
diff -r 57413334669d -r d9c247f7afa3 doc-src/Codegen/Thy/Evaluation.thy
--- a/doc-src/Codegen/Thy/Evaluation.thy	Tue Sep 21 10:02:50 2010 +0200
+++ b/doc-src/Codegen/Thy/Evaluation.thy	Tue Sep 21 14:36:13 2010 +0200
@@ -4,78 +4,202 @@
 
 section {* Evaluation *}
 
-text {* Introduction *}
+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 {* simplifier *}
+text {*
+  The existing infrastructure provides a rich palett 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.
 
-text {* nbe *}
+    \item[Efficiency.]  The more machine-near the technique, the
+      faster it is.
 
-text {* eval target: SML standalone vs. Isabelle/SML, example, soundness *}
+    \item[Trustability.]  Techniques which a huge (and also probably
+      more configurable infrastructure) are more fragile and less
+      trustable.
+
+  \end{description}
+*}
 
 
-subsection {* Dynamic evaluation *}
-
-text {* value (three variants) *}
+subsubsection {* The simplifier (@{text simp}) *}
 
-text {* methods (three variants) *}
-
-text {* corresponding ML interfaces *}
+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.
+*}
 
 
-subsection {* Static evaluation *}
+subsubsection {* Normalization by evaluation (@{text nbe}) *}
 
-text {* code_simp, nbe (tbd), Eval (tbd, in simple fashion) *}
-
-text {* hand-written: code antiquotation *}
+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.
+*}
 
 
-subsection {* Hybrid techniques *}
+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.
 
-text {* code reflect runtime *}
-
-text {* code reflect external *}
+  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 crucially on the correctness of the code generator; this
+  is one of the reasons why you should not use adaptation (see
+  \secref{sec:adaptation}) frivolously.
+*}
 
 
-text {* FIXME here the old sections follow *}
-
-subsection {* Evaluation oracle *}
+subsection {* Aspects of evaluation *}
 
 text {*
-  Code generation may also be used to \emph{evaluate} expressions
-  (using @{text SML} as target language of course).
-  For instance, the @{command_def value} reduces an expression to a
-  normal form with respect to the underlying code equations:
+  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 will display @{term "7 / (2 :: rat)"}.
-
-  The @{method eval} method tries to reduce a goal by code generation to @{term True}
-  and solves it in that case, but fails otherwise:
+  \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.
 *}
 
-lemma %quote "42 / (12 :: rat) = 7 / 2"
-  by %quote eval
+value %quote [nbe] "42 / (12 :: rat)"
 
 text {*
-  \noindent The soundness of the @{method eval} method depends crucially 
-  on the correctness of the code generator;  this is one of the reasons
-  why you should not use adaptation (see \secref{sec:adaptation}) frivolously.
+  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 not-implemented
+      function.  As sketched in \secref{sec:partiality}, this can be
+      interpreted as partiality.
+     
+    \item Evaluation raise 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 propagted to the user.
+
+  By default return values of plain evaluation are optional, yielding
+  @{text "SOME t'"} in the first case, @{text "NONE"} and in the
+  second 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.
 *}
 
 
-subsubsection {* Code antiquotation *}
+subsection {* Schematic overview *}
+
+(*FIXME rotatebox?*)
 
 text {*
+  \begin{tabular}{ll||c|c|c}
+    & & @{text simp} & @{text nbe} & @{text code} \tabularnewline \hline \hline
+    dynamic & interactive evaluation 
+      & @{command value} @{text "[simp]"} & @{command value} @{text "[nbe]"} & @{command value} @{text "[code]"}
+      \tabularnewline
+    & plain evaluation & & & @{ML "Code_Evaluation.dynamic_value"} \tabularnewline \hline
+    & evaluation method & @{method code_simp} & @{method normalization} & @{method eval} \tabularnewline
+    & property conversion & & & @{ML "Code_Runtime.dynamic_holds_conv"} \tabularnewline \hline
+    & conversion & @{ML "Code_Simp.dynamic_eval_conv"} & @{ML "Nbe.dynamic_eval_conv"}
+      & @{ML "Code_Evaluation.dynamic_eval_conv"} \tabularnewline \hline \hline
+    static & plain evaluation & & & @{ML "Code_Evaluation.static_value"} \tabularnewline \hline
+    & property conversion & &
+      & @{ML "Code_Runtime.static_holds_conv"} \tabularnewline \hline
+    & conversion & @{ML "Code_Simp.static_eval_conv"}
+      & @{ML "Nbe.static_eval_conv"}
+      & @{ML "Code_Evaluation.static_eval_conv"}
+  \end{tabular}
+*}
+
+
+subsection {* Intimate connection between logic and system runtime *}
+
+text {* FIXME *}
+
+
+subsubsection {* Static embedding of generated code into system runtime -- the code antiquotation *}
+
+text {*
+  FIXME
+
   In scenarios involving techniques like reflection it is quite common
-  that code generated from a theory forms the basis for implementing
-  a proof procedure in @{text SML}.  To facilitate interfacing of generated code
-  with system code, the code generator provides a @{text code} antiquotation:
+  that code generated from a theory forms the basis for implementing a
+  proof procedure in @{text SML}.  To facilitate interfacing of
+  generated code with system code, the code generator provides a
+  @{text code} antiquotation:
 *}
 
 datatype %quote form = T | F | And form form | Or form form (*<*)
@@ -101,4 +225,12 @@
 *}
 
 
+subsubsection {* Static embedding of generated code into system runtime -- @{text code_reflect} *}
+
+text {* FIXME @{command_def code_reflect} *}
+
+subsubsection {* Separate compilation -- @{text code_reflect} *}
+
+text {* FIXME *}
+
 end




