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Jun 2, 2026
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Aplr reformat #339

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Remove indentation from text blocks; combine columns of experiments t…
Jun 2, 2026
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Add solid backgrounds to APLR report figures
Jun 2, 2026
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238 changes: 119 additions & 119 deletions doc/reports/aplr1/aplr1.md
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Original file line number Diff line number Diff line change
Expand Up @@ -283,19 +283,19 @@ For the example grammar, the pseudo-start symbol results in the following state;
state nub is inserted into both the work queue and the state nub set:

```
State 0
Kernel
[Answer' ::= · Answer "⊥", {"ε"}]
Added
[Expr ::= · Expr MulOp Expr, {"*", "/", "+", "-", EOI}] prec mul
[Expr ::= · Expr AddOp Expr, {"*", "/", "+", "-", EOI}] prec add
[Expr ::= · INT, {"*", "/", "+", "-", EOI}]
[Answer ::= · Expr EOI, {"⊥"}]
Actions
INT : ShiftPrefix 1
Gotos
Expr : 2
Answer : 3
State 0
Kernel
[Answer' ::= · Answer "⊥", {"ε"}]
Added
[Expr ::= · Expr MulOp Expr, {"*", "/", "+", "-", EOI}] prec mul
[Expr ::= · Expr AddOp Expr, {"*", "/", "+", "-", EOI}] prec add
[Expr ::= · INT, {"*", "/", "+", "-", EOI}]
[Answer ::= · Expr EOI, {"⊥"}]
Actions
INT : ShiftPrefix 1
Gotos
Expr : 2
Answer : 3
```

Note that every symbol immediately to the right of a dot is represented in the **_actions_** or
Expand All @@ -304,9 +304,9 @@ multiple dots. Each item in the goto set for `Expr` is created by advancing the
anywhere it appears before a dot in this state. The following kernel results:

```
[Expr ::= Expr · MulOp Expr, {"*", "/", "+", "-", EOI}] prec mul
[Expr ::= Expr · AddOp Expr, {"*", "/", "+", "-", EOI}] prec add
[Answer ::= Expr · EOI, {"⊥"}]
[Expr ::= Expr · MulOp Expr, {"*", "/", "+", "-", EOI}] prec mul
[Expr ::= Expr · AddOp Expr, {"*", "/", "+", "-", EOI}] prec add
[Answer ::= Expr · EOI, {"⊥"}]
```

A work queue state nub is processed by 1) popping it from the front of the work queue, and 2)
Expand Down Expand Up @@ -459,23 +459,23 @@ graphical depiction.
#### Transitively remergeable

```
State 1 [1.0] | State 19 [1.1]
Kernel | Kernel
[Xn ::= At · Yn Dt, {EOI}] | [Xn ::= At · Yn Dt, {At, Dt}]
[Xn ::= At · Zn Ct, {EOI}] | [Xn ::= At · Zn Ct, {At, Dt}]
[Xn ::= At · Tn, {EOI}] | [Xn ::= At · Tn, {At, Dt}]
Added | Added
[Yn ::= · Tt Wn, {Dt}] | [Yn ::= · Tt Wn, {Dt}]
[Yn ::= · Ut Xn, {Dt}] | [Yn ::= · Ut Xn, {Dt}]
[Zn ::= · Tt Ut, {Ct}] | [Zn ::= · Tt Ut, {Ct}]
[Tn ::= · Ut Xn At, {EOI}] | [Tn ::= · Ut Xn At, {At, Dt}]
Actions | Actions
Tt : ShiftPrefix 5 | Tt : ShiftPrefix 5
Ut : ShiftPrefix 6 | Ut : ShiftPrefix 32
Gotos | Gotos
Yn : 7 | Yn : 33
Zn : 8 | Zn : 34
Tn : 9 | Tn : 35
State 1 [1.0] | State 19 [1.1]
Kernel | Kernel
[Xn ::= At · Yn Dt, {EOI}] | [Xn ::= At · Yn Dt, {At, Dt}]
[Xn ::= At · Zn Ct, {EOI}] | [Xn ::= At · Zn Ct, {At, Dt}]
[Xn ::= At · Tn, {EOI}] | [Xn ::= At · Tn, {At, Dt}]
Added | Added
[Yn ::= · Tt Wn, {Dt}] | [Yn ::= · Tt Wn, {Dt}]
[Yn ::= · Ut Xn, {Dt}] | [Yn ::= · Ut Xn, {Dt}]
[Zn ::= · Tt Ut, {Ct}] | [Zn ::= · Tt Ut, {Ct}]
[Tn ::= · Ut Xn At, {EOI}] | [Tn ::= · Ut Xn At, {At, Dt}]
Actions | Actions
Tt : ShiftPrefix 5 | Tt : ShiftPrefix 5
Ut : ShiftPrefix 6 | Ut : ShiftPrefix 32
Gotos | Gotos
Yn : 7 | Yn : 33
Zn : 8 | Zn : 34
Tn : 9 | Tn : 35
```

The differences between isocoric state set 1 members 1 and 19 correspond to those shown in the
Expand All @@ -484,26 +484,26 @@ graph, namely differing successor states in isocoric state sets 6, 7, 8, and 9.
35}) are transitively remergeable.

```
State 21 [17.0] | State 50 [17.2]
Kernel | Kernel
[Yn ::= Ut Xn ·, {Dt}] | [Yn ::= Ut Xn ·, {Dt}]
[Tn ::= Ut Xn · At, {EOI}] | [Tn ::= Ut Xn · At, {At, Dt}]
Actions | Actions
At : ShiftPrefix 40 | At : ShiftPrefix 62
Dt : Reduce Yn ::= Ut Xn | Dt : Reduce Yn ::= Ut Xn
State 21 [17.0] | State 50 [17.2]
Kernel | Kernel
[Yn ::= Ut Xn ·, {Dt}] | [Yn ::= Ut Xn ·, {Dt}]
[Tn ::= Ut Xn · At, {EOI}] | [Tn ::= Ut Xn · At, {At, Dt}]
Actions | Actions
At : ShiftPrefix 40 | At : ShiftPrefix 62
Dt : Reduce Yn ::= Ut Xn | Dt : Reduce Yn ::= Ut Xn
```

Isocoric state set 17 members 21 and 50 transition to differing successor states in isocoric state
set 23 on `At`, and perform the same reduction on `Dt`. States 21 and 50 are remergeable if the
differing successor states (23{40, 62}) are transitively remergeable.

```
State 40 [23.0] | State 62 [23.1]
Kernel | Kernel
[Tn ::= Ut Xn At ·, {EOI}] | [Tn ::= Ut Xn At ·, {At, Dt}]
Actions | Actions
EOI : Reduce Tn ::= Ut Xn At | At : Reduce Tn ::= Ut Xn At
| Dt : Reduce Tn ::= Ut Xn At
State 40 [23.0] | State 62 [23.1]
Kernel | Kernel
[Tn ::= Ut Xn At ·, {EOI}] | [Tn ::= Ut Xn At ·, {At, Dt}]
Actions | Actions
EOI : Reduce Tn ::= Ut Xn At | At : Reduce Tn ::= Ut Xn At
| Dt : Reduce Tn ::= Ut Xn At
```

Isocoric state set 23 members 40 and 62 contain only disjoint actions, which makes them remergeable
Expand All @@ -512,35 +512,35 @@ Isocoric state set 23 members 40 and 62 contain only disjoint actions, which mak
#### Transitively non-remergeable

```
State 5 [5.0] | State 10 [5.1]
Kernel | Kernel
[Yn ::= Tt · Wn, {Dt}] | [Yn ::= Tt · Wn, {Et}]
[Zn ::= Tt · Ut, {Ct}] | [Zn ::= Tt · Ut, {Dt}]
Added | Added
[Wn ::= · Ut Vn, {Dt}] | [Wn ::= · Ut Vn, {Et}]
Actions | Actions
Ut : ShiftPrefix 17 | Ut : ShiftPrefix 24
Gotos | Gotos
Wn : 18 | Wn : 25
State 5 [5.0] | State 10 [5.1]
Kernel | Kernel
[Yn ::= Tt · Wn, {Dt}] | [Yn ::= Tt · Wn, {Et}]
[Zn ::= Tt · Ut, {Ct}] | [Zn ::= Tt · Ut, {Dt}]
Added | Added
[Wn ::= · Ut Vn, {Dt}] | [Wn ::= · Ut Vn, {Et}]
Actions | Actions
Ut : ShiftPrefix 17 | Ut : ShiftPrefix 24
Gotos | Gotos
Wn : 18 | Wn : 25
```

Isocoric state set 5 members 5 and 10 transition to differing successor states in isocoric state set
15 on `Ut`, and to differing successor states in isocoric state set 16 on `Wn`. States 5 and 10 are
remergeable if the differing successor states (15{17, 24}, 16{18, 25}) are transitively remergeable.

```
State 17 [15.0] | State 24 [15.1]
Kernel | Kernel
[Zn ::= Tt Ut ·, {Ct}] | [Zn ::= Tt Ut ·, {Dt}]
[Wn ::= Ut · Vn, {Dt}] | [Wn ::= Ut · Vn, {Et}]
Added | Added
[Vn ::= ·, {Dt}] | [Vn ::= ·, {Et}]
Actions | Actions
Ct : Reduce Zn ::= Tt Ut |
Dt : Reduce Vn ::= epsilon | Dt : Reduce Zn ::= Tt Ut
| Et : Reduce Vn ::= epsilon
Gotos | Gotos
Vn : 31 | Vn : 41
State 17 [15.0] | State 24 [15.1]
Kernel | Kernel
[Zn ::= Tt Ut ·, {Ct}] | [Zn ::= Tt Ut ·, {Dt}]
[Wn ::= Ut · Vn, {Dt}] | [Wn ::= Ut · Vn, {Et}]
Added | Added
[Vn ::= ·, {Dt}] | [Vn ::= ·, {Et}]
Actions | Actions
Ct : Reduce Zn ::= Tt Ut |
Dt : Reduce Vn ::= epsilon | Dt : Reduce Zn ::= Tt Ut
| Et : Reduce Vn ::= epsilon
Gotos | Gotos
Vn : 31 | Vn : 41
```

Isocoric state set 15 members 17 and 24 contain remergeable disjoint actions on `Ct` and `Et`, but
Expand All @@ -563,70 +563,70 @@ All experiments run Hocc main-0-g207645c72297ae6e3406f427382f6de14766c80d. Time
statistics are collected with garbage collection (GC) disabled, e.g.

```sh
time -v hocc -gc no -resolve yes -src Gawk -algorithm lalr
time -v hocc -gc no -resolve yes -src Gawk -algorithm lalr
```

GC overhead would dominate run time and memory usage for the smallest and largest automata, but it
also makes the state counts easier to interpret, so the state counts are generated with precise
post-remerging GC enabled, e.g.

```sh
hocc -gc post -resolve yes -src Gawk -algorithm lalr -verbose
hocc -gc post -resolve yes -src Gawk -algorithm lalr -verbose
```

The reported time/memory statistics are the best of three runs on an Apple MacBook M5 Pro, running
[Ubuntu](https://en.wikipedia.org/wiki/Ubuntu) Linux 24.04.03 as a virtual machine hosted by
[Parallels](https://en.wikipedia.org/wiki/Parallels_Desktop_for_Mac).

| Grammar | Algorithm | Resolve | Time (h:m:s) | Max RSS (kB) | States |
|---------|:----------|---------|-------------:|-------------:|-------:|
| Gawk | LALR(1) | yes | 0.08 | 36864 | 320 |
| | PGM LR(1) | | 0.08 | 36736 | 320 |
| | IELR⁺(1) | | 2.37 | 254464 | 367 |
| | APLR(1) | | 1.04 | 79616 | 367 |
| | LR(1) | | 0.23 | 52096 | 2359 |
| | | | | | |
| | LALR(1) | no | 0.08 | 36864 | 320 |
| | PGM LR(1) | | 0.08 | 36864 | 320 |
| | IELR⁺(1) | | 5.25 | 642176 | 367 |
| | APLR(1) | | 1.01 | 80640 | 367 |
| | LR(1) | | 0.23 | 52224 | 2467 |
| | | | | | |
| Gpic | LALR(1) | yes | 0.32 | 45056 | 423 |
| | PGM LR(1) | | 0.35 | 46488 | 423 |
| | IELR⁺(1) | | 1.91 | 116992 | 428 |
| | APLR(1) | | 1.50 | 132096 | 428 |
| | LR(1) | | 1.11 | 98304 | 4834 |
| | | | | | |
| | LALR(1) | no | 0.31 | 45184 | 426 |
| | PGM LR(1) | | 0.35 | 46848 | 426 |
| | IELR⁺(1) | | 2.61 | 139392 | 448 |
| | APLR(1) | | 1.47 | 133376 | 448 |
| | LR(1) | | 1.08 | 97792 | 4871 |
| | | | | | |
| Lyken | LALR(1) | yes | 0.84 | 89600 | 1340 |
| | PGM LR(1) | | 1.82 | 96640 | 1340 |
| | IELR⁺(1) | | 5:59.97 | 6200832 | 1352 |
| | APLR(1) | | 11.97 | 868480 | 1352 |
| | LR(1) | | 10.47 | 755584 | 18755 |
| | | | | | |
| | LALR(1) | no | 0.84 | 90240 | 1375 |
| | PGM LR(1) | | 1.83 | 97280 | 1375 |
| | IELR⁺(1) | | 12:39.39 | 30538880 | 1857 |
| | APLR(1) | | 1:15.34 | 1480576 | 1742 |
| | LR(1) | | 10.51 | 761472 | 19590 |
| | | | | | |
| OCaml | LALR(1) | yes | 2.94 | 82048 | 1878 |
| | PGM LR(1) | | 3.48 | 82304 | 1878 |
| | IELR⁺(1) | | 35.43 | 1158784 | 1878 |
| | APLR(1) | | 2:16.48 | 3483648 | 1878 |
| | LR(1) | | 1:45.42 | 2349312 | 106607 |
| | | | | | |
| | LALR(1) | no | 2.95 | 82304 | 1878 |
| | PGM LR(1) | | 3.50 | 83200 | 1878 |
| | IELR⁺(1) | | 3:21.70 | 5528192 | 4585 |
| | APLR(1) | | 9:26:25___ | 4801664 | 4586 |
| | LR(1) | | 1:45.44 | 2345344 | 106607 |
| Grammar / Resolve | Algorithm | Time (h:m:s) | Max RSS (kB) | States |
|------------------:|:----------|-------------:|-------------:|-------:|
| Gawk / yes | LALR(1) | 0.08 | 36864 | 320 |
| | PGM LR(1) | 0.08 | 36736 | 320 |
| | IELR⁺(1) | 2.37 | 254464 | 367 |
| | APLR(1) | 1.04 | 79616 | 367 |
| | LR(1) | 0.23 | 52096 | 2359 |
| | | | | |
| / no | LALR(1) | 0.08 | 36864 | 320 |
| | PGM LR(1) | 0.08 | 36864 | 320 |
| | IELR⁺(1) | 5.25 | 642176 | 367 |
| | APLR(1) | 1.01 | 80640 | 367 |
| | LR(1) | 0.23 | 52224 | 2467 |
| | | | | |
| Gpic / yes | LALR(1) | 0.32 | 45056 | 423 |
| | PGM LR(1) | 0.35 | 46488 | 423 |
| | IELR⁺(1) | 1.91 | 116992 | 428 |
| | APLR(1) | 1.50 | 132096 | 428 |
| | LR(1) | 1.11 | 98304 | 4834 |
| | | | | |
| / no | LALR(1) | 0.31 | 45184 | 426 |
| | PGM LR(1) | 0.35 | 46848 | 426 |
| | IELR⁺(1) | 2.61 | 139392 | 448 |
| | APLR(1) | 1.47 | 133376 | 448 |
| | LR(1) | 1.08 | 97792 | 4871 |
| | | | | |
| Lyken / yes | LALR(1) | 0.84 | 89600 | 1340 |
| | PGM LR(1) | 1.82 | 96640 | 1340 |
| | IELR⁺(1) | 5:59.97 | 6200832 | 1352 |
| | APLR(1) | 11.97 | 868480 | 1352 |
| | LR(1) | 10.47 | 755584 | 18755 |
| | | | | |
| / no | LALR(1) | 0.84 | 90240 | 1375 |
| | PGM LR(1) | 1.83 | 97280 | 1375 |
| | IELR⁺(1) | 12:39.39 | 30538880 | 1857 |
| | APLR(1) | 1:15.34 | 1480576 | 1742 |
| | LR(1) | 10.51 | 761472 | 19590 |
| | | | | |
| OCaml / yes | LALR(1) | 2.94 | 82048 | 1878 |
| | PGM LR(1) | 3.48 | 82304 | 1878 |
| | IELR⁺(1) | 35.43 | 1158784 | 1878 |
| | APLR(1) | 2:16.48 | 3483648 | 1878 |
| | LR(1) | 1:45.42 | 2349312 | 106607 |
| | | | | |
| / no | LALR(1) | 2.95 | 82304 | 1878 |
| | PGM LR(1) | 3.50 | 83200 | 1878 |
| | IELR⁺(1) | 3:21.70 | 5528192 | 4585 |
| | APLR(1) | 9:26:25___ | 4801664 | 4586 |
| | LR(1) | 1:45.44 | 2345344 | 106607 |

The performance numbers are best interpreted relative to each other, rather than in absolute terms.
Hocc is written in OCaml, using purely functional code and data structures. So far, so good, but
Expand Down
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