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[icfp] p? -> f, because ?functions always return #t or #f

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ben 2016-03-16 10:27:24 -04:00
parent c32c1a3be9
commit 764bb66365
1 changed files with 7 additions and 9 deletions
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icfp-2016/solution.scrbl
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@ -1,6 +1,4 @@
#lang scribble/sigplan @onecolumn #lang scribble/sigplan @onecolumn
@; TODO color p?, e
@; Better notation for erasure, maybe just color differently
@require["common.rkt"] @require["common.rkt"]
@ -24,22 +22,22 @@ Using @exact|{\RktMeta{expr}}| to denote the set of syntactically valid, symboli
@exact|{$$\interp\ : \big\{\RktMeta{expr} \rightarrow ({\RktVal{val}} \cup {\tt \RktVal{\#false}})\big\}$$}| @exact|{$$\interp\ : \big\{\RktMeta{expr} \rightarrow ({\RktVal{val}} \cup {\tt \RktVal{\#false}})\big\}$$}|
If @exact|{\RktMeta{p?} $\in \interp$}| and @exact|{\RktMeta{e} $\in \RktMeta{expr}$}|, If @exact|{\RktMeta{f} $\in \interp$}| and @exact|{\RktMeta{e} $\in \RktMeta{expr}$}|,
it may be useful to think of it may be useful to think of
@exact|{\RktMeta{(p? e)}}| as @emph{evidence} that the expression @exact|{\RktMeta{e}}| @exact|{\RktMeta{(f e)}}| as @emph{evidence} that the expression @exact|{\RktMeta{e}}|
is recognized by @exact|{\RktMeta{p?}}|. is recognized by @exact|{\RktMeta{f}}|.
Alternatively, @exact|{\RktMeta{(p? e)}}| is a kind of interpolant@~cite[c-jsl-1997], Alternatively, @exact|{\RktMeta{(f e)}}| is a kind of interpolant@~cite[c-jsl-1997],
representing data embedded in @exact|{\RktMeta{e}}| that justifies a certain representing data embedded in @exact|{\RktMeta{e}}| that justifies a certain
program transformation. program transformation.
Correct interpretation functions @exact|{\RktMeta{p?}}| obey two guidelines: Correct interpretation functions @exact|{\RktMeta{f}}| obey two guidelines:
@itemize[ @itemize[
@item{ @item{
The expressions for which @exact|{\RktMeta{p?}}| returns a non-@racket[#false] The expressions for which @exact|{\RktMeta{f}}| returns a non-@racket[#false]
value must have some common structure. value must have some common structure.
} }
@item{ @item{
Non-@racket[#false] results @exact|{\RktMeta{(p? e)}}| are computed by a Non-@racket[#false] results @exact|{\RktMeta{(f e)}}| are computed by a
uniform algorithm and must have some common structure. uniform algorithm and must have some common structure.
} }
] ]