# Chapter 31: Evaluating Expressions

## 31.1 Introduction

In this chapter we look at the process of evaluating a J expression. Evaluating a complete expression proceeds by a sequence of basic steps, such as obtaining the value assigned to a name, or applying a function to its argument(s). For example, given

       x =: 3

then the expression

       4+5*x
    19

is (in outline) evaluated by the steps:

1. obtain the value assigned to `x` giving `3`
2. compute `5 * 3` giving `15`
3. compute `4 + 15` giving `19`

The sequence in which the steps take place is governed by the grammatical (or "parsing") rules of the J language. The parsing rules have various consequences, or effects, which can be stated informally, for example:

- verbs have long right scope (this is the "rightmost-first" rule we saw above)
- verbs have short left scope
- adverbs and conjunctions get applied before verbs
- adverbs and conjunctions have long left scope and short right scope
- names denoting nouns are evaluated as soon as encountered
- names denoting functions are not evaluated until the function is applied
- names with no assigned values are assumed to denote verbs
- long trains of verbs are resolved into trains of length 2 or 3

and we will look at how the parsing rules give rise to these effects. To illustrate the process, we can use a function which models, or simulates, the evaluation process step by step, showing it at work in slow motion.

This function, an adverb called `EVM`,is based on the description of the parsing algorithm given in the J Dictionary, section IIE. It is defined in a downloadable J script.

## 31.2 First Example

Evaluation of an expression such as `2+3` can be modelled by offering the argument `'2+3'` (a string, notice) to the modelling adverb `EVM`.

`2+3` | `'2+3' EVM`

    5

    5

We see that `'2+3' EVM` computes the same value as `2+3`, but `EVM` also produces a trace, or history, of the evaluation process. The history of `2+3` looks like this:

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 2 + 3` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ 2 +` |  | `3` | `` | `` | `` |  | ``
`2` |  | `§ 2` |  | `+` | `3` | `` | `` |  | ``
`3` |  | `§` |  | `2` | `+` | `3` | `` |  | ``
`4` |  | `` |  | `§` | `2` | `+` | `3` |  | `dyad`
`5` |  | `` |  | `§` | `5` | `` | `` |  | ``

We see successive stages of the process. Each stage is defined by the values of two variables. Firstly there is a "queue", initially containing the expression being evaluated, divided into words and preceded by a symbol to mark the beginning. Secondly, there is a "stack", initially empty. Stage 0 shows queue and stack at the outset.

At each stage the stack is inspected to see if anything can be done, that is, whether the first few words in the stack form a pattern to which a rule applies. There are 9 of these rules, and each one is tried in turn. If no rule applies, then a word is transferred from the tail of the queue to the head of the stack, and we go to the next stage and try again. This process takes us from stage 0 to stage 4.

At stage 4, we find that a rule is applicable. This rule is identified as `dyad` in the rightmost column. Informally, the `dyad` rule is:

if the first four items in the stack are something, noun, verb, noun, then apply verb to noun and noun to get new-noun, and replace the first four items in the stack by two, namely original-something followed by new-noun.

Stage 5 shows the results of applying the "dyad" rule recognized at in stage 4. The rules are tried again, with no result, and there are no more words in the queue, so we have finished. The final result is the second item of the stack.

The history is represented by 3 global variables, `Qh` `Sh` and `Rh`. The history can be displayed directly in the execution window by entering the expression `Qh,.Sh,.Rh`.

       Qh ,. Sh ,. Rh
    +----+-+-+-+----+-+-+-+----+
    |mark|2|+|3|    | | | |    |
    +----+-+-+-+----+-+-+-+----+
    |mark|2|+| |3   | | | |    |
    +----+-+-+-+----+-+-+-+----+
    |mark|2| | |+   |3| | |    |
    +----+-+-+-+----+-+-+-+----+
    |mark| | | |2   |+|3| |    |
    +----+-+-+-+----+-+-+-+----+
    |    | | | |mark|2|+|3|dyad|
    +----+-+-+-+----+-+-+-+----+
    |    | | | |mark|5| | |    |
    +----+-+-+-+----+-+-+-+----+

However, a more readable display is produced by the `show` function which computes, from `Qh` `Sh` and `Rh`, a fragment of HTML. This HTML is not for viewing in the execution window but rather for pasting into a web page such as this one. Corresponding to `Qh` `Sh` and `Rh` as above we would see:

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 2 + 3` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ 2 +` |  | `3` | `` | `` | `` |  | ``
`2` |  | `§ 2` |  | `+` | `3` | `` | `` |  | ``
`3` |  | `§` |  | `2` | `+` | `3` | `` |  | ``
`4` |  | `` |  | `§` | `2` | `+` | `3` |  | `dyad`
`5` |  | `` |  | `§` | `5` | `` | `` |  | ``

## 31.3 Parsing Rules

In this section an example is shown of each of the 9 parsing rules. Each rule looks for a pattern of items at the front of the stack, such as something verb noun verb. Each item of the stack is classified as one of the following: verb, noun, adjective, conjunction, name, left-parenthesis, right-parenthesis, assignment-symbol (`=.` or `=:`) or beginning-mark.

To aid in a compact statement of the rules, larger classes of items can be formed. For example, an item is classified as an "EDGE" if it is a beginning-mark, an assignment-symbol or a left-parenthesis.

The rules are always tried in the same order, the order in which they are presented below, beginning with the 'monad rule' and ending with the 'parenthesis rule'.

### 31.3.1 Monad Rule

If the first 3 items of the stack are an "EDGE" followed by a verb followed by a noun, then the verb is applied (monadically) to the noun to give a result-value symbolized by `Z` say, and the value `Z` replaces the verb and noun in the stack. The scheme for transforming the items of the stack is:

          monad rule: EDGE VERB NOUN etc  =>   EDGE Z etc

where `Z` is the result computed by applying `VERB` to `NOUN`. For example:

`*: 4` | `'*: 4' EVM`

    16

    16

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ *: 4` |  | `` | `` | `` |  | ``
`1` |  | `§ *:` |  | `4` | `` | `` |  | ``
`2` |  | `§` |  | `*:` | `4` | `` |  | ``
`3` |  | `` |  | `§` | `*:` | `4` |  | `monad`
`4` |  | `` |  | `§` | `16` | `` |  | ``

### 31.3.2 Second Monad Rule

An item in the stack is classified as "EAVN" if it is an EDGE or an adverb or verb or noun. The scheme is:

        monad2 rule: EAVN VERB1 VERB2 NOUN etc => EAVN VERB1 Z  etc

where `Z` is `VERB2` monadically applied to NOUN. For example:

`- *: 4` | `'- *: 4' EVM`

    _16

    _16

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ - *: 4` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ - *:` |  | `4` | `` | `` | `` |  | ``
`2` |  | `§ -` |  | `*:` | `4` | `` | `` |  | ``
`3` |  | `§` |  | `-` | `*:` | `4` | `` |  | ``
`4` |  | `` |  | `§` | `-` | `*:` | `4` |  | `monad2`
`5` |  | `` |  | `§` | `-` | `16` | `` |  | `monad`
`6` |  | `` |  | `§` | `_16` | `` | `` |  | ``

### 31.3.3 Dyad Rule

The scheme is

          dyad rule:  EAVN NOUN1 VERB NOUN2 etc => EAVN Z etc

where `Z` is `VERB` applied dyadically to `NOUN1` and `NOUN2`. For example.

`3 * 4` | `'3 * 4' EVM`

    12

    12

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 3 * 4` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ 3 *` |  | `4` | `` | `` | `` |  | ``
`2` |  | `§ 3` |  | `*` | `4` | `` | `` |  | ``
`3` |  | `§` |  | `3` | `*` | `4` | `` |  | ``
`4` |  | `` |  | `§` | `3` | `*` | `4` |  | `dyad`
`5` |  | `` |  | `§` | `12` | `` | `` |  | ``

### 31.3.4 Adverb Rule

An item which is a verb or a noun is classified as a "VN" The scheme is:

          adverb rule: EAVN VN ADVERB etc => EAVN Z etc

where `Z` is the result of applying `ADVERB` to `VN`. For example:

`+ / 1 2 3` | `'+ / 1 2 3' EVM`

    6

    6

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ + / 1 2 3` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ + /` |  | `1 2 3` | `` | `` | `` |  | ``
`2` |  | `§ +` |  | `/` | `1 2 3` | `` | `` |  | ``
`3` |  | `§` |  | `+` | `/` | `1 2 3` | `` |  | ``
`4` |  | `` |  | `§` | `+` | `/` | `1 2 3` |  | `adv`
`5` |  | `` |  | `§` | `+/` | `1 2 3` | `` |  | `monad`
`6` |  | `` |  | `§` | `6` | `` | `` |  | ``

### 31.3.5 Conjunction Rule

The scheme is:

          conjunction  EAVN VN1 CONJ VN1 etc => EAVN Z etc

where `Z` is the result of applying conjunction `CONJ` to arguments `VN1` and `VN2`. For example:

`1 & + 2` | `'1 & + 2' EVM`

    3

    3

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 1 & + 2` |  | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ 1 & +` |  | `2` | `` | `` | `` | `` |  | ``
`2` |  | `§ 1 &` |  | `+` | `2` | `` | `` | `` |  | ``
`3` |  | `§ 1` |  | `&` | `+` | `2` | `` | `` |  | ``
`4` |  | `§` |  | `1` | `&` | `+` | `2` | `` |  | ``
`5` |  | `` |  | `§` | `1` | `&` | `+` | `2` |  | `conj`
`6` |  | `` |  | `§` | `1&+` | `2` | `` | `` |  | `monad`
`7` |  | `` |  | `§` | `3` | `` | `` | `` |  | ``

### 31.3.6 Trident Rule

The scheme is:

          trident rule: EAVN VERB1 VERB2 VERB3 etc => EAVN Z etc

where `Z` is a single verb defined as the fork `(VERB1 VERB2 VERB3)`. For example:

       f=: +/
       g=: %
       h=: #

`(f g h) 1 2` | `'(f g h) 1 2' EVM`

    1.5

    1.5

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ ( f g h ) 1 2` |  | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ ( f g h )` |  | `1 2` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ ( f g h` |  | `)` | `1 2` | `` | `` | `` | `` |  | ``
`3` |  | `§ ( f g` |  | `h` | `)` | `1 2` | `` | `` | `` |  | ``
`4` |  | `§ ( f` |  | `g` | `h` | `)` | `1 2` | `` | `` |  | ``
`5` |  | `§ (` |  | `f` | `g` | `h` | `)` | `1 2` | `` |  | ``
`6` |  | `§` |  | `(` | `f` | `g` | `h` | `)` | `1 2` |  | `trident`
`7` |  | `§` |  | `(` | `f g h` | `)` | `1 2` | `` | `` |  | `paren`
`8` |  | `§` |  | `f g h` | `1 2` | `` | `` | `` | `` |  | ``
`9` |  | `` |  | `§` | `f g h` | `1 2` | `` | `` | `` |  | `monad`
`10` |  | `` |  | `§` | `1.5` | `` | `` | `` | `` |  | ``

### 31.3.7 Bident Rule

The scheme is:

          bident rule: EDGE CAVN1 CAVN2 etc => EDGE Z etc

and there are altogether these 6 cases for the bident rule:

`CAVN1` | `CAVN2` | `Z`
verb | verb | verb (a hook)
adverb | adverb | adverb
conjunction | verb | adverb
conjunction | noun | adverb
noun | conjunction | adverb
verb | conjunction | adverb

The first case (the hook) is described in Chapter 03 and the remaining cases in the schemes for bidents in Chapter 15.

In the following example the expression `(1 &)` is a bident of the form noun conjunction. Therefore it is an adverb.

`+ (1 &) 2` | `'+ (1 &) 2' EVM`

    3

    3

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ + ( 1 & ) 2` |  | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ + ( 1 & )` |  | `2` | `` | `` | `` | `` |  | ``
`2` |  | `§ + ( 1 &` |  | `)` | `2` | `` | `` | `` |  | ``
`3` |  | `§ + ( 1` |  | `&` | `)` | `2` | `` | `` |  | ``
`4` |  | `§ + (` |  | `1` | `&` | `)` | `2` | `` |  | ``
`5` |  | `§ +` |  | `(` | `1` | `&` | `)` | `2` |  | `bident`
`6` |  | `§ +` |  | `(` | `1&` | `)` | `2` | `` |  | `paren`
`7` |  | `§ +` |  | `1&` | `2` | `` | `` | `` |  | ``
`8` |  | `§` |  | `+` | `1&` | `2` | `` | `` |  | ``
`9` |  | `` |  | `§` | `+` | `1&` | `2` | `` |  | `adv`
`10` |  | `` |  | `§` | `1&+` | `2` | `` | `` |  | `monad`
`11` |  | `` |  | `§` | `3` | `` | `` | `` |  | ``

### 31.3.8 Assignment Rule

We write `NN` to denote a noun or a name. and `Asgn` for the assignment symbol `=:` or `=.`. The scheme is:

          assign rule: NN Asgn CAVN etc => Z etc

where `Z` is the value of `CAVN`.

`1 + x =: 6` | `'1 + x =: 6' EVM`

    7

    7

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 1 + x =: 6` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ 1 + x =:` |  | `6` | `` | `` | `` |  | ``
`2` |  | `§ 1 + x` |  | `=:` | `6` | `` | `` |  | ``
`3` |  | `§ 1 +` |  | `x` | `=:` | `6` | `` |  | `assign`
`4` |  | `§ 1 +` |  | `6` | `` | `` | `` |  | ``
`5` |  | `§ 1` |  | `+` | `6` | `` | `` |  | ``
`6` |  | `§` |  | `1` | `+` | `6` | `` |  | ``
`7` |  | `` |  | `§` | `1` | `+` | `6` |  | `dyad`
`8` |  | `` |  | `§` | `7` | `` | `` |  | ``

### 31.3.9 Parenthesis Rule

The scheme is:

         paren rule: ( CAVN ) etc => Z etc

where `Z` is the value of `CAVN`. For example:

`(1+2)*3` | `'(1+2)*3' EVM`

    9

    9

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ ( 1 + 2 ) * 3` |  | `` | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ ( 1 + 2 ) *` |  | `3` | `` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ ( 1 + 2 )` |  | `*` | `3` | `` | `` | `` | `` | `` |  | ``
`3` |  | `§ ( 1 + 2` |  | `)` | `*` | `3` | `` | `` | `` | `` |  | ``
`4` |  | `§ ( 1 +` |  | `2` | `)` | `*` | `3` | `` | `` | `` |  | ``
`5` |  | `§ ( 1` |  | `+` | `2` | `)` | `*` | `3` | `` | `` |  | ``
`6` |  | `§ (` |  | `1` | `+` | `2` | `)` | `*` | `3` | `` |  | ``
`7` |  | `§` |  | `(` | `1` | `+` | `2` | `)` | `*` | `3` |  | `dyad`
`8` |  | `§` |  | `(` | `3` | `)` | `*` | `3` | `` | `` |  | `paren`
`9` |  | `§` |  | `3` | `*` | `3` | `` | `` | `` | `` |  | ``
`10` |  | `` |  | `§` | `3` | `*` | `3` | `` | `` | `` |  | `dyad`
`11` |  | `` |  | `§` | `9` | `` | `` | `` | `` | `` |  | ``

### 31.3.10 Examples of Transfer

The following example shows that when a name is transferred from queue to stack, if the name denotes a value which is a noun, then the value, not the name, moves to the queue.

`a =: 6` | `(a=:7) , a`

    6

    7 6

`a=: 6` | `'(a =: 7) , a' EVM`

    6

    7 6

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ ( a =: 7 ) , a` |  | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ ( a =: 7 ) ,` |  | `6` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ ( a =: 7 )` |  | `,` | `6` | `` | `` | `` | `` |  | ``
`3` |  | `§ ( a =: 7` |  | `)` | `,` | `6` | `` | `` | `` |  | ``
`4` |  | `§ ( a =:` |  | `7` | `)` | `,` | `6` | `` | `` |  | ``
`5` |  | `§ ( a` |  | `=:` | `7` | `)` | `,` | `6` | `` |  | ``
`6` |  | `§ (` |  | `a` | `=:` | `7` | `)` | `,` | `6` |  | `assign`
`7` |  | `§ (` |  | `7` | `)` | `,` | `6` | `` | `` |  | ``
`8` |  | `§` |  | `(` | `7` | `)` | `,` | `6` | `` |  | `paren`
`9` |  | `§` |  | `7` | `,` | `6` | `` | `` | `` |  | ``
`10` |  | `` |  | `§` | `7` | `,` | `6` | `` | `` |  | `dyad`
`11` |  | `` |  | `§` | `7 6` | `` | `` | `` | `` |  | ``

By contrast, if the name is that of a verb, then the name is transferred into the stack without evaluating it. Hence a subsequent assignment changes the verb applied.

`f=: +` | `((f=:-) , f) 4`

    +

    _4 _4

`f =: +` | `'((f =: -),f) 4' EVM`

    +

    _4 _4

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ ( ( f =: - ) , f ) 4` |  | `` | `` | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ ( ( f =: - ) , f )` |  | `4` | `` | `` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ ( ( f =: - ) , f` |  | `)` | `4` | `` | `` | `` | `` | `` | `` |  | ``
`3` |  | `§ ( ( f =: - ) ,` |  | `f` | `)` | `4` | `` | `` | `` | `` | `` |  | ``
`4` |  | `§ ( ( f =: - )` |  | `,` | `f` | `)` | `4` | `` | `` | `` | `` |  | ``
`5` |  | `§ ( ( f =: -` |  | `)` | `,` | `f` | `)` | `4` | `` | `` | `` |  | ``
`6` |  | `§ ( ( f =:` |  | `-` | `)` | `,` | `f` | `)` | `4` | `` | `` |  | ``
`7` |  | `§ ( ( f` |  | `=:` | `-` | `)` | `,` | `f` | `)` | `4` | `` |  | ``
`8` |  | `§ ( (` |  | `f` | `=:` | `-` | `)` | `,` | `f` | `)` | `4` |  | `assign`
`9` |  | `§ ( (` |  | `-` | `)` | `,` | `f` | `)` | `4` | `` | `` |  | ``
`10` |  | `§ (` |  | `(` | `-` | `)` | `,` | `f` | `)` | `4` | `` |  | `paren`
`11` |  | `§ (` |  | `-` | `,` | `f` | `)` | `4` | `` | `` | `` |  | ``
`12` |  | `§` |  | `(` | `-` | `,` | `f` | `)` | `4` | `` | `` |  | `trident`
`13` |  | `§` |  | `(` | `- , f` | `)` | `4` | `` | `` | `` | `` |  | `paren`
`14` |  | `§` |  | `- , f` | `4` | `` | `` | `` | `` | `` | `` |  | ``
`15` |  | `` |  | `§` | `- , f` | `4` | `` | `` | `` | `` | `` |  | `monad`
`16` |  | `` |  | `§` | `_4 _4` | `` | `` | `` | `` | `` | `` |  | ``

### 31.3.11 Review of Parsing Rules

rule |  | stack before |  | stack after |  | where Z is ...
monad |  | EDGE | Verb | Noun | etc |  | EDGE | Z | etc |  | Verb applied to Noun
monad2 |  | EAVN | Verb1 | Verb2 | Noun |  | EAVN | Verb1 | Z |  | Verb2 applied to Noun
dyad |  | EAVN | Noun1 | Verb | Noun2 |  | EAVN | Z | etc |  | Verb applied to Noun1 and Noun2
adverb |  | EAVN | VN | Adv | etc |  | EAVN | Z | etc |  | Adv applied to VN
conj |  | EAVN | VN1 | Conj | VN2 |  | EAVN | Z | etc |  | Conj applied to VN1 and VN2

trident |  | EAVN | Verb1 | Verb2 | Verb3 |  | EAVN | Z | etc |  | fork (Verb1 Verb2 Verb3)
bident |  | EDGE | CAVN1 | CAVN2 | etc |  | EDGE | Z | etc |  | bident (CAVN1 CAVN2)
assign |  | NN | Asgn | CAVN | etc |  | Z | etc | etc |  | CAVN
paren |  | ( | CAVN | ) | etc |  | Z | etc | etc |  | CAVN

## 31.4 Effects of Parsing Rules

Now we look at some of the effects, of the parsing rules. In what follows, notice how the parsing rules in effect give rise to implicit parentheses.

### 31.4.1 Dyad Has Long Right Scope

Consider the expression `4+3-2`, which means `4+(3-2)`.

`4 + 3 - 2` | `4 + (3-2)` | `'4+3-2' EVM`

    5

    5

    5

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ 4 + 3 - 2` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ 4 + 3 -` |  | `2` | `` | `` | `` |  | ``
`2` |  | `§ 4 + 3` |  | `-` | `2` | `` | `` |  | ``
`3` |  | `§ 4 +` |  | `3` | `-` | `2` | `` |  | ``
`4` |  | `§ 4` |  | `+` | `3` | `-` | `2` |  | `dyad`
`5` |  | `§ 4` |  | `+` | `1` | `` | `` |  | ``
`6` |  | `§` |  | `4` | `+` | `1` | `` |  | ``
`7` |  | `` |  | `§` | `4` | `+` | `1` |  | `dyad`
`8` |  | `` |  | `§` | `5` | `` | `` |  | ``

Here we have an example of a general rule: a dyadic verb takes as its right argument as much as possible, so in this example `+` is applied to `3-2`, not just `3`.

Further, a dyadic verb takes as left argument as little as possible. In this example the left argument of `-` is just `3`, not `4+3`. Hence a dyadic verb is said to have a "long right scope" and a "short left scope".

### 31.4.2 Operators Before Verbs

Adverbs and conjunctions get applied first, and then the resulting verbs:

`* & 1 % 2` | `* & (1 % 2)` | `(*&1) % 2`

    0.5

    *&(0.5)

    0.5

       '* &  1 % 2' EVM
    0.5
       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ * & 1 % 2` |  | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ * & 1 %` |  | `2` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ * & 1` |  | `%` | `2` | `` | `` | `` | `` |  | ``
`3` |  | `§ * &` |  | `1` | `%` | `2` | `` | `` | `` |  | ``
`4` |  | `§ *` |  | `&` | `1` | `%` | `2` | `` | `` |  | ``
`5` |  | `§` |  | `*` | `&` | `1` | `%` | `2` | `` |  | ``
`6` |  | `` |  | `§` | `*` | `&` | `1` | `%` | `2` |  | `conj`
`7` |  | `` |  | `§` | `*&1` | `%` | `2` | `` | `` |  | `monad2`
`8` |  | `` |  | `§` | `*&1` | `0.5` | `` | `` | `` |  | `monad`
`9` |  | `` |  | `§` | `0.5` | `` | `` | `` | `` |  | ``

### 31.4.3 Operators Have Long Left Scope

An adverb or a conjunction takes as its left argument as much as possible. In the following, look at the structure of the resulting verbs: evidently the `/` adverb and the `@` conjunction take everything to their left:

`f @ g /` | `f & g @ h` | `'f&g@h' EVM`

    (f@g)/

    (f&g)@h

    (f&g)@h

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ f & g @ h` |  | `` | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ f & g @` |  | `h` | `` | `` | `` | `` | `` |  | ``
`2` |  | `§ f & g` |  | `@` | `h` | `` | `` | `` | `` |  | ``
`3` |  | `§ f &` |  | `g` | `@` | `h` | `` | `` | `` |  | ``
`4` |  | `§ f` |  | `&` | `g` | `@` | `h` | `` | `` |  | ``
`5` |  | `§` |  | `f` | `&` | `g` | `@` | `h` | `` |  | ``
`6` |  | `` |  | `§` | `f` | `&` | `g` | `@` | `h` |  | `conj`
`7` |  | `` |  | `§` | `f&g` | `@` | `h` | `` | `` |  | `conj`
`8` |  | `` |  | `§` | `(f&g)@h` | `` | `` | `` | `` |  | ``

Thus operators are said to have a "long left scope". In the example of `f&g@h` we see that the right argument of `&` is just `g`, not `g@h` . Thus conjunctions have "short right scope".

### 31.4.4 Train on the Left

The long left scope of an adverb does not extend through a train: parentheses may be needed to get the desired effect. Suppose `f g h` is intended as a train, then compare the following:

`f g h /` | `(f g h) /`

    f g (h/)

    (f g h)/

       'f g h / ' EVM
    f g h/
       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ f g h /` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ f g h` |  | `/` | `` | `` | `` |  | ``
`2` |  | `§ f g` |  | `h` | `/` | `` | `` |  | ``
`3` |  | `§ f` |  | `g` | `h` | `/` | `` |  | `adv`
`4` |  | `§ f` |  | `g` | `h/` | `` | `` |  | ``
`5` |  | `§` |  | `f` | `g` | `h/` | `` |  | ``
`6` |  | `` |  | `§` | `f` | `g` | `h/` |  | `trident`
`7` |  | `` |  | `§` | `f g (h/)` | `` | `` |  | ``

Similarly for a conjunction (with a right argument)

`f g h @ +` | `'f g h @ +' EVM`

    f g (h@+)

    f g (h@+)

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ f g h @ +` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ f g h @` |  | `+` | `` | `` | `` |  | ``
`2` |  | `§ f g h` |  | `@` | `+` | `` | `` |  | ``
`3` |  | `§ f g` |  | `h` | `@` | `+` | `` |  | ``
`4` |  | `§ f` |  | `g` | `h` | `@` | `+` |  | `conj`
`5` |  | `§ f` |  | `g` | `h@+` | `` | `` |  | ``
`6` |  | `§` |  | `f` | `g` | `h@+` | `` |  | ``
`7` |  | `` |  | `§` | `f` | `g` | `h@+` |  | `trident`
`8` |  | `` |  | `§` | `f g (h@+)` | `` | `` |  | ``

However, for a conjunction with no right argument, the left scope does extend through a train:

`f g h @` | `'f g h @' EVM`

    (f g h)@

    (f g h)@

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ f g h @` |  | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ f g h` |  | `@` | `` | `` | `` | `` |  | ``
`2` |  | `§ f g` |  | `h` | `@` | `` | `` | `` |  | ``
`3` |  | `§ f` |  | `g` | `h` | `@` | `` | `` |  | ``
`4` |  | `§` |  | `f` | `g` | `h` | `@` | `` |  | ``
`5` |  | `` |  | `§` | `f` | `g` | `h` | `@` |  | `trident`
`6` |  | `` |  | `§` | `f g h` | `@` | `` | `` |  | `bident`
`7` |  | `` |  | `§` | `(f g h)@` | `` | `` | `` |  | ``

By contrast, in the case of of `f @ g /`, notice how the "conj" rule is applied before there is a chance to apply the "adverb" rule"

`f @ g /` | `'f @ g / ' EVM`

    (f@g)/

    (f@g)/

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ f @ g /` |  | `` | `` | `` | `` | `` |  | ``
`1` |  | `§ f @ g` |  | `/` | `` | `` | `` | `` |  | ``
`2` |  | `§ f @` |  | `g` | `/` | `` | `` | `` |  | ``
`3` |  | `§ f` |  | `@` | `g` | `/` | `` | `` |  | ``
`4` |  | `§` |  | `f` | `@` | `g` | `/` | `` |  | ``
`5` |  | `` |  | `§` | `f` | `@` | `g` | `/` |  | `conj`
`6` |  | `` |  | `§` | `f@g` | `/` | `` | `` |  | `adv`
`7` |  | `` |  | `§` | `(f@g)/` | `` | `` | `` |  | ``

### 31.4.5 Presumption of Verb

A name with no value assigned is presumed to be a verb. For example, in the following the three names make a fork:

`Maple Leaf Rag` | `'Maple Leaf Rag' EVM`

    Maple Leaf Rag

    Maple Leaf Rag

       show ''

|  | queue |  | stack |  | rule
`0` |  | `§ Maple Leaf Rag` |  | `` | `` | `` | `` |  | ``
`1` |  | `§ Maple Leaf` |  | `Rag` | `` | `` | `` |  | ``
`2` |  | `§ Maple` |  | `Leaf` | `Rag` | `` | `` |  | ``
`3` |  | `§` |  | `Maple` | `Leaf` | `Rag` | `` |  | ``
`4` |  | `` |  | `§` | `Maple` | `Leaf` | `Rag` |  | `trident`
`5` |  | `` |  | `§` | `Maple Leaf Rag` | `` | `` |  | ``

This is the end of Chapter 31

Table of Contents

Copyright © Roger Stokes 2002. This material may be freely reproduced, provided that this copyright notice is also reproduced.

last updated 4 Aug 2002