R3 — Naming things

Goal: give names to values and to formulas, understand why the two behave differently, and learn the command that gets you out of trouble.

Assignment is :=

> a := 3
a := 3.0
> a + 1
4.0

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The echo repeats what was stored, which is worth reading rather than skipping — later in this lesson it is how you tell a value from a formula.

Why not =?

Because = already means something, and it is not assignment:

> a = 4
false

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That is an equation, and Leonardo answered it: a is 3, so a = 4 is false. An equation is a thing you can state, test and solve, which is what makes solve(x^2 = 4, x) meaningful in R5. Had = been assignment, none of that would be sayable.

Two symbols, two jobs: := stores, = relates.

A formula keeps its variables

Assign something containing a free variable and you get a definition rather than a value:

> g := sin(t) + t
g := (sin(t) + t)
> g
(sin(t) + t)

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Look at the echo: it repeated the formula, where a := 3 repeated a number. Nothing was computed, because t has no value and there was nothing to compute. Give t one and g follows:

> t := 0
t := 0.0
> g
0.0

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Definitions are late-bound, and that is the point

A definition is re-read every time you use it, so redefining what it depends on updates it — without touching the definition:

> h := 2 * g
h := (2.0 * g)
> h
0.0
> t := 1
t := 1.0
> h
3.68294

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h means “twice whatever g is”, and g means “sin(t) + t for whatever t is”. Change t, and both move. That is how you build a model up in layers and then explore it by changing one number at the bottom.

When you want the opposite, freeze it

Sometimes a name should record a result rather than a relationship. consolidate evaluates now and stores the answer, so later changes cannot reach it:

> frozen := consolidate(2 * g)
frozen := 3.68294
> t := 2
t := 2.0
> frozen
3.68294
> h
5.81859

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h moved with t; frozen did not. Use consolidate for a measurement you have already taken, and plain := for a relationship you want kept live.

Seeing what you have

> env
precision = 5
a := 3.0
frozen := 3.68294
t := 2.0
g := (sin(t) + t)
h := (2.0 * g)

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env lists the settings as well as the names — values first, then definitions — so it answers both “what did I call that?” and “what state am I in?”.

unset — the command that gets you unstuck

> unset t
t unset
> g
(sin(t) + t)

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With t gone, g is a formula again.

This is the most useful command in the lesson, because the commonest confusion at this prompt is an answer that comes back as a number when you expected algebra. The cause is almost always a name still bound from earlier. Two things bind without your typing :=:

• a := you have forgotten about, which env will show you;
• solve, which stores its own answer — see R5, where it earns its own section.

When something reads oddly, env then unset is the fix.

Names the language has taken

> e := 3
cannot assign to 'e': it is a built-in constant
> simplify := 1
cannot assign to 'simplify': it is a reserved word

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Constants and command words are refused rather than silently shadowed — otherwise the binding would be unreachable, since e always parses as the constant and simplify always starts a command.

Try it yourself

Define area as the area of a circle of radius r, evaluate it at r = 2, then make area symbolic again.

Answers

```text > area := pi * r^2 area := (3.14159 * (r ^ 2.0)) > r := 2 r := 2.0 > area 12.56637 > unset r r unset > area (3.14159 * (r ^ 2.0)) ``` *[run this session](https://lycogrypho.github.io/Leonardo/app/#s=precision%205%0Acolors%20dark%0Apretty%20off%0Alatex%20off%0Anames%20off%0Alogic%20minmax%0Alogic%20symmetric%20off%0Aexact%20precision%2030%0Aexact%20off%0Aa%20%3A%3D%203.0%0Afrozen%20%3A%3D%203.682941969615793%0Aarea%20%3A%3D%20(3.141592653589793%20*%20(r%20%5E%202.0))%0Ag%20%3A%3D%20(sin(t)%20%2B%20t)%0Ah%20%3A%3D%20(2.0%20*%20g))* Note the first echo: `area` stored the *formula*, with `pi` already folded to a number because that much was computable.

What you learned

• := stores, = relates. An equation is a value you can test and solve.
• A right-hand side with free variables becomes a late-bound definition that tracks its dependencies; consolidate freezes the current answer instead.
• The echo tells you which you got: a number or a formula.
• env shows bindings and settings; unset is what you reach for when an answer is unexpectedly numeric.

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