From: Matthijs Kooijman Date: Mon, 7 Dec 2009 13:38:16 +0000 (+0100) Subject: Some more fixed resulting from Jan's comments. X-Git-Tag: final-thesis~55 X-Git-Url: https://git.stderr.nl/gitweb?a=commitdiff_plain;ds=sidebyside;h=736a0a7980ef55a90b3d439a49f71c74086eb002;p=matthijs%2Fmaster-project%2Freport.git Some more fixed resulting from Jan's comments. --- diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex index aa168e0..322b240 100644 --- a/Chapters/Normalization.tex +++ b/Chapters/Normalization.tex @@ -376,16 +376,16 @@ {\defref{intended normal form definition} \typebufferlam{IntendedNormal}} - When looking at such a program from a hardware perspective, the - top level lambda abstractions define the input ports. Lambda - abstractions cannot appear anywhere else. The variable reference - in the body of the recursive let expression is the output port. - Most function applications bound by the let expression define a - component instantiation, where the input and output ports are - mapped to local signals or arguments. Some of the others use a - built-in construction (\eg\ the \lam{case} expression) or call a - built-in function (\eg\ \lam{+} or \lam{map}). For these, a - hardcoded \small{VHDL} translation is available. + When looking at such a program from a hardware perspective, the top + level lambda abstractions (\italic{lambda}) define the input ports. + Lambda abstractions cannot appear anywhere else. The variable reference + in the body of the recursive let expression (\italic{toplet}) is the + output port. Most binders bound by the let expression define a + component instantiation (\italic{userapp}), where the input and output + ports are mapped to local signals (\italic{userarg}). Some of the others + use a built-in construction (\eg\ the \lam{case} expression) or call a + built-in function (\italic{builtinapp}) such as \lam{+} or \lam{map}. + For these, a hardcoded \small{VHDL} translation is available. \section[sec:normalization:transformation]{Transformation notation} To be able to concisely present transformations, we use a specific format @@ -676,17 +676,25 @@ dictionaries, functions. \defref{representable} - A \emph{built-in function} is a function supplied by the Cλash framework, whose - implementation is not valid Cλash. The implementation is of course valid - Haskell, for simulation, but it is not expressable in Cλash. - \defref{built-in function} \defref{user-defined function} + A \emph{built-in function} is a function supplied by the Cλash + framework, whose implementation is not used to generate \VHDL. This is + either because it is no valid Cλash (like most list functions that need + recursion) or because a Cλash implementation would be unwanted (for the + addition operator, for example, we would rather use the \VHDL addition + operator to let the synthesis tool decide what kind of adder to use + instead of explicitly describing one in Cλash). \defref{built-in + function} - For these functions, Cλash has a \emph{built-in hardware translation}, so calls - to these functions can still be translated. These are functions like - \lam{map}, \lam{hwor} and \lam{length}. + These are functions like \lam{map}, \lam{hwor}, \lam{+} and \lam{length}. - A \emph{user-defined} function is a function for which we do have a Cλash - implementation available. + For these functions, Cλash has a \emph{built-in hardware translation}, + so calls to these functions can still be translated. Built-in functions + must have a valid Haskell implementation, of course, to allow + simulation. + + A \emph{user-defined} function is a function for which no built-in + translation is available and whose definition will thus need to be + translated to Cλash. \defref{user-defined function} \subsubsection[sec:normalization:predicates]{Predicates} Here, we define a number of predicates that can be used below to concisely @@ -2323,12 +2331,11 @@ \todo{Define β-reduction and η-reduction?} - Note that the normal form of such a system consists of the set of nodes - (expressions) without outgoing edges, since those are the expressions to which - no transformation applies anymore. We call this set of nodes the \emph{normal - set}. The set of nodes containing expressions in intended normal - form \refdef{intended normal form} is called the \emph{intended - normal set}. + In such a graph a node (expression) is in normal form if it has no + outgoing edges (meaning no transformation applies to it). The set of + nodes without outgoing edges is called the \emph{normal set}. Similarly, + the set of nodes containing expressions in intended normal form + \refdef{intended normal form} is called the \emph{intended normal set}. From such a graph, we can derive some properties easily: \startitemize[KR]