Derivation modes

 

Let us com­pare pro­duc­tions by the same gram­mar
“-gr.tryDerivationModes” in all deriva­tion modes.

The gram­mar com­pris­es two sub­gram­mars. The sec­ond one (gram#2) uses the ORD deriva­tion mode in all exam­ples. We show the trace of a deriva­tion and the result­ing production.

'A' and 'B' are vari­ables. 'a', 'b', 'e' and 'f' are ter­mi­nal sym­bols that are used to label sound objects.

[Derivation mode]
gram#1[1] S --> A B B A B B A
gram#1[2] A B --> a B
gram#1[3] B A --> B b
gram#1[4] B B A --> e B A
gram#1[5] B B --> f B

ORD
gram#2[1] f B --> f f
gram#2[2] e B --> e e
gram#2[3] A e --> c e

---

ORD

[Step #1] Selected: [1] LEFT S --> A B B A B B A
A B B A B B A
[Step #2] Selected: [2] LEFT A B --> a B
a B B A B B A
[Step #3] Selected: [2] LEFT A B --> a B
a B B a B B A
[Step #4] Selected: [3] LEFT B A --> B b
a B B a B B b
[Step #5] Selected: [5] LEFT B B --> f B
a f B a B B b
[Step #6] Selected: [5] LEFT B B --> f B
a f B a f B b
[Step #7] Selected: gram#2[1] LEFT f B --> f f
a f f a f B b
[Step #8] Selected: gram#2[1] LEFT f B --> f f
a f f a f f b

Result:  a f f a f f b

In this mode, the rules are applied in order and the rewrit­ing posi­tions are searched from left to right. This process is the fastest way to find a unique solution.

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RND  (default deriva­tion mode)

[Step #1] Selected: [1] RND S --> A B B A B B A
A B B A B B A
[Step #2] Selected: [4] RND B B A --> e B A
A e B A B B A
[Step #3] Selected: [3] RND B A --> B b
A e B A B B b
[Step #4] Selected: [2] RND A B --> a B
A e B a B B b
[Step #5] Selected: [5] RND B B --> f B
A e B a f B b
[Step #6] Selected: gram#2[1] LEFT f B --> f f
A e B a f f b
[Step #7] Selected: gram#2[2] LEFT e B --> e e
A e e a f f b
[Step #8] Selected: gram#2[3] LEFT A e --> c e
c e e a f f b

Result:  c e e a f f b
More results:
a f f a f f b
a f f a e e b
a f f b f f b
a f f b e e b
a e e a f f b
a e e b f f b
a e e a e e b
a e e b e e b
a e e c e e b
a f f c e e b
c e e b f f b
c e e a e e b
c e e b e e b
c e e c e e b

Rules are select­ed at ran­dom, with prob­a­bil­i­ties depend­ing on their weights. The rewrit­ing posi­tion is also select­ed at ran­dom unless it is spec­i­fied as "LEFT" or "RIGHT."

---

LIN

[Step #1] Selected: [1] LEFT S --> A B B A B B A
A B B A B B A
[Step #2] Selected: [2] LEFT A B --> a B
a B B A B B A
[Step #3] Selected: [4] LEFT B B A --> e B A
a e B A B B A
[Step #4] Selected: [3] LEFT B A --> B b
a e B b B B A
[Step #5] Selected: [4] LEFT B B A --> e B A
a e B b e B A
[Step #6] Selected: [3] LEFT B A --> B b
a e B b e B b
[Step #7] Selected: gram#2[2] LEFT e B --> e e
a e e b e B b
[Step #8] Selected: gram#2[2] LEFT e B --> e e
a e e b e e b

Result:  a e e b e e b
More results:
a e e a f f b
a e e b e e b
a e e b f f b
a f f a e e b
a f f a f f b
a f f b e e b
a f f b f f b

Here, rules are select­ed at ran­dom but the rewrit­ing posi­tion is searched from left to right, unless it is spec­i­fied as "RIGHT" or "RND".

---

SUB

[Step #1] Selected: [1] RND S --> A B B A B B A
A B B A B B A
[Step #2] Selected: [2] RND A B --> a B
[Step #3] Selected: [4] RND B B A --> e B A
[Step #4] Selected: [2] RND A B --> a B
[Step #5] Selected: [4] RND B B A --> e B A
[Step #6] Selected: [3] RND B A --> B b
[Step #7] Selected: gram#2[2] LEFT e B --> e e
[Step #8] Selected: gram#2[2] LEFT e B --> e e

Result:  a e e a e e b

Here, all eli­gi­ble rules are applied at once. The process is repeat­ed until no rule is eligible.

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SUB1

[Step #1] Selected: [1] LEFT S --> A B B A B B A
[Step #2] Selected: [2] LEFT A B --> a B
[Step #3] Selected: [2] LEFT A B --> a B
[Step #4] Selected: [3] LEFT B A --> B b
[Step #5] Selected: [5] LEFT B B --> f B
[Step #6] Selected: [5] LEFT B B --> f B
[Step #7] Selected: gram#2[1] LEFT f B --> f f
[Step #8] Selected: gram#2[1] LEFT f B --> f f

Result:  a f f a f f b

This is sim­i­lar to "SUB," except that rewrit­ing posi­tions are searched from left to right, and the set of eli­gi­ble rules is applied only once.

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POSLONG

[Step #1] Selected: [1] LEFT S --> A B B A B B A
A B B A B B A
[Step #2] Selected: [2] LEFT A B --> a B
a B B A B B A
[Step #3] Selected: [4] LEFT B B A --> e B A
a e B A B B A
[Step #4] Selected: [2] LEFT A B --> a B
a e B a B B A
[Step #5] Selected: [4] LEFT B B A --> e B A
a e B a e B A
[Step #6] Selected: [3] LEFT B A --> B b
a e B a e B b
[Step #7] Selected: gram#2[2] LEFT e B --> e e
a e e a e B b
[Step #8] Selected: gram#2[2] LEFT e B --> e e

Result:  a e e a e e b

This is sim­i­lar to SUB1, except that rewrit­ings only occur in the posi­tions of the longest sub­strings matched by a rule.