From 2afb23928e1984d475cc460e1672e8f6fa0e4dbe Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Wed, 11 Aug 2021 17:21:31 -0400 Subject: Allow clicking on header to get fragment link --- docs/doc/lexical.html | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) (limited to 'docs/doc/lexical.html') diff --git a/docs/doc/lexical.html b/docs/doc/lexical.html index 2ce2cfc9..ec3f6567 100644 --- a/docs/doc/lexical.html +++ b/docs/doc/lexical.html @@ -4,10 +4,10 @@ BQN: Lexical scoping
(github) / BQN / doc
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Lexical scoping

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Lexical scoping

BQN uses lexical scope, like most modern functional programming languages including Javascript, Scheme, and Julia, and like Dyalog APL's dfns (tradfns are dynamically scoped). This document describes how lexical scoping works, and a few small details relevant to BQN's version of it.

In short, every block is a separate scope that can refer to identifiers in containing scopes. When evaluated, the block makes a variable for each identifier defined in it (including arguments and operands). The blocks that it contains will now access these variables. In the first level of a block, variables must be defined before they can be used, but in child blocks, a variable can be used regardless of where it's defined, as long as the definition is evaluated before the child block is.

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Scopes

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Scopes

Scoping is a mechanism that allows the same variable name to refer to different variables depending on program context. For example, the following code uses the name a in two ways: once for a value at the top level, and once locally in a function. With scoping, once you write {} to create a block, you can define any name you want inside without worrying whether it's taken.

↗️
    a ← 6
     F ← { a × 1 + a ← 𝕩 }
@@ -35,7 +35,7 @@

Each call creates the list of indices i, then calls itself using 𝕊 on each element of 𝕩 if it's a list, then couples i to the result. This requires i to be unaffected by other calls to the function, which works because i is scoped not only to the source code location but also to the particular evaluation of the block that creates it.

These examples probably work like you expect—they're meant to highlight the features that scoping should have, in order to help show how less intuitive cases work later on.

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Visibility

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Visibility

A scope can view and modify (with ↩) variables in other scopes that contain it. We say these variables are visible in the inner scopes. Variables at the top level of a program are visible to all the code in that program, so that we might call them "global". That would be a little misleading though, because for example each file is an entire program, so if one file is imported from another then it can't read the first file's variables.

↗️
    counter ← 0
     inc ← 6
@@ -77,7 +77,7 @@ ERROR
 42

The function C3_7 uses the versions of counter and inc created in _makeCount, even though it's called not from inside _makeCount, but from the top-level program. This is what it means for BQN's scoping to be lexical rather than dynamic. Which identifiers are visible is determined by where the code containing them is located in the source code, not how it's called at runtime. The static nature of lexical scoping makes it much easier to keep track of how variables are used (for compilers, this means optimization opportunities), and for this reason dynamic scoping is very rare in programming languages today.

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Post-definition

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Post-definition

In the top level a block, a variable can only be used after it's defined, and the compiler rejects any code that tries to use an undefined variable. But blocks contained in that block see variables it defines regardless of the positioning. Below, PlusC references the variable c that's defined after it (but when code is executed one line at a time like it is here, I still have to put both definitions on the same line so they are compiled together).

↗️
    PlusC ← { 𝕩+c } ⋄ c←¯1
     PlusC 7
@@ -88,7 +88,7 @@ ERROR
 ERROR

Why define things this way? It's easier to see if you imagine the variable used is also a function. It's normal for a function to call other functions defined at the top level, of course. And it would be pretty unpleasant for BQN to enforce a specific ordering for them. It would also make recursive functions impossible except by using 𝕊, and mutually recursive ones completely impossible. A simple rule that makes all these things just work smoothly seems much better than any alternative.

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Closures

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Closures

Let's run _makeCount from above a few more times.

↗️
    C4_2 ← 4‿2 _makeCount  # Start at 4; increment by 2
     C1_4 ← 1‿4 _makeCount  #          1;              4
@@ -121,12 +121,12 @@ ERROR

The variable Mean is visible only within the outer immediate block. The only way it can be accessed is by code in this block: the two calls in the returned function, which will later be renamed stdDev. Nothing in the block modifies it, so its value is constant. It's just a little utility that exists only for code in the block. Making it visible elsewhere is as simple as moving it out of the block, but it's best not to do this without reason. Keeping a variable in the smallest possible scope makes it easier to understand the program, because it reduces the amount of information needed to understand scopes where that variable doesn't apply.

Neither the specification nor a typical implementation keep track of what is and isn't a closure, although an advanced interpreter will probably work with some related properties. The existence of closures is an ordinary feature of lexical scoping and not a special case. However, it's sometimes a useful term for discussing the operation of a program. We might define a closure as a block that can be run and access variables from a parent scope even after the block that created that scope finishes execution.

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Environments form a tree

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Environments form a tree

So a block has access to every environment that it might need a variable from, for as long as it needs. This idea is a little fuzzy, so let's clarify by describing how an implementation would support figure out what can access where.

The mechanism is that each environment can have a parent environment (the topmost environment, which corresponds to the entire program, has no parent). When a variable is accessed, it might be in the current environment, or its parent, or that environment's parent, and so on. Every environment corresponds to one block in the source code, and its parent corresponds to the parent block, so a compiler can figure out how many levels up it will have to go based on the source code.

We've seen that one block can create many environments. An environment can have only one parent, but many children, so environments form a tree. A forest to be precise, as one execution of BQN can involve multiple programs.

How does an environment know which of the many environments corresponding to the parent scope is its parent? This information is saved when the block is reached in the program and a block instance is created. Unless it's an immediate block, the block instance won't be run right away: a block instance isn't the same as a block evaluation. But each block evaluation starts with a block instance, and that's where it gets the parent environment. Unlike block evaluation, which can happen anywhere, a block instance is created only during evaluation of the parent block. So the saved parent environment is simply the current environment.

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Mutation

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Mutation

The value of a variable can be modified with ↩. It's similar to definition ← in that it sets the value of the variable, but the way it interacts with scoping is completely different. Defining creates a new variable in the current scope, and modifying refers to an existing variable in the current scope or a parent. In scoping terms, modifying is more like an ordinary variable reference than a definition.

When a variable's modified, functions with access to it see the new value. They have access to the variable, not any particular value that it has.

↗️
    factor ← 3
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