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+++ b/doc-src/Codegen/Evaluation.thy Mon Aug 27 23:00:38 2012 +0200
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+theory Evaluation
+imports Setup
+begin
+
+section {* Evaluation \label{sec:evaluation} *}
+
+text {*
+ Recalling \secref{sec:principle}, code generation turns a system of
+ equations into a program with the \emph{same} equational semantics.
+ As a consequence, this program can be used as a \emph{rewrite
+ engine} for terms: rewriting a term @{term "t"} using a program to a
+ term @{term "t'"} yields the theorems @{prop "t \<equiv> t'"}. This
+ application of code generation in the following is referred to as
+ \emph{evaluation}.
+*}
+
+
+subsection {* Evaluation techniques *}
+
+text {*
+ The existing infrastructure provides a rich palette of evaluation
+ techniques, each comprising different aspects:
+
+ \begin{description}
+
+ \item[Expressiveness.] Depending on how good symbolic computation
+ is supported, the class of terms which can be evaluated may be
+ bigger or smaller.
+
+ \item[Efficiency.] The more machine-near the technique, the
+ faster it is.
+
+ \item[Trustability.] Techniques which a huge (and also probably
+ more configurable infrastructure) are more fragile and less
+ trustable.
+
+ \end{description}
+*}
+
+
+subsubsection {* The simplifier (@{text simp}) *}
+
+text {*
+ The simplest way for evaluation is just using the simplifier with
+ the original code equations of the underlying program. This gives
+ fully symbolic evaluation and highest trustablity, with the usual
+ performance of the simplifier. Note that for operations on abstract
+ datatypes (cf.~\secref{sec:invariant}), the original theorems as
+ given by the users are used, not the modified ones.
+*}
+
+
+subsubsection {* Normalization by evaluation (@{text nbe}) *}
+
+text {*
+ Normalization by evaluation \cite{Aehlig-Haftmann-Nipkow:2008:nbe}
+ provides a comparably fast partially symbolic evaluation which
+ permits also normalization of functions and uninterpreted symbols;
+ the stack of code to be trusted is considerable.
+*}
+
+
+subsubsection {* Evaluation in ML (@{text code}) *}
+
+text {*
+ Highest performance can be achieved by evaluation in ML, at the cost
+ of being restricted to ground results and a layered stack of code to
+ be trusted, including code generator configurations by the user.
+
+ Evaluation is carried out in a target language \emph{Eval} which
+ inherits from \emph{SML} but for convenience uses parts of the
+ Isabelle runtime environment. The soundness of computation carried
+ out there depends crucially on the correctness of the code
+ generator setup; this is one of the reasons why you should not use
+ adaptation (see \secref{sec:adaptation}) frivolously.
+*}
+
+
+subsection {* Aspects of evaluation *}
+
+text {*
+ Each of the techniques can be combined with different aspects. The
+ most important distinction is between dynamic and static evaluation.
+ Dynamic evaluation takes the code generator configuration \qt{as it
+ is} at the point where evaluation is issued. Best example is the
+ @{command_def value} command which allows ad-hoc evaluation of
+ terms:
+*}
+
+value %quote "42 / (12 :: rat)"
+
+text {*
+ \noindent By default @{command value} tries all available evaluation
+ techniques and prints the result of the first succeeding one. A particular
+ technique may be specified in square brackets, e.g.
+*}
+
+value %quote [nbe] "42 / (12 :: rat)"
+
+text {*
+ To employ dynamic evaluation in the document generation, there is also
+ a @{text value} antiquotation. By default, it also tries all available evaluation
+ techniques and prints the result of the first succeeding one, unless a particular
+ technique is specified in square brackets.
+
+ Static evaluation freezes the code generator configuration at a
+ certain point and uses this context whenever evaluation is issued
+ later on. This is particularly appropriate for proof procedures
+ which use evaluation, since then the behaviour of evaluation is not
+ changed or even compromised later on by actions of the user.
+
+ As a technical complication, terms after evaluation in ML must be
+ turned into Isabelle's internal term representation again. Since
+ this is also configurable, it is never fully trusted. For this
+ reason, evaluation in ML comes with further aspects:
+
+ \begin{description}
+
+ \item[Plain evaluation.] A term is normalized using the provided
+ term reconstruction from ML to Isabelle; for applications which
+ do not need to be fully trusted.
+
+ \item[Property conversion.] Evaluates propositions; since these
+ are monomorphic, the term reconstruction is fixed once and for all
+ and therefore trustable.
+
+ \item[Conversion.] Evaluates an arbitrary term @{term "t"} first
+ by plain evaluation and certifies the result @{term "t'"} by
+ checking the equation @{term "t \<equiv> t'"} using property
+ conversion.
+
+ \end{description}
+
+ \noindent The picture is further complicated by the roles of
+ exceptions. Here three cases have to be distinguished:
+
+ \begin{itemize}
+
+ \item Evaluation of @{term t} terminates with a result @{term
+ "t'"}.
+
+ \item Evaluation of @{term t} terminates which en exception
+ indicating a pattern match failure or a non-implemented
+ function. As sketched in \secref{sec:partiality}, this can be
+ interpreted as partiality.
+
+ \item Evaluation raises any other kind of exception.
+
+ \end{itemize}
+
+ \noindent For conversions, the first case yields the equation @{term
+ "t = t'"}, the second defaults to reflexivity @{term "t = t"}.
+ Exceptions of the third kind are propagated to the user.
+
+ By default return values of plain evaluation are optional, yielding
+ @{text "SOME t'"} in the first case, @{text "NONE"} in the
+ second, and propagating the exception in the third case. A strict
+ variant of plain evaluation either yields @{text "t'"} or propagates
+ any exception, a liberal variant caputures any exception in a result
+ of type @{text "Exn.result"}.
+
+ For property conversion (which coincides with conversion except for
+ evaluation in ML), methods are provided which solve a given goal by
+ evaluation.
+*}
+
+
+subsection {* Schematic overview *}
+
+text {*
+ \newcommand{\ttsize}{\fontsize{5.8pt}{8pt}\selectfont}
+ \fontsize{9pt}{12pt}\selectfont
+ \begin{tabular}{ll||c|c|c}
+ & & @{text simp} & @{text nbe} & @{text code} \tabularnewline \hline \hline
+ \multirow{5}{1ex}{\rotatebox{90}{dynamic}}
+ & interactive evaluation
+ & @{command value} @{text "[simp]"} & @{command value} @{text "[nbe]"} & @{command value} @{text "[code]"}
+ \tabularnewline
+ & plain evaluation & & & \ttsize@{ML "Code_Evaluation.dynamic_value"} \tabularnewline \cline{2-5}
+ & evaluation method & @{method code_simp} & @{method normalization} & @{method eval} \tabularnewline
+ & property conversion & & & \ttsize@{ML "Code_Runtime.dynamic_holds_conv"} \tabularnewline \cline{2-5}
+ & conversion & \ttsize@{ML "Code_Simp.dynamic_conv"} & \ttsize@{ML "Nbe.dynamic_conv"}
+ & \ttsize@{ML "Code_Evaluation.dynamic_conv"} \tabularnewline \hline \hline
+ \multirow{3}{1ex}{\rotatebox{90}{static}}
+ & plain evaluation & & & \ttsize@{ML "Code_Evaluation.static_value"} \tabularnewline \cline{2-5}
+ & property conversion & &
+ & \ttsize@{ML "Code_Runtime.static_holds_conv"} \tabularnewline \cline{2-5}
+ & conversion & \ttsize@{ML "Code_Simp.static_conv"}
+ & \ttsize@{ML "Nbe.static_conv"}
+ & \ttsize@{ML "Code_Evaluation.static_conv"}
+ \end{tabular}
+*}
+
+
+subsection {* Intimate connection between logic and system runtime *}
+
+text {*
+ The toolbox of static evaluation conversions forms a reasonable base
+ to interweave generated code and system tools. However in some
+ situations more direct interaction is desirable.
+*}
+
+
+subsubsection {* Static embedding of generated code into system runtime -- the @{text code} antiquotation *}
+
+text {*
+ The @{text code} antiquotation allows to include constants from
+ generated code directly into ML system code, as in the following toy
+ example:
+*}
+
+datatype %quote form = T | F | And form form | Or form form (*<*)
+
+(*>*) ML %quotett {*
+ fun eval_form @{code T} = true
+ | eval_form @{code F} = false
+ | eval_form (@{code And} (p, q)) =
+ eval_form p andalso eval_form q
+ | eval_form (@{code Or} (p, q)) =
+ eval_form p orelse eval_form q;
+*}
+
+text {*
+ \noindent @{text code} takes as argument the name of a constant;
+ after the whole ML is read, the necessary code is generated
+ transparently and the corresponding constant names are inserted.
+ This technique also allows to use pattern matching on constructors
+ stemming from compiled datatypes. Note that the @{text code}
+ antiquotation may not refer to constants which carry adaptations;
+ here you have to refer to the corresponding adapted code directly.
+
+ For a less simplistic example, theory @{text Approximation} in
+ the @{text Decision_Procs} session is a good reference.
+*}
+
+
+subsubsection {* Static embedding of generated code into system runtime -- @{text code_reflect} *}
+
+text {*
+ The @{text code} antiquoation is lightweight, but the generated code
+ is only accessible while the ML section is processed. Sometimes this
+ is not appropriate, especially if the generated code contains datatype
+ declarations which are shared with other parts of the system. In these
+ cases, @{command_def code_reflect} can be used:
+*}
+
+code_reflect %quote Sum_Type
+ datatypes sum = Inl | Inr
+ functions "Sum_Type.Projl" "Sum_Type.Projr"
+
+text {*
+ \noindent @{command_def code_reflect} takes a structure name and
+ references to datatypes and functions; for these code is compiled
+ into the named ML structure and the \emph{Eval} target is modified
+ in a way that future code generation will reference these
+ precompiled versions of the given datatypes and functions. This
+ also allows to refer to the referenced datatypes and functions from
+ arbitrary ML code as well.
+
+ A typical example for @{command code_reflect} can be found in the
+ @{theory Predicate} theory.
+*}
+
+
+subsubsection {* Separate compilation -- @{text code_reflect} *}
+
+text {*
+ For technical reasons it is sometimes necessary to separate
+ generation and compilation of code which is supposed to be used in
+ the system runtime. For this @{command code_reflect} with an
+ optional @{text "file"} argument can be used:
+*}
+
+code_reflect %quote Rat
+ datatypes rat = Frct
+ functions Fract
+ "(plus :: rat \<Rightarrow> rat \<Rightarrow> rat)" "(minus :: rat \<Rightarrow> rat \<Rightarrow> rat)"
+ "(times :: rat \<Rightarrow> rat \<Rightarrow> rat)" "(divide :: rat \<Rightarrow> rat \<Rightarrow> rat)"
+ file "examples/rat.ML"
+
+text {*
+ \noindent This merely generates the referenced code to the given
+ file which can be included into the system runtime later on.
+*}
+
+end
+