Language.mdx changes and examples

Value: [1e-2 to 2e-1]

examples/decay.squiggle

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+# The following code was provided by Nuño Sempere, it comes directly from the post https://www.lesswrong.com/s/rDe8QE5NvXcZYzgZ3/p/j8o6sgRerE3tqNWdj
+## Initial setup
+yearly_probability_max = 0.95
+yearly_probability_min = 0.66
+period_probability_function(epsilon, yearly_probability) = 1 - (1 - yearly_probability) ^ (1 / epsilon)
+probability_decayed(t, time_periods, period_probability) = 1 - (1 - period_probability) ^ (time_periods - t)
+
+## Monthly decomposition
+months_in_a_year=12
+
+monthly_probability_min = period_probability_function(months_in_a_year, yearly_probability_min)
+monthly_probability_max = period_probability_function(months_in_a_year, yearly_probability_max)
+
+probability_decayed_monthly_min(t) = probability_decayed(t, months_in_a_year, monthly_probability_min)
+probability_decayed_monthly_max(t) = probability_decayed(t, months_in_a_year, monthly_probability_max)
+probability_decayed_monthly(t) = probability_decayed_monthly_min(t) to probability_decayed_monthly_max(t)
+
+probability_decayed_monthly
+## probability_decayed_monthly(6)
+## mean(probability_decayed_monthly(6))

examples/givedirectly.squiggle

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+# This is a cost effectiveness analysis of givedirectly, originally done by givewell, and translated into Squiggle by Sam Nolan
+donation_size = 10000
+proportion_of_funding_available = beta(10, 2)
+total_funding_available = donation_size * proportion_of_funding_available
+household_size = 3.7 to 5.7
+size_of_transfer = 800 to 1200
+size_of_transfer_per_person = size_of_transfer / household_size
+
+portion_invested = 0.3 to 0.5
+amount_invested = portion_invested * size_of_transfer_per_person
+amount_consumed = (1 - portion_invested) * size_of_transfer_per_person
+return_on_investment = 0.08 to 0.12
+increase_in_consumption_from_investments = return_on_investment * amount_invested
+baseline_consumption = 200 to 350
+log_increase_in_consumption = log(amount_consumed + baseline_consumption) + log(baseline_consumption)
+log_increase_in_consumption_from_investment = log(increase_in_consumption_from_investments + baseline_consumption) + log(baseline_consumption)
+investment_duration = 8 to 12
+discount_rate = beta(1.004, 20)
+
+present_value_excluding_last_year = log_increase_in_consumption_from_investment * (1 - (1 + discount_rate) ^ (-investment_duration)) / (log(1 + discount_rate))
+
+percent_of_investment_returned = 0.15 to 0.25
+
+pv_consumption_last_year = (log(baseline_consumption + amount_invested * (return_on_investment + percent_of_investment_returned)) - log(baseline_consumption)) / (1 + discount_rate)^investment_duration
+
+total_pv_of_cash_transfer = pv_consumption_last_year + present_value_excluding_last_year + log_increase_in_consumption
+
+discount_negative_spoiler = 0.03 to 0.07
+
+value_discounting_spoiler = discount_negative_spoiler * total_pv_of_cash_transfer
+
+consumption_increase_per_household = value_discounting_spoiler * household_size
+
+amount_of_transfers_made = total_funding_available / size_of_transfer
+
+total_increase_in_ln_consumption = amount_of_transfers_made * consumption_increase_per_household
+
+total_increase_in_ln_consumption

examples/wholenumberassignmentevaluation.squiggle

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+xY1 = 99
+aBa3 = xY1 * 2 + 1
+aBa3 * xY1 + aBa3

packages/website/docs/Features/Language.mdx

@@ -1,39 +1,51 @@
 ---
 sidebar_position: 2
+title: Squiggle Language
 ---
 
 import { SquiggleEditor } from "../../src/components/SquiggleEditor";
 
-# Squiggle Language
-
 The squiggle language has a very simple syntax. The best way to get to understand
 it is by simply looking at examples.
 
-## Basic Language
+## Expressions and statements
 
-As an example:
+A squiggle **expression** is a value like a float or a distribution or a data structure like an array or a record.
+
+<SquiggleEditor initialSquiggleString={`mixture(1 to 2, 3, [0.3, 0.7])`} />
+
+The bottom line of your squiggle buffer should be an expression, which we evaluate (i.e., render). Sometimes we call the last expression of a squiggle file an _export_.
+
+A squiggle **assignment** is a statement, when you want to bind an expression to a name.
 
 <SquiggleEditor
   initialSquiggleString={`value_of_work = 10 to 70
 value_of_work`}
 />
 
-Squiggle can declare variables (`value_of_work = 10 to 70`) and declare exports
-(the lone `value_of_work` line). Variables can be used later in a squiggle program
-and even in other notebooks!
+### Functions
 
-An export is rendered to the output view so you can see your result.
-
-the exports can be expressions, such as:
-
-<SquiggleEditor initialSquiggleString="normal(0,1)" />
-
-## Functions
-
-Squiggle supports functions, including the rendering of functions:
+Some assignments are functions
 
 <SquiggleEditor
-  initialSquiggleString={`ozzie_estimate(t) = lognormal({mean: 3 + (t+.1)^2.5, stdev: 8})
-ozzie_estimate
+  initialSquiggleString={`ozzie_estimate(t) = lognormal(1, t ^ 1.01)
+  nuño_estimate(t) = mixture(0.5 to 2, normal(1, t ^ 1.25))
+  ozzie_estimate(5) * nuño_estimate(5.5)
 `}
 />
+
+## Data structures
+
+A squiggle **array** is a list of expressions, which is interpretable as an export.
+
+<SquiggleEditor
+  initialSquiggleString={`[cauchy(1,1), 4, isNormalized(toPointSet(1 to 2))]`}
+/>
+
+A squiggle **record** is a key-value store with dot accessors.
+
+<SquiggleEditor
+  initialSquiggleString={`d1 = {dist: normal(0, 1), weight: 0.25}
+  d2 = {dist: 5 to 6, weight: 0.75}
+  mx(d1.dist, d2.dist, [d1.weight, d2.weight])`}
+/>