diff --git a/.github/workflows/codeql-analysis.yml b/.github/workflows/codeql-analysis.yml
index c7750177..2aef3ae3 100644
--- a/.github/workflows/codeql-analysis.yml
+++ b/.github/workflows/codeql-analysis.yml
@@ -18,13 +18,6 @@ on:
       - production
       - staging
       - develop
-  pull_request:
-    # The branches below must be a subset of the branches above
-    branches:
-      - master
-      - production
-      - staging
-      - develop
   schedule:
     - cron: "42 19 * * 0"
 
diff --git a/.parcelrc b/.parcelrc
deleted file mode 100644
index f5a5c2d5..00000000
--- a/.parcelrc
+++ /dev/null
@@ -1,6 +0,0 @@
-{
-    "extends": "@parcel/config-default",
-    "transformers": {
-        "*.res": ["@parcel/transformer-raw"]
-    }
-}
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 7e0d1fc6..c85a3438 100644
--- a/packages/website/docs/Features/Functions.mdx
+++ b/packages/website/docs/Features/Functions.mdx
@@ -1,12 +1,15 @@
 ---
+title: "Functions Reference"
 sidebar_position: 7
 ---
 
 import { SquiggleEditor } from "../../src/components/SquiggleEditor";
 
-# Squiggle Functions Reference
+_The source of truth for this document is [this file of code](https://github.com/quantified-uncertainty/squiggle/blob/develop/packages/squiggle-lang/src/rescript/ReducerInterface/ReducerInterface_GenericDistribution.res)_
 
-## Distributions
+## Inventory distributions
+
+We provide starter distributions, computed symbolically.
 
 ### Normal distribution
 
@@ -15,6 +18,10 @@ and standard deviation.
 
 <SquiggleEditor initialSquiggleString="normal(5, 1)" />
 
+#### Validity
+
+- `sd > 0`
+
 ### Uniform distribution
 
 The `uniform(low, high)` function creates a uniform distribution between the
@@ -22,86 +29,281 @@ two given numbers.
 
 <SquiggleEditor initialSquiggleString="uniform(3, 7)" />
 
+#### Validity
+
+- `low < high`
+
 ### Lognormal distribution
 
 The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters
-mu and sigma. The log of lognormal(mu, sigma) is a normal distribution with parameters
-mean mu and standard deviation sigma.
+`mu` and `sigma`. The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`.
 
 <SquiggleEditor initialSquiggleString="lognormal(0, 0.7)" />
 
-An alternative format is also available. The "to" notation creates a lognormal
+An alternative format is also available. The `to` notation creates a lognormal
 distribution with a 90% confidence interval between the two numbers. We add
-this convinience as lognormal distributions are commonly used in practice.
+this convenience as lognormal distributions are commonly used in practice.
 
 <SquiggleEditor initialSquiggleString="2 to 10" />
 
+#### Future feature:
+
 Furthermore, it's also possible to create a lognormal from it's actual mean
 and standard deviation, using `lognormalFromMeanAndStdDev`.
 
+TODO: interpreter/parser doesn't provide this in current `develop` branch
+
 <SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
 
+#### Validity
+
+- `sigma > 0`
+- In `x to y` notation, `x < y`
+
 ### Beta distribution
 
-The `beta(a, b)` function creates a beta distribution with parameters a and b:
+The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`:
 
-<SquiggleEditor initialSquiggleString="beta(20, 20)" />
+<SquiggleEditor initialSquiggleString="beta(10, 20)" />
+
+#### Validity
+
+- `a > 0`
+- `b > 0`
+- Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1`
 
 ### Exponential distribution
 
-The `exponential(mean)` function creates an exponential distribution with the given
-mean.
+The `exponential(rate)` function creates an exponential distribution with the given
+rate.
 
-<SquiggleEditor initialSquiggleString="exponential(1)" />
+<SquiggleEditor initialSquiggleString="exponential(1.11)" />
 
-### The Triangular distribution
+#### Validity
+
+- `rate > 0`
+
+### Triangular distribution
 
 The `triangular(a,b,c)` function creates a triangular distribution with lower
-bound a, mode b and upper bound c.
+bound `a`, mode `b` and upper bound `c`.
+
+#### Validity
+
+- `a < b < c`
 
 <SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
 
-### Multimodal distriutions
+### Scalar (constant dist)
 
-The multimodal function combines 2 or more other distributions to create a weighted
+Squiggle, when the context is right, automatically casts a float to a constant distribution.
+
+## Operating on distributions
+
+Here are the ways we combine distributions.
+
+### Mixture of distributions
+
+The `mixture` function combines 2 or more other distributions to create a weighted
 combination of the two. The first positional arguments represent the distributions
 to be combined, and the last argument is how much to weigh every distribution in the
 combination.
 
-<SquiggleEditor initialSquiggleString="mx(uniform(0,1), normal(1,1), [0.5, 0.5])" />
+<SquiggleEditor initialSquiggleString="mixture(uniform(0,1), normal(1,1), [0.5, 0.5])" />
 
 It's possible to create discrete distributions using this method.
 
-<SquiggleEditor initialSquiggleString="mx(0, 1, [0.2,0.8])" />
+<SquiggleEditor initialSquiggleString="mixture(0, 1, [0.2,0.8])" />
 
 As well as mixed distributions:
 
-<SquiggleEditor initialSquiggleString="mx(3, 8, 1 to 10, [0.2, 0.3, 0.5])" />
+<SquiggleEditor initialSquiggleString="mixture(3, 8, 1 to 10, [0.2, 0.3, 0.5])" />
 
-## Other Functions
+An alias of `mixture` is `mx`
 
-### PDF of a distribution
+#### Validity
 
-The `pdf(distribution, x)` function returns the density of a distribution at the
+Using javascript's variable arguments notation, consider `mx(...dists, weights)`:
+
+- `dists.length == weights.length`
+
+### Addition
+
+A horizontal right shift
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 + dist2`}
+/>
+
+### Subtraction
+
+A horizontal left shift
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 - dist2`}
+/>
+
+### Multiplication
+
+TODO: provide intuition pump for the semantics
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 * dist2`}
+/>
+
+We also provide concatenation of two distributions as a syntax sugar for `*`
+
+<SquiggleEditor initialSquiggleString="(0.1 to 1) triangular(1,2,3)" />
+
+### Division
+
+TODO: provide intuition pump for the semantics
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 / dist2`}
+/>
+
+### Exponentiation
+
+TODO: provide intuition pump for the semantics
+
+<SquiggleEditor initialSquiggleString={`(0.1 to 1) ^ beta(2, 3)`} />
+
+### Taking the base `e` exponential
+
+<SquiggleEditor
+  initialSquiggleString={`dist = triangular(1,2,3)
+exp(dist)`}
+/>
+
+### Taking logarithms
+
+<SquiggleEditor
+  initialSquiggleString={`dist = triangular(1,2,3)
+log(dist)`}
+/>
+
+<SquiggleEditor
+  initialSquiggleString={`dist = beta(1,2)
+log10(dist)`}
+/>
+
+Base `x`
+
+<SquiggleEditor
+  initialSquiggleString={`x = 2
+dist = beta(2,3)
+log(dist, x)`}
+/>
+
+#### Validity
+
+- `x` must be a scalar
+- See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304)
+
+### Pointwise addition
+
+**Pointwise operations are done with `PointSetDist` internals rather than `SampleSetDist` internals**.
+
+TODO: this isn't in the new interpreter/parser yet.
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 .+ dist2`}
+/>
+
+### Pointwise subtraction
+
+TODO: this isn't in the new interpreter/parser yet.
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 .- dist2`}
+/>
+
+### Pointwise multiplication
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 .* dist2`}
+/>
+
+### Pointwise division
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 ./ dist2`}
+/>
+
+### Pointwise exponentiation
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dist1 .^ dist2`}
+/>
+
+### Pointwise logarithm
+
+TODO: write about the semantics and the case handling re scalar vs. dist and log base.
+
+<SquiggleEditor
+  initialSquiggleString={`dist1 = 1 to 10
+dist2 = triangular(1,2,3)
+dotLog(dist1, dist2)`}
+/>
+
+## Standard functions on distributions
+
+### Probability density function
+
+The `pdf(dist, x)` function returns the density of a distribution at the
 given point x.
 
 <SquiggleEditor initialSquiggleString="pdf(normal(0,1),0)" />
 
-### Inverse of a distribution
+#### Validity
 
-The `inv(distribution, prob)` gives the value x or which the probability for all values
-lower than x is equal to prob. It is the inverse of `cdf`.
+- `x` must be a scalar
+- `dist` must be a distribution
 
-<SquiggleEditor initialSquiggleString="inv(normal(0,1),0.5)" />
+### Cumulative density function
 
-### CDF of a distribution
-
-The `cdf(distribution,x)` gives the cumulative probability of the distribution
+The `cdf(dist, x)` gives the cumulative probability of the distribution
 or all values lower than x. It is the inverse of `inv`.
 
 <SquiggleEditor initialSquiggleString="cdf(normal(0,1),0)" />
 
-### Mean of a distribution
+#### Validity
+
+- `x` must be a scalar
+- `dist` must be a distribution
+
+### Inverse CDF
+
+The `inv(dist, prob)` gives the value x or which the probability for all values
+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
+
+### Mean
 
 The `mean(distribution)` function gives the mean (expected value) of a distribution.
 
@@ -112,3 +314,55 @@ The `mean(distribution)` function gives the mean (expected value) of a distribut
 The `sample(distribution)` samples a given distribution.
 
 <SquiggleEditor initialSquiggleString="sample(normal(0, 10))" />
+
+## Normalization
+
+Some distribution operations (like horizontal shift) return an unnormalized distriibution.
+
+We provide a `normalize` function
+
+<SquiggleEditor initialSquiggleString="normalize((0.1 to 1) + triangular(0.1, 1, 10))" />
+
+#### Validity - Input to `normalize` must be a dist
+
+We provide a predicate `isNormalized`, for when we have simple control flow
+
+<SquiggleEditor initialSquiggleString="isNormalized((0.1 to 1) * triangular(0.1, 1, 10))" />
+
+#### Validity
+
+- Input to `isNormalized` must be a dist
+
+## Convert any distribution to a sample set distribution
+
+`toSampleSet` has two signatures
+
+It is unary when you use an internal hardcoded number of samples
+
+<SquiggleEditor initialSquiggleString="toSampleSet(0.1 to 1)" />
+
+And binary when you provide a number of samples (floored)
+
+<SquiggleEditor initialSquiggleString="toSampleSet(0.1 to 1, 100)" />
+
+## `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(0.1 to 1, 100))" />
+
+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(0.1 to 1, 0.5)" />
+
+You can cut off from the right
+
+<SquiggleEditor initialSquiggleString="truncateRight(0.1 to 1, 10)" />
+
+You can cut off from both sides
+
+<SquiggleEditor initialSquiggleString="truncate(0.1 to 1, 0.5, 1.5)" />
diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md
index c1c0fd79..91adf1a1 100644
--- a/packages/website/docs/Internal/Invariants.md
+++ b/packages/website/docs/Internal/Invariants.md
@@ -1,5 +1,5 @@
 ---
-title: Statistical properties of algebraic combinations of distributions for property testing.
+title: Invariants of Probability Distributions
 urlcolor: blue
 author:
   - Nuño Sempere
@@ -7,13 +7,17 @@ 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.
+
 _This document right now is normative and aspirational, not a description of the testing that's currently done_.
 
+## Algebraic combinations
+
 The academic keyword to search for in relation to this document is "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". Squiggle doesn't yet support getting the standard deviation, denoted by $\sigma$, but such support could yet be added.
 
-## Means and standard deviations
+### Means and standard deviations
 
-### Sums
+#### Sums
 
 $$
 mean(f+g) = mean(f) + mean(g)
@@ -29,7 +33,7 @@ $$
 mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2}))
 $$
 
-### Subtractions
+#### Subtractions
 
 $$
 mean(f-g) = mean(f) - mean(g)
@@ -39,7 +43,7 @@ $$
 \sigma(f-g) = \sqrt{\sigma(f)^2 + \sigma(g)^2}
 $$
 
-### Multiplications
+#### Multiplications
 
 $$
 mean(f \cdot g) = mean(f) \cdot mean(g)
@@ -49,15 +53,15 @@ $$
 \sigma(f \cdot g) = \sqrt{ (\sigma(f)^2 + mean(f)) \cdot (\sigma(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2}
 $$
 
-### Divisions
+#### Divisions
 
 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.
 
-## Probability density functions (pdfs)
+### Probability density functions (pdfs)
 
 Specifying the pdf of the sum/multiplication/... of distributions as a function of the pdfs of the individual arguments can still be done. But it requires integration. My sense is that this is still doable, and I (Nuño) provide some _pseudocode_ to do this.
 
-### Sums
+#### Sums
 
 Let $f, g$ be two independently distributed functions. Then, the pdf of their sum, evaluated at a point $z$, expressed as $(f + g)(z)$, is given by:
 
@@ -110,15 +114,31 @@ let pdfOfSum = (pdf1, pdf2, cdf1, cdf2, z) => {
 };
 ```
 
-## Cumulative density functions
+### Cumulative density functions
 
 TODO
 
-## Inverse cumulative density functions
+### Inverse cumulative density functions
 
 TODO
 
-# To do:
+## `pdf`, `cdf`, and `inv`
+
+With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$,
+
+### `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`
+
+$$
+\texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf)
+$$
+
+## To do:
 
 - Provide sources or derivations, useful as this document becomes more complicated
 - Provide definitions for the probability density function, exponential, inverse, log, etc.
diff --git a/packages/website/docusaurus.config.js b/packages/website/docusaurus.config.js
index c5d03327..4971b1b0 100644
--- a/packages/website/docusaurus.config.js
+++ b/packages/website/docusaurus.config.js
@@ -49,7 +49,7 @@ const config = {
           sidebarPath: require.resolve("./sidebars.js"),
           // Please change this to your repo.
           editUrl:
-            "https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/",
+            "https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/",
           remarkPlugins: [math],
           rehypePlugins: [katex],
         },
@@ -57,7 +57,7 @@ const config = {
           showReadingTime: true,
           // Please change this to your repo.
           editUrl:
-            "https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/",
+            "https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/",
         },
         theme: {
           customCss: require.resolve("./src/css/custom.css"),
@@ -73,7 +73,7 @@ const config = {
         title: "Squiggle",
         logo: {
           alt: "Squiggle Logo",
-          src: "img/logo.svg",
+          src: "img/quri-logo.png",
         },
         items: [
           {
@@ -85,7 +85,7 @@ const config = {
           { to: "/blog", label: "Blog", position: "left" },
           { to: "/playground", label: "Playground", position: "left" },
           {
-            href: "https://github.com/QURIresearch/squiggle",
+            href: "https://github.com/quantified-uncertainty/squiggle",
             label: "GitHub",
             position: "right",
           },
@@ -103,7 +103,7 @@ const config = {
               },
               {
                 label: "GitHub",
-                href: "https://github.com/QURIresearch/squiggle",
+                href: "https://github.com/quantified-uncertainty/squiggle",
               },
             ],
           },
diff --git a/packages/website/src/pages/index.js b/packages/website/src/pages/index.js
index 452c7ef0..4cbddcac 100644
--- a/packages/website/src/pages/index.js
+++ b/packages/website/src/pages/index.js
@@ -22,10 +22,7 @@ function HomepageHeader() {
 export default function Home() {
   const { siteConfig } = useDocusaurusContext();
   return (
-    <Layout
-      title={`Hello from ${siteConfig.title}`}
-      description="Description will go into a meta tag in <head />"
-    >
+    <Layout title={`${siteConfig.title}`} description="An estimation language">
       <HomepageHeader />
       <main>
         <HomepageFeatures />
diff --git a/packages/website/static/img/favicon.ico b/packages/website/static/img/favicon.ico
index c01d54bc..d318e234 100644
Binary files a/packages/website/static/img/favicon.ico and b/packages/website/static/img/favicon.ico differ
diff --git a/packages/website/static/img/quri-logo.png b/packages/website/static/img/quri-logo.png
new file mode 100644
index 00000000..14932c80
Binary files /dev/null and b/packages/website/static/img/quri-logo.png differ