From 9cdffc309beeecc4fa3b516200d3a71581c1617b Mon Sep 17 00:00:00 2001
From: Quinn Dougherty <quinnd@riseup.net>
Date: Wed, 20 Apr 2022 12:09:57 -0400
Subject: [PATCH] functions reference is almost done

---
 packages/website/.prettierignore             |  2 +
 packages/website/docs/Features/Functions.mdx | 62 +++++++++++++++-----
 packages/website/docs/Internal/Invariants.md |  8 ++-
 3 files changed, 55 insertions(+), 17 deletions(-)
 create mode 100644 packages/website/.prettierignore

diff --git a/packages/website/.prettierignore b/packages/website/.prettierignore
new file mode 100644
index 00000000..d858cd65
--- /dev/null
+++ b/packages/website/.prettierignore
@@ -0,0 +1,2 @@
+.docusaurus
+build
diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx
index 5e09004c..5cba7c11 100644
--- a/packages/website/docs/Features/Functions.mdx
+++ b/packages/website/docs/Features/Functions.mdx
@@ -9,7 +9,7 @@ _The source of truth for this document is [this file of code](https://github.com
 
 # Inventory distributions
 
-We provide starter distributions, computed symbolically. 
+We provide starter distributions, computed symbolically.
 
 ## Normal distribution
 
@@ -19,6 +19,7 @@ and standard deviation.
 <SquiggleEditor initialSquiggleString="normal(5, 1)" />
 
 ### Validity
+
 - `sd > 0`
 
 ## Uniform distribution
@@ -29,6 +30,7 @@ two given numbers.
 <SquiggleEditor initialSquiggleString="uniform(3, 7)" />
 
 ### Validity
+
 - `low < high`
 
 ## Lognormal distribution
@@ -44,13 +46,15 @@ this convinience as lognormal distributions are commonly used in practice.
 
 <SquiggleEditor initialSquiggleString="2 to 10" />
 
-### Future feature: 
+### Future feature:
+
 Furthermore, it's also possible to create a lognormal from it's actual mean
 and standard deviation, using `lognormalFromMeanAndStdDev`.
 
 <SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
 
 ### Validity
+
 - `sigma > 0`
 - In `x to y` notation, `x < y`
 
@@ -61,6 +65,7 @@ The `beta(a, b)` function creates a beta distribution with parameters `a` and `b
 <SquiggleEditor initialSquiggleString="beta(20, 20)" />
 
 ### Validity
+
 - `a > 0`
 - `b > 0`
 - Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1`
@@ -73,6 +78,7 @@ rate.
 <SquiggleEditor initialSquiggleString="exponential(1)" />
 
 ### Validity
+
 - `rate > 0`
 
 ## Triangular distribution
@@ -81,17 +87,18 @@ The `triangular(a,b,c)` function creates a triangular distribution with lower
 bound `a`, mode `b` and upper bound `c`.
 
 ### Validity
+
 - `a < b < c`
 
 <SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
 
 ## Scalar (constant dist)
 
-Squiggle, when the context is right, automatically casts a float to a constant distribution. 
+Squiggle, when the context is right, automatically casts a float to a constant distribution.
 
 # Operating on distributions
 
-Here are the ways we combine distributions. 
+Here are the ways we combine distributions.
 
 ## Mixture of distributions
 
@@ -110,10 +117,12 @@ As well as mixed distributions:
 
 <SquiggleEditor initialSquiggleString="mx(3, 8, 1 to 10, [0.2, 0.3, 0.5])" />
 
-An alias of `mx` is `mixture` 
+An alias of `mx` is `mixture`
 
 ### Validity
-Using javascript's variable arguments notation, consider `mx(...dists, weights)`: 
+
+Using javascript's variable arguments notation, consider `mx(...dists, weights)`:
+
 - `dists.length == weights.length`
 
 ## Addition (horizontal right shift)
@@ -124,7 +133,7 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)`
 
 <SquiggleEditor initialSquiggleString="dist1 = 1 to 10; dist2 = triangular(1,2,3); dist1 - dist2">
 
-## Multiplication (??) 
+## Multiplication (??)
 
 <SquiggleEditor initialSquiggleString="dist1 = 1 to 10; dist2 = triangular(1,2,3); dist1 * dist2">
 
@@ -136,16 +145,17 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)`
 
 <SquiggleEditor initialSquiggleString="dist = triangular(1,2,3); exp(dist)">
 
-## Taking the base `e` and base `10` logarithm 
+## Taking the base `e` and base `10` logarithm
 
 <SquiggleEditor initialSquiggleString="dist = triangular(1,2,3); log(dist)">
 
 <SquiggleEditor initialSquiggleString="dist = beta(1,2); log10(dist)">
 
 ### Validity
+
 - See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304)
 
-# Standard functions on distributions 
+# Standard functions on distributions
 
 ## Probability density function
 
@@ -155,6 +165,7 @@ given point x.
 <SquiggleEditor initialSquiggleString="pdf(normal(0,1),0)" />
 
 ### Validity
+
 - `x` must be a scalar
 - `dist` must be a distribution
 
@@ -166,6 +177,7 @@ or all values lower than x. It is the inverse of `inv`.
 <SquiggleEditor initialSquiggleString="cdf(normal(0,1),0)" />
 
 ### Validity
+
 - `x` must be a scalar
 - `dist` must be a distribution
 
@@ -177,6 +189,7 @@ lower than x is equal to prob. It is the inverse of `cdf`.
 <SquiggleEditor initialSquiggleString="inv(normal(0,1),0.5)" />
 
 ### Validity
+
 - `prob` must be a scalar (please only put it in `(0,1)`)
 - `dist` must be a distribution
 
@@ -194,19 +207,19 @@ The `sample(distribution)` samples a given distribution.
 
 # Normalization
 
-Some distribution operations (like horizontal shift) return an unnormalized distriibution. 
+Some distribution operations (like horizontal shift) return an unnormalized distriibution.
 
 We provide a `normalize` function
 
 <SquiggleEditor initialSquiggleString="normalize((1e-1 to 1e0) + triangular(1e-1, 1e0, 1e1))" />
-### Valdity
-- Input to `normalize` must be a dist
+### Valdity - Input to `normalize` must be a dist
 
-We provide a predicate `isNormalized`, for when we have simple control flow 
+We provide a predicate `isNormalized`, for when we have simple control flow
 
 <SquiggleEditor initialSquiggleString="isNormalized((1e-1 to 1e0) * triangular(1e-1, 1e0, 1e1))" />
 
-### Validity 
+### Validity
+
 - Input to `isNormalized` must be a dist
 
 # Convert any distribution to a sample set distribution
@@ -221,3 +234,24 @@ And binary when you provide a number of samples (truncated)
 
 <SquiggleEditor initialSquiggleString="toSampleSet(1e-1 to 1e0, 1e2)" />
 
+# `inspect`
+
+You may like to debug by right clicking your browser and using the _inspect_ functionality on the webpage, and viewing the _console_ tab. Then, wrap your squiggle output with `inspect` to log an internal representation.
+
+<SquiggleEditor initialSquiggleString="inspect(toSampleSet(1e-1 to 1e0, 1e2))" />
+
+Save for a logging side effect, `inspect` does nothing to input and returns it.
+
+# Truncate
+
+You can cut off from the left
+
+<SquiggleEditor initialSquiggleString="truncateLeft(1e-1 to 1e0, 5e-1)" />
+
+You can cut off from the right
+
+<SquiggleEditor initialSquiggleString="truncateLeft(1e-1 to 1e0, 1e1)" />
+
+You can cut off from both sides
+
+<SquiggleEditor initialSquiggleString="truncate(1e-1 to 1e0, 5e-1, 1e1))" />
diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md
index 633c904b..85fd56be 100644
--- a/packages/website/docs/Internal/Invariants.md
+++ b/packages/website/docs/Internal/Invariants.md
@@ -7,7 +7,7 @@ author:
 abstract: This document outlines some properties about algebraic combinations of distributions. It is meant to facilitate property tests for [Squiggle](https://squiggle-language.com/), an estimation language for forecasters. So far, we are focusing on the means, the standard deviation and the shape of the pdfs.
 ---
 
-Invariants to check with property tests. 
+Invariants to check with property tests.
 
 _This document right now is normative and aspirational, not a description of the testing that's currently done_.
 
@@ -122,16 +122,18 @@ TODO
 
 TODO
 
-# `pdf`, `cdf`, and `inv` 
+# `pdf`, `cdf`, and `inv`
 
-With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$, 
+With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$,
 
 ## `cdf` and `inv` are inverses
+
 $$
 \forall x \in (0,1), cdf(inv(x)) = x \land \forall x \in \texttt{dom}(cdf), x = inv(cdf(x))
 $$
 
 ## The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf`
+
 $$
 \texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf)
 $$