Expand all leading tabs in markdown files
Given how problematic leading tabs in markdown files can be,
we have expanded all leading tabs in markdown files by:
```sh
find * -type f -name '*.md' -print |
while read -r file; do
rm -f "$file.tmp" ;
expand < "$file" > "$file.tmp" ;
mv -f -v "$file.tmp" "$file" ;
done
```
Given the previous changes to `bin/pandoc-wrapper.sh` and other recent
commits and recent pull requests, the were were **NO** changes to
any HTML files. This is a **good thing** as the expression goes.
No there are no leading tabs in any markdown files.
A check to catch any re-introduction of leading tabs
into any markdown file is on the way.
BTW: We do not have anything against leading tabs in files,
even though we have had to deal with their impact on forming
HTML from markdown files (as well as the calc source code).
It is just that this is one of those cases where tabs conflict
(sometimes caused by people wanting to change the classic
8-space tab model) with a desired outcome.
Perform `make www` to perform the above and test under macOS.
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@@ -92,10 +92,10 @@ has the value `a`. Another function called `K` is defined as `\x\y(x)`
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and it evaluates as follows:
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```
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K p q
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-> \x\y(x) p q
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-> \y(p) q
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-> p
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K p q
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-> \x\y(x) p q
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-> \y(p) q
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-> p
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```
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Another function of interest is `S`, defined as `\f\g\x((f x) (g x))`.
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@@ -106,15 +106,15 @@ variables or lambda abstractions. In fact, even `I` is unnecessary,
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since it is equivalent to `S K K`:
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```
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I z
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-> \a(a) z
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-> z
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I z
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-> \a(a) z
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-> z
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S K K z
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-> \f\g\x((f x) (g x)) K K z
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-> (K z) (K z)
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-> \x\y(x) z (K z)
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-> z
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S K K z
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-> \f\g\x((f x) (g x)) K K z
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-> (K z) (K z)
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-> \x\y(x) z (K z)
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-> z
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```
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The algorithm for translating lambda expressions into combinator
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@@ -122,9 +122,9 @@ expressions works as follows. There are three forms of lambda expression
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to consider: variables, applications, and abstractions.
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```
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trans v -> v (variable)
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trans a b -> (trans a) (trans b ) (application)
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trans \ab -> abs a (trans b) (abstraction)
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trans v -> v (variable)
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trans a b -> (trans a) (trans b ) (application)
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trans \ab -> abs a (trans b) (abstraction)
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```
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There are a further three cases to consider for the body of lambda
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@@ -132,33 +132,33 @@ expressions, where we need to do the magic that transforms away the
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variables.
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```
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abs a f x -> S (abs a f) (abs a x)
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abs a b -> K b (b != a)
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abs a a -> I
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abs a f x -> S (abs a f) (abs a x)
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abs a b -> K b (b != a)
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abs a a -> I
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```
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E.g. suppose we had combinator expressions for `+` and `3` and we wanted
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to see what the combinator expression for doubling 3 looked like:
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```
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trans \x(+ x x) 3
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-> (trans \x(+ x x)) (trans 3)
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-> (abs x (trans + x x)) 3
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-> (abs x + x x) 3
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-> S (abs x + x) (abs x x) 3
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-> S (S (abs x +) (abs x x)) I 3
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-> S (S (K +) I) I 3
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-> S (S (K +) I) I 3
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trans \x(+ x x) 3
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-> (trans \x(+ x x)) (trans 3)
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-> (abs x (trans + x x)) 3
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-> (abs x + x x) 3
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-> S (abs x + x) (abs x x) 3
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-> S (S (abs x +) (abs x x)) I 3
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-> S (S (K +) I) I 3
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-> S (S (K +) I) I 3
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```
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We can then check that this evaluates to the expected result:
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```
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S (S (K +) I) I 3
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-> S (K +) I 3 (I 3)
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-> K + 3 (I 3) (I 3)
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-> + (I 3) (I 3)
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-> + 3 3
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S (S (K +) I) I 3
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-> S (K +) I 3 (I 3)
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-> K + 3 (I 3) (I 3)
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-> + (I 3) (I 3)
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-> + 3 3
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```
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It is possible to perform a slightly more compact translation with a
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@@ -166,24 +166,24 @@ couple of simple optimisations. For example, note that `K (a b)` is the
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same as `S (K a) (K b)`, because
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```
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K (a b) x
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-> a b
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K (a b) x
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-> a b
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```
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and
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```
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S (K a) (K b) x
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-> K a x (K b x)
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-> a b
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S (K a) (K b) x
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-> K a x (K b x)
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-> a b
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```
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Also, `S (K a) I` is the same as just `a` because
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```
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S (K a) I x
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-> K a x (I x)
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-> a x
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S (K a) I x
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-> K a x (I x)
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-> a x
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```
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The program simply reads a lambda expression from the standard input,
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