This transformation ensures that the return value of a function is always a
simple local variable reference.
- This transformation only applies to the entire body of a
- function instead of any subexpression in a function. This is
- achieved by the contexts, like \lam{x = E}, though this is
- strictly not correct (you could read this as "if there is any
- function \lam{x} that binds \lam{E}, any \lam{E} can be
- transformed, while we only mean the \lam{E} that is bound by
- \lam{x}).
-
- Note that the return value is not simplified if its not
- representable. Otherwise, this would cause a direct loop with
- the inlining of unrepresentable bindings. If the return value is
- not representable because it has a function type, η-expansion
- should make sure that this transformation will eventually apply.
- If the value is not representable for other reasons, the
- function result itself is not representable, meaning this
- function is not translatable anyway.
+ The basic idea of this transformation is to take the body of a
+ function and bind it with a let expression (so the body of that let
+ expression becomes a variable reference that can be used as the output
+ port). If the body of the function happens to have lambda abstractions
+ at the top level (which is allowed by the intended normal
+ form\refdef{intended normal form definition}), we take the body of the
+ inner lambda instead. If that happens to be a let expression already
+ (which is allowed by the intended normal form), we take the body of
+ that let (which is not allowed to be anything but a variable reference
+ according the the intended normal form).
+
+ This transformation uses the context conditions in a special way.
+ These contexts, like \lam{x = λv1 ... λvn.E}, are above the dotted
+ line and provide a condition on the environment (\ie\ they require a
+ certain top level binding to be present). These ensure that
+ expressions are only transformed when they are in the functions
+ \quote{return value} directly. This means the context conditions have
+ to interpreted in the right way: not \quote{if there is any function
+ \lam{x} that binds \lam{E}, any \lam{E} can be transformed}, but we
+ mean only the \lam{E} that is bound by \lam{x}).
+
+ Be careful when reading the transformations: Not the entire function
+ from the context is transformed, just a part of it.
+
+ Note that the return value is not simplified if it is not representable.
+ Otherwise, this would cause a loop with the inlining of
+ unrepresentable bindings in
+ \in{section}[sec:normalization:nonrepinline]. If the return value is
+ not representable because it has a function type, η-expansion should
+ make sure that this transformation will eventually apply. If the
+ value is not representable for other reasons, the function result
+ itself is not representable, meaning this function is not translatable
+ anyway.
\starttrans
- x = E \lam{E} is representable
- ~ \lam{E} is not a lambda abstraction
- E \lam{E} is not a let expression
- --------------------------- \lam{E} is not a local variable reference
- letrec x = E in x
- \stoptrans
-
- \starttrans
- x = λv0 ... λvn.E \lam{E} is representable
- ~ \lam{E} is not a lambda abstraction
- E \lam{E} is not a let expression
- --------------------------- \lam{E} is not a local variable reference
- letrec x = E in x
+ x = λv1 ... λvn.E \lam{n} can be zero
+ ~ \lam{E} is representable
+ E \lam{E} is not a lambda abstraction
+ --------------------------- \lam{E} is not a let expression
+ letrec y = E in y \lam{E} is not a local variable reference
\stoptrans
\starttrans
- x = λv0 ... λvn.let ... in E
- ~ \lam{E} is representable
- E \lam{E} is not a local variable reference
- -----------------------------
- letrec x = E in x
+ x = λv1 ... λvn.letrec binds in E \lam{n} can be zero
+ ~ \lam{E} is representable
+ letrec binds in E \lam{E} is not a local variable reference
+ ------------------------------------
+ letrec binds; y = E in y
\stoptrans
\startbuffer[from]
\stopbuffer
\startbuffer[to]
- x = letrec x = add 1 2 in x
+ x = letrec y = add 1 2 in y
\stopbuffer
\transexample{retvalsimpl}{Return value simplification}{from}{to}
+
+ \startbuffer[from]
+ x = λa. add 1 a
+ \stopbuffer
+
+ \startbuffer[to]
+ x = λa. letrec
+ y = add 1 a
+ in
+ y
+ \stopbuffer
+
+ \transexample{retvalsimpllam}{Return value simplification with a lambda abstraction}{from}{to}
- \todo{More examples}
+ \startbuffer[from]
+ x = letrec
+ a = add 1 2
+ in
+ add a 3
+ \stopbuffer
+
+ \startbuffer[to]
+ x = letrec
+ a = add 1 2
+ y = add a 3
+ in
+ y
+ \stopbuffer
+
+ \transexample{retvalsimpllet}{Return value simplification with a let expression}{from}{to}
\subsection[sec:normalization:argsimpl]{Representable arguments simplification}
This section contains just a single transformation that deals with
to specialize away any unrepresentable literals that are used as
function arguments. The following two transformations do exactly this.
- \subsubsection{Non-representable binding inlining}
+ \subsubsection[sec:normalization:nonrepinline]{Non-representable binding inlining}
This transform inlines let bindings that are bound to a
non-representable value. Since we can never generate a signal
assignment for these bindings (we cannot declare a signal assignment
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