup}) consist of plain text. Its internal structure consists of paragraphs and (nested) lists, using special Isabelle symbols and some rules for indentation and blank lines. This quasi-visual format resembles 🪙‹Markdown›\<
complexity of that notationis avoided.
This is a summary of the main principles of minimal Markdown in Isabelle:
🪙 List items start with the following markers 🪙[itemize:] 🍋‹🪙› 🪙[enumerate:] 🍋‹🪙› 🪙[description:] 🍋‹🪙›
🪙 Adjacent list items with same indentation and same marker are grouped
into a single list.
🪙 Singleton blank lines separate paragraphs.
🪙 Multiple blank lines escape from the current list hierarchy.
Notable differences to official Markdown:
🪙 Indentation of list items needs to match exactly.
🪙 Indentation is unlimited (official Markdown interprets four spaces as
block quote).
🪙 List items always consist of paragraphs --- there is no notion of
``tight'' list.
🪙Section headings are expressed via Isar document markup commands
(\secref{sec:markup}).
🪙 URLs, font styles, other special content is expressed via antiquotations
(\secref{sec:antiq}), usually with proper nesting of sub-languages via text cartouches. ›
section‹Document markers and command tags \label{sec:document-markers}›
text‹ \emph{Document markers} are formal comments of the form ‹🍋‹marker_body›\›
(using the control symbol 🍋‹🍋›) and may occur anywhere within the
outer syntax of a command: the inner syntax of a marker body resembles that for attributes (\secref{sec:syn-att}). In contrast, \emph{Command tags} may
only occur after a command keyword and are treated as special markers as
explained below.
Document markers are stripped from the document output, but surrounding
white-space is preserved: e.g.\ a marker at the end of a line does not
affect the subsequent line break. Markers operate within the semantic
presentation context of a command, and may modify it to change the overall
appearance of a command span (e.g.\ by adding tags).
Each document marker has its own syntax defined in the theorycontext; the
following markers are predefined in Isabelle/Pure:
🪙‹🍋‹title arg›\›, ‹🍋‹creator arg›\›, ‹🍋‹contributor arg›\›, ‹🍋‹date arg›\›, ‹🍋‹license arg›\›, and‹🍋‹description arg›\› produce markup in the PIDE
document, without any immediate effect on typesetting. This vocabulary is
taken from the Dublin Core Metadata
Initiative🪙‹🪙‹https://www.dublincore.org/specifications/dublin-core/dcmi-terms›\›.
The argument is an uninterpreted string, except for @{document_marker
description}, which consists of words that are subject to spell-checking.
🪙‹🍋‹tag name›\› updates the list of command tags in the presentation context: later declarations take precedence, so ‹🍋‹tag a, tag b, tag c›\›
produces a reversed list. The default tags are given by the original 🪙‹keywords›declaration of a command, and the system option
@{system_option_ref document_tags}.
The optional ‹scope› tells how far the tagging is applied to subsequent proofstructure: ``🪙‹("proof")›'' means it applies to the following proof text, and ``🪙‹(command)›'' means it only applies to the current command.
The default within a proof body is ``🪙‹("proof")›'', but for toplevel goal
statements it is ``🪙‹(command)›''. Thus a ‹tag› marker for🪙‹theorem›, 🪙‹lemma› etc. does \emph{not} affect its proofby default.
An old-style command tag 🍋‹%›\<open>name›is treated like a document marker ‹🍋‹tag (proof) name›\
document markers. The head of the resulting tags in the presentation contextis turned into {\LaTeX} environments to modify the type-setting.
The following tags are pre-declared for certain classes of commands, and
serve as default markup for certain kinds of commands:
🪙 \begin{tabular}{ll} ‹document› & document markup commands java.lang.NullPointerException ‹theory› & theorybegin/end java.lang.NullPointerException ‹proof› & all proof commands java.lang.NullPointerException ‹ML› & all commands involving ML code java.lang.NullPointerException \end{tabular} 🪙
The Isabelle document preparation system 🍋‹"isabelle-system"› allows
tagged command regions to be presented specifically, e.g.\ to fold proof
texts, or drop parts of the text completely.
For example ``🪙‹by auto›~‹🍋‹tag invisible›\›'' causes that piece of proofto
be treated as ‹invisible› instead of ‹proof› (the default), which may be
shown or hidden depending on the document setup. In contrast, ``🪙‹by auto›~
Explicit tag specifications within a proofapplyto all subsequent commands
of the same level of nesting. For example, ``🪙‹proof›~‹🍋‹tag invisible› …›~
some of its parts are tagged differently).
🪙
Command tags merely produce certain markup environments for type-setting.
The meaning of these is determined by {\LaTeX} macros, as defined in 🍋‹~~/lib/texinputs/isabelle.sty› or by the document author. The Isabelle
document preparation tools also provide some high-level options to specify
the meaning of arbitrary tags to ``keep'', ``drop'', or ``fold'' the
corresponding parts of the text. Logic sessions may also specify ``document
versions'', where given tags are interpreted in some particular way. Again
see 🍋‹"isabelle-system"›for further details. ›
The @{antiquotation rail} antiquotation allows to include syntax diagrams
into Isabelle documents. {\LaTeX} requires the style file 🍋‹~~/lib/texinputs/railsetup.sty›, which can be used via 🍋‹\usepackage{railsetup}›in🍋‹root.tex›, for example.
The rail specification language is quoted here as Isabelle @{syntax string}
or text @{syntax"cartouche"}; it has its own grammar given below.
The lexical syntax of ‹identifier› coincides with that of @{syntax
short_ident} in regular Isabelle syntax, but ‹string›uses single quotes
instead of double quotes of the standard @{syntax string} category.
Each ‹rule›defines a formal language (with optional name), using a notation
that is similar to EBNF or regular expressions with recursion. The meaning and visual appearance of these rail language elements is illustrated by the
following representative examples.
🪙 Empty 🍋‹()›
🪙‹()›
🪙 Nonterminal 🍋‹A›
🪙‹A›
🪙 Nonterminal via Isabelle antiquotation 🍋‹@{syntax method}›
🪙‹@{syntax method}›
🪙 Terminal 🍋‹'xyz'›
🪙‹'xyz'›
🪙 Terminal in keyword style 🍋‹@'xyz'›
🪙‹@'xyz'›
🪙 Terminal via Isabelle antiquotation 🍋‹@@{method rule}›
🪙‹@@{method rule}›
🪙 Concatenation 🍋‹A B C›
🪙‹A B C›
🪙 Newline inside concatenation 🍋‹A B C 🍋 D E F›
🪙‹A B C 🍋 D E F›
🪙 Variants 🍋‹A | B | C›
🪙‹A | B | C›
🪙 Option 🍋‹A ?›
🪙‹A ?›
🪙 Repetition 🍋‹A *›
🪙‹A *›
🪙 Repetition with separator 🍋‹A * sep›
🪙‹A * sep›
🪙 Strict repetition 🍋‹A +›
🪙‹A +›
🪙 Strict repetition with separator 🍋‹A + sep›
🪙‹A + sep› ›
end
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