fixed up default.nix
with correct pandoc command
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@ -7,11 +7,10 @@ nix-build
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o result/property-tests.pdf
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```
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Without `nix`, you can install `pandoc` yourself and run
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```sh
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pandoc -s property-tests.md -o property-tests.pdf
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```
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Without `nix`, you can install `pandoc` and `pdflatex` yourself and see `make.sh` for the rendering command.
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## _Details_
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The `properties-tests.pdf` document is _normative and aspirational_. It does not document tests as they exist in the codebase, but somewhat represents how we think squiggle ought to be tested.
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The `invariants.pdf` document is _normative and aspirational_. It does not document tests as they exist in the codebase, but represents how we think squiggle ought to be tested.
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We are partially bottlenecked by the rescript ecosystem's maturity with respect to property-based testing.
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@ -4,22 +4,23 @@
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# Style sheets https://github.com/citation-style-language/styles/
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with pkgs;
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let deps = [
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pandoc
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(texlive.combine
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{ inherit (texlive) scheme-small datetime; }
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)
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]; in
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stdenv.mkDerivation {
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name = "render_squiggle_properties";
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src = ./.;
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buildInputs = [pandoc];
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buildInputs = deps;
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buildPhase = ''
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echo rendering...
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pandoc \
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--from markdown \
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--to latex \
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--out properties.pdf \
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--pdf-engine xelatex \
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properties.md \
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pandoc -s invariants.md -o invariants.pdf
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echo rendered.
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'';
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installPhase = ''
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mkdir -p $out
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cp properties.pdf $out/properties.pdf
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cp invariants.pdf $out/invariants.pdf
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'';
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}
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BIN
packages/squiggle-lang/__tests__/docs/invariants-apr12.pdf
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packages/squiggle-lang/__tests__/docs/invariants-apr12.pdf
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@ -1,38 +1,51 @@
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# Property tests for squiggle
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# Squiggle invariants
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Here are some property tests for squiggle. I am testing mostly for the mean and the standard deviation. I know that squiggle doesn't yet have functions for the standard deviation, but they could be added.
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The keywords to search for are "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)".
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## Sums
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## Means and standard deviations
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### Sums
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$$ mean(f+g) = mean(f) + mean(g) $$
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$$ Std(f+g) = sqrt(std(f)^2 + std(g)^2) $$
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$$ std(f+g) = \sqrt{std(f)^2 + std(g)^2} $$
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In the case of normal distributions,
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$$ normal(a,b) + normal(c,d) = normal(a+c, sqrt(b^2 + d^2) $$
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$$ mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2})) $$
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## Substractions
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### Subtractions
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$$ mean(f-g) = mean(f) - mean(g) $$
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$$ std(f-g) = sqrt(std(f)^2 + std(g)^2) $$
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$$ std(f-g) = \sqrt{std(f)^2 + std(g)^2} $$
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## Multiplications
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### Multiplications
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$$ mean(f \cdot g) = mean(f) \cdot mean(g) $$
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$$ std(f \cdot g) = sqrt( (std(f)^2 + mean(f)) \cdot (std(g)^2 + mean(g)) - (mean(f) \cdot mean(y))^2) $$
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$$ std(f \cdot g) = \sqrt{ (std(f)^2 + mean(f)) \cdot (std(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2} $$
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## Divisions
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### Divisions
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Divisions are tricky, and in general we don't have good expressions to characterize properties of ratios. In particular, the ratio of two normals is a Cauchy distribution, which doesn't have to have a mean.
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## To do:
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# To do:
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- Provide sources or derivations, useful as this document becomes more complicated
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- Provide definitions for the probability density function, exponential, inverse, log, etc.
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- Provide at least some tests for division
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- See if playing around with characteristic functions turns out anything useful
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## Probability density functions
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TODO
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## Cumulative density functions
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TODO
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## Inverse cumulative density functions
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TODO
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@ -1 +1 @@
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pandoc -s property-tests.md -o property-tests.pdf
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pandoc -s invariants.md -o invariants.pdf
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