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\begin{isabellebody}%
\def\isabellecontext{Codegen}%
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\isadelimtheory
\isanewline
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\endisadelimtheory
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\isatagtheory
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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\isadelimML
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\endisadelimML
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\isatagML
%
\endisatagML
{\isafoldML}%
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\isadelimML
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\endisadelimML
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\isamarkupchapter{Code generation from Isabelle theories%
}
\isamarkuptrue%
%
\isamarkupsection{Introduction%
}
\isamarkuptrue%
%
\isamarkupsubsection{Motivation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Executing formal specifications as programs is a well-established
topic in the theorem proving community. With increasing
application of theorem proving systems in the area of
software development and verification, its relevance manifests
for running test cases and rapid prototyping. In logical
calculi like constructive type theory,
a notion of executability is implicit due to the nature
of the calculus. In contrast, specifications in Isabelle
can be highly non-executable. In order to bridge
the gap between logic and executable specifications,
an explicit non-trivial transformation has to be applied:
code generation.
This tutorial introduces a generic code generator for the
Isabelle system \cite{isa-tutorial}.
Generic in the sense that the
\qn{target language} for which code shall ultimately be
generated is not fixed but may be an arbitrary state-of-the-art
functional programming language (currently, the implementation
supports SML \cite{SML}, OCaml \cite{OCaml} and Haskell
\cite{haskell-revised-report}).
We aim to provide a
versatile environment
suitable for software development and verification,
structuring the process
of code generation into a small set of orthogonal principles
while achieving a big coverage of application areas
with maximum flexibility.
Conceptually the code generator framework is part
of Isabelle's \isa{Pure} meta logic; the object logic
\isa{HOL} which is an extension of \isa{Pure}
already comes with a reasonable framework setup and thus provides
a good working horse for raising code-generation-driven
applications. So, we assume some familiarity and experience
with the ingredients of the \isa{HOL} \emph{Main} theory
(see also \cite{isa-tutorial}).%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Overview%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The code generator aims to be usable with no further ado
in most cases while allowing for detailed customization.
This manifests in the structure of this tutorial:
we start with a generic example \secref{sec:example}
and introduce code generation concepts \secref{sec:concept}.
Section
\secref{sec:basics} explains how to use the framework naively,
presuming a reasonable default setup. Then, section
\secref{sec:advanced} deals with advanced topics,
introducing further aspects of the code generator framework
in a motivation-driven manner. Last, section \secref{sec:ml}
introduces the framework's internal programming interfaces.
\begin{warn}
Ultimately, the code generator which this tutorial deals with
is supposed to replace the already established code generator
by Stefan Berghofer \cite{Berghofer-Nipkow:2002}.
So, for the moment, there are two distinct code generators
in Isabelle.
Also note that while the framework itself is
object-logic independent, only \isa{HOL} provides a reasonable
framework setup.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsection{An example: a simple theory of search trees \label{sec:example}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
When writing executable specifications using \isa{HOL},
it is convenient to use
three existing packages: the datatype package for defining
datatypes, the function package for (recursive) functions,
and the class package for overloaded definitions.
We develope a small theory of search trees; trees are represented
as a datatype with key type \isa{{\isacharprime}a} and value type \isa{{\isacharprime}b}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isacharequal}\ Leaf\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}linorder{\isachardoublequoteclose}\ {\isacharprime}b\isanewline
\ \ {\isacharbar}\ Branch\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent Note that we have constrained the type of keys
to the class of total orders, \isa{linorder}.
We define \isa{find} and \isa{update} functions:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ find\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isasymColon}linorder{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}find\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ it\ {\isacharequal}\ {\isacharparenleft}if\ it\ {\isacharequal}\ key\ then\ Some\ val\ else\ None{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ {\isacharbar}\ {\isachardoublequoteopen}find\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ t{\isadigit{2}}{\isacharparenright}\ it\ {\isacharequal}\ {\isacharparenleft}if\ it\ {\isasymle}\ key\ then\ find\ t{\isadigit{1}}\ it\ else\ find\ t{\isadigit{2}}\ it{\isacharparenright}{\isachardoublequoteclose}\isanewline
\isanewline
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ update\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}linorder\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}\isanewline
\ \ \ \ if\ it\ {\isacharequal}\ key\ then\ Leaf\ key\ entry\isanewline
\ \ \ \ \ \ else\ if\ it\ {\isasymle}\ key\isanewline
\ \ \ \ \ \ then\ Branch\ {\isacharparenleft}Leaf\ it\ entry{\isacharparenright}\ it\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\isanewline
\ \ \ \ \ \ else\ Branch\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ it\ {\isacharparenleft}Leaf\ it\ entry{\isacharparenright}\isanewline
\ \ \ {\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ {\isacharbar}\ {\isachardoublequoteopen}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ t{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}\isanewline
\ \ \ \ if\ it\ {\isasymle}\ key\isanewline
\ \ \ \ \ \ then\ {\isacharparenleft}Branch\ {\isacharparenleft}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ t{\isadigit{1}}{\isacharparenright}\ key\ t{\isadigit{2}}{\isacharparenright}\isanewline
\ \ \ \ \ \ else\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ {\isacharparenleft}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ t{\isadigit{2}}{\isacharparenright}{\isacharparenright}\isanewline
\ \ \ {\isacharparenright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent For testing purpose, we define a small example
using natural numbers \isa{nat} (which are a \isa{linorder})
as keys and list of nats as values:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
\isanewline
\ \ example\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}nat{\isacharcomma}\ nat\ list{\isacharparenright}\ searchtree{\isachardoublequoteclose}\isanewline
\isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}example\ {\isacharequal}\ update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\ {\isacharparenleft}update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ {\isacharparenleft}update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\ {\isacharparenleft}Leaf\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent Then we generate code%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ example\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}tree{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent which looks like:
\lstsml{Thy/examples/tree.ML}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsection{Code generation concepts and process \label{sec:concept}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
\begin{figure}[h]
\centering
\includegraphics[width=0.7\textwidth]{codegen_process}
\caption{code generator -- processing overview}
\label{fig:process}
\end{figure}
The code generator employs a notion of executability
for three foundational executable ingredients known
from functional programming:
\emph{defining equations}, \emph{datatypes}, and
\emph{type classes}. A defining equation as a first approximation
is a theorem of the form \isa{f\ t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n\ {\isasymequiv}\ t}
(an equation headed by a constant \isa{f} with arguments
\isa{t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n} and right hand side \isa{t}).
Code generation aims to turn defining equations
into a functional program by running through
a process (see figure \ref{fig:process}):
\begin{itemize}
\item Out of the vast collection of theorems proven in a
\qn{theory}, a reasonable subset modeling
defining equations is \qn{selected}.
\item On those selected theorems, certain
transformations are carried out
(\qn{preprocessing}). Their purpose is to turn theorems
representing non- or badly executable
specifications into equivalent but executable counterparts.
The result is a structured collection of \qn{code theorems}.
\item These \qn{code theorems} then are \qn{translated}
into an Haskell-like intermediate
language.
\item Finally, out of the intermediate language the final
code in the desired \qn{target language} is \qn{serialized}.
\end{itemize}
From these steps, only the two last are carried out
outside the logic; by keeping this layer as
thin as possible, the amount of code to trust is
kept to a minimum.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsection{Basics \label{sec:basics}%
}
\isamarkuptrue%
%
\isamarkupsubsection{Invoking the code generator%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Thanks to a reasonable setup of the \isa{HOL} theories, in
most cases code generation proceeds without further ado:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ fac\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ \ \ {\isachardoublequoteopen}fac\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
\ \ {\isacharbar}\ {\isachardoublequoteopen}fac\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ Suc\ n\ {\isacharasterisk}\ fac\ n{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent This executable specification is now turned to SML code:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ fac\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}fac{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent The \isa{{\isasymEXPORTCODE}} command takes a space-separated list of
constants together with \qn{serialization directives}
These start with a \qn{target language}
identifier, followed by a file specification
where to write the generated code to.
Internally, the defining equations for all selected
constants are taken, including any transitively required
constants, datatypes and classes, resulting in the following
code:
\lstsml{Thy/examples/fac.ML}
The code generator will complain when a required
ingredient does not provide a executable counterpart,
e.g.~generating code
for constants not yielding
a defining equation (e.g.~the Hilbert choice
operation \isa{SOME}):%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimML
%
\endisadelimML
%
\isatagML
%
\endisatagML
{\isafoldML}%
%
\isadelimML
%
\endisadelimML
\isacommand{definition}\isamarkupfalse%
\isanewline
\ \ pick{\isacharunderscore}some\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}pick{\isacharunderscore}some\ xs\ {\isacharequal}\ {\isacharparenleft}SOME\ x{\isachardot}\ x\ {\isasymin}\ set\ xs{\isacharparenright}{\isachardoublequoteclose}%
\isadelimML
%
\endisadelimML
%
\isatagML
%
\endisatagML
{\isafoldML}%
%
\isadelimML
%
\endisadelimML
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ pick{\isacharunderscore}some\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}fail{\isacharunderscore}const{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent will fail.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Theorem selection%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The list of all defining equations in a theory may be inspected
using the \isa{{\isasymPRINTCODESETUP}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{print{\isacharunderscore}codesetup}\isamarkupfalse%
%
\begin{isamarkuptext}%
\noindent which displays a table of constant with corresponding
defining equations (the additional stuff displayed
shall not bother us for the moment).
The typical \isa{HOL} tools are already set up in a way that
function definitions introduced by \isa{{\isasymDEFINITION}},
\isa{{\isasymFUN}},
\isa{{\isasymFUNCTION}}, \isa{{\isasymPRIMREC}},
\isa{{\isasymRECDEF}} are implicitly propagated
to this defining equation table. Specific theorems may be
selected using an attribute: \emph{code func}. As example,
a weight selector function:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
\isanewline
\ \ pick\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}nat\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ list\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
\isanewline
\ \ {\isachardoublequoteopen}pick\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ n\ {\isacharequal}\ {\isacharparenleft}let\ {\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}\ {\isacharequal}\ x\ in\isanewline
\ \ \ \ if\ n\ {\isacharless}\ k\ then\ v\ else\ pick\ xs\ {\isacharparenleft}n\ {\isacharminus}\ k{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent We want to eliminate the explicit destruction
of \isa{x} to \isa{{\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}pick\ {\isacharparenleft}{\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}{\isacharhash}xs{\isacharparenright}\ n\ {\isacharequal}\ {\isacharparenleft}if\ n\ {\isacharless}\ k\ then\ v\ else\ pick\ xs\ {\isacharparenleft}n\ {\isacharminus}\ k{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
\ \ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ simp%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ pick\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}pick{\isadigit{1}}{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent This theorem now is used for generating code:
\lstsml{Thy/examples/pick1.ML}
\noindent It might be convenient to remove the pointless original
equation, using the \emph{func del} attribute:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemmas}\isamarkupfalse%
\ {\isacharbrackleft}code\ func\ del{\isacharbrackright}\ {\isacharequal}\ pick{\isachardot}simps\ \isanewline
\isanewline
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ pick\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}pick{\isadigit{2}}{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/pick2.ML}
\noindent Syntactic redundancies are implicitly dropped. For example,
using a modified version of the \isa{fac} function
as defining equation, the then redundant (since
syntactically subsumed) original defining equations
are dropped, resulting in a warning:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}fac\ n\ {\isacharequal}\ {\isacharparenleft}case\ n\ of\ {\isadigit{0}}\ {\isasymRightarrow}\ {\isadigit{1}}\ {\isacharbar}\ Suc\ m\ {\isasymRightarrow}\ n\ {\isacharasterisk}\ fac\ m{\isacharparenright}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
\ \ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}cases\ n{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ fac\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}fac{\isacharunderscore}case{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/fac_case.ML}
\begin{warn}
The attributes \emph{code} and \emph{code del}
associated with the existing code generator also apply to
the new one: \emph{code} implies \emph{code func},
and \emph{code del} implies \emph{code func del}.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Type classes%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Type classes enter the game via the Isar class package.
For a short introduction how to use it, see \cite{isabelle-classes};
here we just illustrate its impact on code generation.
In a target language, type classes may be represented
natively (as in the case of Haskell). For languages
like SML, they are implemented using \emph{dictionaries}.
Our following example specifies a class \qt{null},
assigning to each of its inhabitants a \qt{null} value:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
\ null\ {\isacharequal}\ type\ {\isacharplus}\isanewline
\ \ \isakeyword{fixes}\ null\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\isanewline
\isanewline
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ head\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}null\ list\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\isanewline
\isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}head\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ null{\isachardoublequoteclose}\isanewline
\ \ {\isacharbar}\ {\isachardoublequoteopen}head\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}%
\begin{isamarkuptext}%
We provide some instances for our \isa{null}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instance}\isamarkupfalse%
\ option\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharparenright}\ null\isanewline
\ \ {\isachardoublequoteopen}null\ {\isasymequiv}\ None{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ list\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharparenright}\ null\isanewline
\ \ {\isachardoublequoteopen}null\ {\isasymequiv}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
Constructing a dummy example:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
\isanewline
\ \ {\isachardoublequoteopen}dummy\ {\isacharequal}\ head\ {\isacharbrackleft}Some\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ None{\isacharbrackright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
Type classes offer a suitable occasion to introduce
the Haskell serializer. Its usage is almost the same
as SML, but, in accordance with conventions
some Haskell systems enforce, each module ends
up in a single file. The module hierarchy is reflected in
the file system, with root directory given as file specification.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ dummy\ \isakeyword{in}\ Haskell\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lsthaskell{Thy/examples/Codegen.hs}
\noindent (we have left out all other modules).
\medskip
The whole code in SML with explicit dictionary passing:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ dummy\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}class{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/class.ML}
\medskip
\noindent or in OCaml:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ dummy\ \isakeyword{in}\ OCaml\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}class{\isachardot}ocaml{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/class.ocaml}
\medskip The explicit association of constants
to classes can be inspected using the \isa{{\isasymPRINTCLASSES}}
command.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsection{Recipes and advanced topics \label{sec:advanced}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
In this tutorial, we do not attempt to give an exhaustive
description of the code generator framework; instead,
we cast a light on advanced topics by introducing
them together with practically motivated examples. Concerning
further reading, see
\begin{itemize}
\item the Isabelle/Isar Reference Manual \cite{isabelle-isar-ref}
for exhaustive syntax diagrams.
\item or \cite{Haftmann-Nipkow:2007:codegen} which deals with foundational issues
of the code generator framework.
\end{itemize}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Library theories \label{sec:library}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The \isa{HOL} \isa{Main} theory already provides a code
generator setup
which should be suitable for most applications. Common extensions
and modifications are available by certain theories of the \isa{HOL}
library; beside being useful in applications, they may serve
as a tutorial for customizing the code generator setup.
\begin{description}
\item[\isa{Code{\isacharunderscore}Integer}] represents \isa{HOL} integers by big
integer literals in target languages.
\item[\isa{Code{\isacharunderscore}Char}] represents \isa{HOL} characters by
character literals in target languages.
\item[\isa{Code{\isacharunderscore}Char{\isacharunderscore}chr}] like \isa{Code{\isacharunderscore}Char},
but also offers treatment of character codes; includes
\isa{Code{\isacharunderscore}Integer}.
\item[\isa{Efficient{\isacharunderscore}Nat}] \label{eff_nat} implements natural numbers by integers,
which in general will result in higher efficency; pattern
matching with \isa{{\isadigit{0}}} / \isa{Suc}
is eliminated; includes \isa{Code{\isacharunderscore}Integer}.
\item[\isa{Code{\isacharunderscore}Index}] provides an additional datatype
\isa{index} which is mapped to target-language built-in integers.
Useful for code setups which involve e.g. indexing of
target-language arrays.
\item[\isa{Code{\isacharunderscore}Message}] provides an additional datatype
\isa{message{\isacharunderscore}string} which is isomorphic to strings;
\isa{message{\isacharunderscore}string}s are mapped to target-language strings.
Useful for code setups which involve e.g. printing (error) messages.
\end{description}
\begin{warn}
When importing any of these theories, they should form the last
items in an import list. Since these theories adapt the
code generator setup in a non-conservative fashion,
strange effects may occur otherwise.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Preprocessing%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Before selected function theorems are turned into abstract
code, a chain of definitional transformation steps is carried
out: \emph{preprocessing}. There are three possibilities
to customize preprocessing: \emph{inline theorems},
\emph{inline procedures} and \emph{generic preprocessors}.
\emph{Inline theorems} are rewriting rules applied to each
defining equation. Due to the interpretation of theorems
of defining equations, rewrites are applied to the right
hand side and the arguments of the left hand side of an
equation, but never to the constant heading the left hand side.
Inline theorems may be declared an undeclared using the
\emph{code inline} or \emph{code inline del} attribute respectively.
Some common applications:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\begin{itemize}
%
\begin{isamarkuptext}%
\item replacing non-executable constructs by executable ones:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
\ \ \ \ {\isachardoublequoteopen}x\ {\isasymin}\ set\ xs\ {\isasymlongleftrightarrow}\ x\ mem\ xs{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
\item eliminating superfluous constants:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
\ \ \ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ simp%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
\item replacing executable but inconvenient constructs:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
\ \ \ \ {\isachardoublequoteopen}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongleftrightarrow}\ List{\isachardot}null\ xs{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\end{itemize}
%
\begin{isamarkuptext}%
\noindent The current set of inline theorems may be inspected using
the \isa{{\isasymPRINTCODESETUP}} command.
\emph{Inline procedures} are a generalized version of inline
theorems written in ML -- rewrite rules are generated dependent
on the function theorems for a certain function. One
application is the implicit expanding of \isa{nat} numerals
to \isa{{\isadigit{0}}} / \isa{Suc} representation. See further
\secref{sec:ml}
\emph{Generic preprocessors} provide a most general interface,
transforming a list of function theorems to another
list of function theorems, provided that neither the heading
constant nor its type change. The \isa{{\isadigit{0}}} / \isa{Suc}
pattern elimination implemented in
theory \isa{EfficientNat} (\secref{eff_nat}) uses this
interface.
\begin{warn}
The order in which single preprocessing steps are carried
out currently is not specified; in particular, preprocessing
is \emph{no} fix point process. Keep this in mind when
setting up the preprocessor.
Further, the attribute \emph{code unfold}
associated with the existing code generator also applies to
the new one: \emph{code unfold} implies \emph{code inline}.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Concerning operational equality%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Surely you have already noticed how equality is treated
by the code generator:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ collect{\isacharunderscore}duplicates\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ \ \ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
\ \ {\isacharbar}\ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharparenleft}z{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ z\ {\isasymin}\ set\ xs\isanewline
\ \ \ \ \ \ then\ if\ z\ {\isasymin}\ set\ ys\isanewline
\ \ \ \ \ \ \ \ then\ collect{\isacharunderscore}duplicates\ xs\ ys\ zs\isanewline
\ \ \ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ xs\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs\isanewline
\ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ {\isacharparenleft}z{\isacharhash}xs{\isacharparenright}\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs{\isacharparenright}{\isachardoublequoteclose}%
\begin{isamarkuptext}%
The membership test during preprocessing is rewritten,
resulting in \isa{op\ mem}, which itself
performs an explicit equality check.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ collect{\isacharunderscore}duplicates\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}collect{\isacharunderscore}duplicates{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/collect_duplicates.ML}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\begin{isamarkuptext}%
Obviously, polymorphic equality is implemented the Haskell
way using a type class. How is this achieved? By an
almost trivial definition in the HOL setup:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimML
%
\endisadelimML
%
\isatagML
%
\endisatagML
{\isafoldML}%
%
\isadelimML
%
\endisadelimML
\isacommand{class}\isamarkupfalse%
\ eq\ {\isacharparenleft}\isakeyword{attach}\ {\isachardoublequoteopen}op\ {\isacharequal}{\isachardoublequoteclose}{\isacharparenright}\ {\isacharequal}\ type%
\begin{isamarkuptext}%
This merely introduces a class \isa{eq} with corresponding
operation \isa{op\ {\isacharequal}};
the preprocessing framework does the rest.
For datatypes, instances of \isa{eq} are implicitly derived
when possible.
Though this \isa{eq} class is designed to get rarely in
the way, a subtlety
enters the stage when definitions of overloaded constants
are dependent on operational equality. For example, let
us define a lexicographic ordering on tuples:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimML
%
\endisadelimML
%
\isatagML
%
\endisatagML
{\isafoldML}%
%
\isadelimML
%
\endisadelimML
\isacommand{instance}\isamarkupfalse%
\ {\isacharasterisk}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}ord{\isacharcomma}\ ord{\isacharparenright}\ ord\isanewline
\ \ less{\isacharunderscore}prod{\isacharunderscore}def{\isacharcolon}\isanewline
\ \ \ \ {\isachardoublequoteopen}p{\isadigit{1}}\ {\isacharless}\ p{\isadigit{2}}\ {\isasymequiv}\ let\ {\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharequal}\ p{\isadigit{1}}{\isacharsemicolon}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{2}}\ in\isanewline
\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def{\isacharcolon}\isanewline
\ \ \ \ {\isachardoublequoteopen}p{\isadigit{1}}\ {\isasymle}\ p{\isadigit{2}}\ {\isasymequiv}\ let\ {\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharequal}\ p{\isadigit{1}}{\isacharsemicolon}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{2}}\ in\isanewline
\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{lemmas}\isamarkupfalse%
\ {\isacharbrackleft}code\ func\ del{\isacharbrackright}\ {\isacharequal}\ less{\isacharunderscore}prod{\isacharunderscore}def\ less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ ord{\isacharunderscore}prod\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isasymle}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
\ \ %
\endisadelimproof
%
\isatagproof
\isacommand{unfolding}\isamarkupfalse%
\ less{\isacharunderscore}prod{\isacharunderscore}def\ less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
Then code generation will fail. Why? The definition
of \isa{op\ {\isasymle}} depends on equality on both arguments,
which are polymorphic and impose an additional \isa{eq}
class constraint, thus violating the type discipline
for class operations.
The solution is to add \isa{eq} explicitly to the first sort arguments in the
code theorems:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
\ ord{\isacharunderscore}prod{\isacharunderscore}code\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}ord{\isacharcomma}\ eq{\isacharbraceright}{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\isanewline
\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}ord{\isacharcomma}\ eq{\isacharbraceright}{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isasymle}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\isanewline
\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
\ \ %
\endisadelimproof
%
\isatagproof
\isacommand{unfolding}\isamarkupfalse%
\ ord{\isacharunderscore}prod\ \isacommand{by}\isamarkupfalse%
\ rule{\isacharplus}%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
\noindent Then code generation succeeds:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}eq{\isacharcomma}\ ord{\isacharbraceright}\ {\isasymtimes}\ {\isacharprime}b{\isasymColon}ord\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}lexicographic{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/lexicographic.ML}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\begin{isamarkuptext}%
In general, code theorems for overloaded constants may have more
restrictive sort constraints than the underlying instance relation
between class and type constructor as long as the whole system of
constraints is coregular; code theorems violating coregularity
are rejected immediately. Consequently, it might be necessary
to delete disturbing theorems in the code theorem table,
as we have done here with the original definitions \isa{less{\isacharunderscore}prod{\isacharunderscore}def}
and \isa{less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def}.
In some cases, the automatically derived defining equations
for equality on a particular type may not be appropriate.
As example, watch the following datatype representing
monomorphic parametric types (where type constructors
are referred to by natural numbers):%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
\ monotype\ {\isacharequal}\ Mono\ nat\ {\isachardoublequoteopen}monotype\ list{\isachardoublequoteclose}%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
Then code generation for SML would fail with a message
that the generated code conains illegal mutual dependencies:
the theorem \isa{Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymequiv}\ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ typargs{\isadigit{1}}\ {\isacharequal}\ typargs{\isadigit{2}}} already requires the
instance \isa{monotype\ {\isasymColon}\ eq}, which itself requires
\isa{Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymequiv}\ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ typargs{\isadigit{1}}\ {\isacharequal}\ typargs{\isadigit{2}}}; Haskell has no problem with mutually
recursive \isa{instance} and \isa{function} definitions,
but the SML serializer does not support this.
In such cases, you have to provide you own equality equations
involving auxiliary constants. In our case,
\isa{list{\isacharunderscore}all{\isadigit{2}}} can do the job:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
\ monotype{\isacharunderscore}eq{\isacharunderscore}list{\isacharunderscore}all{\isadigit{2}}\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymlongleftrightarrow}\isanewline
\ \ \ \ \ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ list{\isacharunderscore}all{\isadigit{2}}\ {\isacharparenleft}op\ {\isacharequal}{\isacharparenright}\ typargs{\isadigit{1}}\ typargs{\isadigit{2}}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
\ \ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ add{\isacharcolon}\ list{\isacharunderscore}all{\isadigit{2}}{\isacharunderscore}eq\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
%
\begin{isamarkuptext}%
does not depend on instance \isa{monotype\ {\isasymColon}\ eq}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ {\isacharequal}\ {\isacharcolon}{\isacharcolon}\ monotype\ {\isasymRightarrow}\ monotype\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}monotype{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/monotype.ML}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Programs as sets of theorems%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
As told in \secref{sec:concept}, code generation is based
on a structured collection of code theorems.
For explorative purpose, this collection
may be inspected using the \isa{{\isasymCODETHMS}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{code{\isacharunderscore}thms}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ mod\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\noindent prints a table with \emph{all} defining equations
for \isa{op\ mod}, including
\emph{all} defining equations those equations depend
on recursivly. \isa{{\isasymCODETHMS}} provides a convenient
mechanism to inspect the impact of a preprocessor setup
on defining equations.
Similarly, the \isa{{\isasymCODEDEPS}} command shows a graph
visualizing dependencies between defining equations.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Customizing serialization%
}
\isamarkuptrue%
%
\isamarkupsubsubsection{Basics%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Consider the following function and its corresponding
SML code:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
\isanewline
\ \ in{\isacharunderscore}interval\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymtimes}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isasymlongleftrightarrow}\ k\ {\isasymle}\ n\ {\isasymand}\ n\ {\isasymle}\ l{\isachardoublequoteclose}%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ in{\isacharunderscore}interval\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}literal{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/bool_literal.ML}
\noindent Though this is correct code, it is a little bit unsatisfactory:
boolean values and operators are materialized as distinguished
entities with have nothing to do with the SML-builtin notion
of \qt{bool}. This results in less readable code;
additionally, eager evaluation may cause programs to
loop or break which would perfectly terminate when
the existing SML \qt{bool} would be used. To map
the HOL \qt{bool} on SML \qt{bool}, we may use
\qn{custom serializations}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
\ bool\isanewline
\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}bool{\isachardoublequoteclose}{\isacharparenright}\isanewline
\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
\ True\ \isakeyword{and}\ False\ \isakeyword{and}\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}true{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}false{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}{\isacharunderscore}\ andalso\ {\isacharunderscore}{\isachardoublequoteclose}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
%
\begin{isamarkuptext}%
The \isa{{\isasymCODETYPE}} commad takes a type constructor
as arguments together with a list of custom serializations.
Each custom serialization starts with a target language
identifier followed by an expression, which during
code serialization is inserted whenever the type constructor
would occur. For constants, \isa{{\isasymCODECONST}} implements
the corresponding mechanism. Each ``\verb|_|'' in
a serialization expression is treated as a placeholder
for the type constructor's (the constant's) arguments.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ in{\isacharunderscore}interval\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}mlbool{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/bool_mlbool.ML}
\noindent This still is not perfect: the parentheses
around the \qt{andalso} expression are superfluous.
Though the serializer
by no means attempts to imitate the rich Isabelle syntax
framework, it provides some common idioms, notably
associative infixes with precedences which may be used here:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
\ \ {\isacharparenleft}SML\ \isakeyword{infixl}\ {\isadigit{1}}\ {\isachardoublequoteopen}andalso{\isachardoublequoteclose}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
\isanewline
\isanewline
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ in{\isacharunderscore}interval\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}infix{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/bool_infix.ML}
\medskip
Next, we try to map HOL pairs to SML pairs, using the
infix ``\verb|*|'' type constructor and parentheses:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
\ {\isacharasterisk}\isanewline
\ \ {\isacharparenleft}SML\ \isakeyword{infix}\ {\isadigit{2}}\ {\isachardoublequoteopen}{\isacharasterisk}{\isachardoublequoteclose}{\isacharparenright}\isanewline
\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
\ Pair\isanewline
\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}{\isacharbang}{\isacharparenleft}{\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharcomma}{\isacharslash}\ {\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
%
\begin{isamarkuptext}%
The initial bang ``\verb|!|'' tells the serializer to never put
parentheses around the whole expression (they are already present),
while the parentheses around argument place holders
tell not to put parentheses around the arguments.
The slash ``\verb|/|'' (followed by arbitrary white space)
inserts a space which may be used as a break if necessary
during pretty printing.
These examples give a glimpse what mechanisms
custom serializations provide; however their usage
requires careful thinking in order not to introduce
inconsistencies -- or, in other words:
custom serializations are completely axiomatic.
A further noteworthy details is that any special
character in a custom serialization may be quoted
using ``\verb|'|''; thus, in
``\verb|fn '_ => _|'' the first
``\verb|_|'' is a proper underscore while the
second ``\verb|_|'' is a placeholder.
The HOL theories provide further
examples for custom serializations and form
a recommended tutorial on how to use them properly.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsubsection{Haskell serialization%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
For convenience, the default
HOL setup for Haskell maps the \isa{eq} class to
its counterpart in Haskell, giving custom serializations
for the class (\isa{{\isasymCODECLASS}}) and its operation:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}class}\isamarkupfalse%
\ eq\isanewline
\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Eq{\isachardoublequoteclose}\ \isakeyword{where}\ {\isachardoublequoteopen}op\ {\isacharequal}{\isachardoublequoteclose}\ {\isasymequiv}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharequal}{\isacharequal}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}\isanewline
\isanewline
\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ {\isacharequal}{\isachardoublequoteclose}\isanewline
\ \ {\isacharparenleft}Haskell\ \isakeyword{infixl}\ {\isadigit{4}}\ {\isachardoublequoteopen}{\isacharequal}{\isacharequal}{\isachardoublequoteclose}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
%
\begin{isamarkuptext}%
A problem now occurs whenever a type which
is an instance of \isa{eq} in HOL is mapped
on a Haskell-builtin type which is also an instance
of Haskell \isa{Eq}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{typedecl}\isamarkupfalse%
\ bar\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ bar\ {\isacharcolon}{\isacharcolon}\ eq%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
%
\isadelimtt
\isanewline
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
\ bar\isanewline
\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Integer{\isachardoublequoteclose}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
%
\begin{isamarkuptext}%
The code generator would produce
an additional instance, which of course is rejected.
To suppress this additional instance, use
\isa{{\isasymCODEINSTANCE}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtt
%
\endisadelimtt
%
\isatagtt
\isacommand{code{\isacharunderscore}instance}\isamarkupfalse%
\ bar\ {\isacharcolon}{\isacharcolon}\ eq\isanewline
\ \ {\isacharparenleft}Haskell\ {\isacharminus}{\isacharparenright}%
\endisatagtt
{\isafoldtt}%
%
\isadelimtt
%
\endisadelimtt
%
\isamarkupsubsubsection{Pretty printing%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The serializer provides ML interfaces to set up
pretty serializations for expressions like lists, numerals
and characters; these are
monolithic stubs and should only be used with the
theories introduces in \secref{sec:library}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Constructor sets for datatypes%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Conceptually, any datatype is spanned by a set of
\emph{constructors} of type \isa{{\isasymtau}\ {\isacharequal}\ {\isasymdots}\ {\isasymRightarrow}\ {\isasymkappa}\ {\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isasymdots}\ {\isasymalpha}\isactrlisub n}
where \isa{{\isacharbraceleft}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlisub n{\isacharbraceright}} is excactly the set of \emph{all}
type variables in \isa{{\isasymtau}}. The HOL datatype package
by default registers any new datatype in the table
of datatypes, which may be inspected using
the \isa{{\isasymPRINTCODESETUP}} command.
In some cases, it may be convenient to alter or
extend this table; as an example, we show
how to implement finite sets by lists
using the conversion \isa{{\isachardoublequote}set\ {\isasymColon}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isachardoublequote}}
as constructor:%
\end{isamarkuptext}%
\isamarkuptrue%
\ %
\isadelimML
%
\endisadelimML
%
\isatagML
%
\endisatagML
{\isafoldML}%
%
\isadelimML
%
\endisadelimML
\isanewline
\isacommand{code{\isacharunderscore}datatype}\isamarkupfalse%
\ set\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceright}\ {\isacharequal}\ set\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ simp%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}insert\ x\ {\isacharparenleft}set\ xs{\isacharparenright}\ {\isacharequal}\ set\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ simp%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymin}\ set\ xs\ {\isasymlongleftrightarrow}\ x\ mem\ xs{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}xs\ {\isasymunion}\ set\ ys\ {\isacharequal}\ foldr\ insert\ ys\ xs{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ ys{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymUnion}set\ xs\ {\isacharequal}\ foldr\ {\isacharparenleft}op\ {\isasymunion}{\isacharparenright}\ xs\ {\isacharbraceleft}{\isacharbraceright}{\isachardoublequoteclose}%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
%
\endisadelimproof
\isanewline
\isanewline
\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequoteclose}\ insert\ {\isachardoublequoteopen}op\ {\isasymin}{\isachardoublequoteclose}\ {\isachardoublequoteopen}op\ {\isasymunion}{\isachardoublequoteclose}\ {\isachardoublequoteopen}Union{\isachardoublequoteclose}\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}set{\isacharunderscore}list{\isachardot}ML{\isachardoublequoteclose}%
\begin{isamarkuptext}%
\lstsml{Thy/examples/set_list.ML}
\medskip
Changing the representation of existing datatypes requires
some care with respect to pattern matching and such.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Cyclic module dependencies%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Sometimes the awkward situation occurs that dependencies
between definitions introduce cyclic dependencies
between modules, which in the Haskell world leaves
you to the mercy of the Haskell implementation you are using,
while for SML code generation is not possible.
A solution is to declare module names explicitly.
Let use assume the three cyclically dependent
modules are named \emph{A}, \emph{B} and \emph{C}.
Then, by stating%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{code{\isacharunderscore}modulename}\isamarkupfalse%
\ SML\isanewline
\ \ A\ ABC\isanewline
\ \ B\ ABC\isanewline
\ \ C\ ABC%
\begin{isamarkuptext}%
we explicitly map all those modules on \emph{ABC},
resulting in an ad-hoc merge of this three modules
at serialization time.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Incremental code generation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Code generation is \emph{incremental}: theorems
and abstract intermediate code are cached and extended on demand.
The cache may be partially or fully dropped if the underlying
executable content of the theory changes.
Implementation of caching is supposed to transparently
hid away the details from the user. Anyway, caching
reaches the surface by using a slightly more general form
of the \isa{{\isasymCODETHMS}}, \isa{{\isasymCODEDEPS}}
and \isa{{\isasymEXPORTCODE}} commands: the list of constants
may be omitted. Then, all constants with code theorems
in the current cache are referred to.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Code generation and proof extraction%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
\fixme%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsection{ML interfaces \label{sec:ml}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Since the code generator framework not only aims to provide
a nice Isar interface but also to form a base for
code-generation-based applications, here a short
description of the most important ML interfaces.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Executable theory content: \isa{Code}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
This Pure module implements the core notions of
executable content of a theory.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsubsection{Managing executable content%
}
\isamarkuptrue%
%
\isadelimmlref
%
\endisadelimmlref
%
\isatagmlref
%
\begin{isamarkuptext}%
\begin{mldecls}
\indexml{Code.add-func}\verb|Code.add_func: thm -> theory -> theory| \\
\indexml{Code.del-func}\verb|Code.del_func: thm -> theory -> theory| \\
\indexml{Code.add-funcl}\verb|Code.add_funcl: string * thm list Susp.T -> theory -> theory| \\
\indexml{Code.add-inline}\verb|Code.add_inline: thm -> theory -> theory| \\
\indexml{Code.del-inline}\verb|Code.del_inline: thm -> theory -> theory| \\
\indexml{Code.add-inline-proc}\verb|Code.add_inline_proc: string * (theory -> cterm list -> thm list)|\isasep\isanewline%
\verb| -> theory -> theory| \\
\indexml{Code.del-inline-proc}\verb|Code.del_inline_proc: string -> theory -> theory| \\
\indexml{Code.add-preproc}\verb|Code.add_preproc: string * (theory -> thm list -> thm list)|\isasep\isanewline%
\verb| -> theory -> theory| \\
\indexml{Code.del-preproc}\verb|Code.del_preproc: string -> theory -> theory| \\
\indexml{Code.add-datatype}\verb|Code.add_datatype: (string * typ) list -> theory -> theory| \\
\indexml{Code.get-datatype}\verb|Code.get_datatype: theory -> string|\isasep\isanewline%
\verb| -> (string * sort) list * (string * typ list) list| \\
\indexml{Code.get-datatype-of-constr}\verb|Code.get_datatype_of_constr: theory -> string -> string option|
\end{mldecls}
\begin{description}
\item \verb|Code.add_func|~\isa{thm}~\isa{thy} adds function
theorem \isa{thm} to executable content.
\item \verb|Code.del_func|~\isa{thm}~\isa{thy} removes function
theorem \isa{thm} from executable content, if present.
\item \verb|Code.add_funcl|~\isa{{\isacharparenleft}const{\isacharcomma}\ lthms{\isacharparenright}}~\isa{thy} adds
suspended defining equations \isa{lthms} for constant
\isa{const} to executable content.
\item \verb|Code.add_inline|~\isa{thm}~\isa{thy} adds
inlining theorem \isa{thm} to executable content.
\item \verb|Code.del_inline|~\isa{thm}~\isa{thy} remove
inlining theorem \isa{thm} from executable content, if present.
\item \verb|Code.add_inline_proc|~\isa{{\isacharparenleft}name{\isacharcomma}\ f{\isacharparenright}}~\isa{thy} adds
inline procedure \isa{f} (named \isa{name}) to executable content;
\isa{f} is a computation of rewrite rules dependent on
the current theory context and the list of all arguments
and right hand sides of the defining equations belonging
to a certain function definition.
\item \verb|Code.del_inline_proc|~\isa{name}~\isa{thy} removes
inline procedure named \isa{name} from executable content.
\item \verb|Code.add_preproc|~\isa{{\isacharparenleft}name{\isacharcomma}\ f{\isacharparenright}}~\isa{thy} adds
generic preprocessor \isa{f} (named \isa{name}) to executable content;
\isa{f} is a transformation of the defining equations belonging
to a certain function definition, depending on the
current theory context.
\item \verb|Code.del_preproc|~\isa{name}~\isa{thy} removes
generic preprcoessor named \isa{name} from executable content.
\item \verb|Code.add_datatype|~\isa{cs}~\isa{thy} adds
a datatype to executable content, with generation
set \isa{cs}.
\item \verb|Code.get_datatype_of_constr|~\isa{thy}~\isa{const}
returns type constructor corresponding to
constructor \isa{const}; returns \isa{NONE}
if \isa{const} is no constructor.
\end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\endisatagmlref
{\isafoldmlref}%
%
\isadelimmlref
%
\endisadelimmlref
%
\isamarkupsubsection{Auxiliary%
}
\isamarkuptrue%
%
\isadelimmlref
%
\endisadelimmlref
%
\isatagmlref
%
\begin{isamarkuptext}%
\begin{mldecls}
\indexml{CodeUnit.read-const}\verb|CodeUnit.read_const: theory -> string -> string| \\
\indexml{CodeUnit.head-func}\verb|CodeUnit.head_func: thm -> string * typ| \\
\indexml{CodeUnit.rewrite-func}\verb|CodeUnit.rewrite_func: thm list -> thm -> thm| \\
\end{mldecls}
\begin{description}
\item \verb|CodeUnit.read_const|~\isa{thy}~\isa{s}
reads a constant as a concrete term expression \isa{s}.
\item \verb|CodeUnit.head_func|~\isa{thm}
extracts the constant and its type from a defining equation \isa{thm}.
\item \verb|CodeUnit.rewrite_func|~\isa{rews}~\isa{thm}
rewrites a defining equation \isa{thm} with a set of rewrite
rules \isa{rews}; only arguments and right hand side are rewritten,
not the head of the defining equation.
\end{description}%
\end{isamarkuptext}%
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\isamarkupsubsection{Implementing code generator applications%
}
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\begin{isamarkuptext}%
Implementing code generator applications on top
of the framework set out so far usually not only
involves using those primitive interfaces
but also storing code-dependent data and various
other things.
\begin{warn}
Some interfaces discussed here have not reached
a final state yet.
Changes likely to occur in future.
\end{warn}%
\end{isamarkuptext}%
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\isamarkupsubsubsection{Data depending on the theory's executable content%
}
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\begin{isamarkuptext}%
Due to incrementality of code generation, changes in the
theory's executable content have to be propagated in a
certain fashion. Additionally, such changes may occur
not only during theory extension but also during theory
merge, which is a little bit nasty from an implementation
point of view. The framework provides a solution
to this technical challenge by providing a functorial
data slot \verb|CodeDataFun|; on instantiation
of this functor, the following types and operations
are required:
\medskip
\begin{tabular}{l}
\isa{type\ T} \\
\isa{val\ empty{\isacharcolon}\ T} \\
\isa{val\ merge{\isacharcolon}\ Pretty{\isachardot}pp\ {\isasymrightarrow}\ T\ {\isacharasterisk}\ T\ {\isasymrightarrow}\ T} \\
\isa{val\ purge{\isacharcolon}\ theory\ option\ {\isasymrightarrow}\ CodeUnit{\isachardot}const\ list\ option\ {\isasymrightarrow}\ T\ {\isasymrightarrow}\ T}
\end{tabular}
\begin{description}
\item \isa{T} the type of data to store.
\item \isa{empty} initial (empty) data.
\item \isa{merge} merging two data slots.
\item \isa{purge}~\isa{thy}~\isa{consts} propagates changes in executable content;
if possible, the current theory context is handed over
as argument \isa{thy} (if there is no current theory context (e.g.~during
theory merge, \verb|NONE|); \isa{consts} indicates the kind
of change: \verb|NONE| stands for a fundamental change
which invalidates any existing code, \isa{SOME\ consts}
hints that executable content for constants \isa{consts}
has changed.
\end{description}
An instance of \verb|CodeDataFun| provides the following
interface:
\medskip
\begin{tabular}{l}
\isa{get{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} \\
\isa{change{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ T} \\
\isa{change{\isacharunderscore}yield{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T{\isacharparenright}\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T}
\end{tabular}
\begin{description}
\item \isa{get} retrieval of the current data.
\item \isa{change} update of current data (cached!)
by giving a continuation.
\item \isa{change{\isacharunderscore}yield} update with side result.
\end{description}%
\end{isamarkuptext}%
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\begin{isamarkuptext}%
\emph{Happy proving, happy hacking!}%
\end{isamarkuptext}%
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