ABNF in ACL2 Alessandro Coglio Kestrel Institute Workshop 2017.

ABNF in ACL2 Alessandro Coglio Kestrel Institute Workshop 2017

ABNF in ACL2

A B N F

Augmented Backus-Naur Form

Augmented Backus-Naur Form is a formal context-free grammar notation that adds conveniences and makes slight modifications to Backus-Naur Form.

Augmented Backus-Naur Form is a formal context-free grammar notation that adds conveniences and makes slight modifications to Backus-Naur Form, e.g.: numeric range terminal notations case-insensitive string terminal notations DIGIT = %x30-39 HEXDIG = DIGIT / "A" / "B" / "C" / "D" / "E" / "F" h16 = 1*4HEXDIG repetition prefixes, min. (default 0) to max. (default ∞) message-body = *OCTET RWS = 1*( SP / HTAB )

Augmented Backus-Naur Form

A B N F

ABNF is specified by two RFCs (i.e. Internet standards).

ABNF specif RFCs

The RFCs use natural language to informally specify ABNF.

specifies ABNF language

ABNF language informally specifies

specifies ABNF language

specifies ABNF language syntax semantics

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies ABNF language syntax semantics

And they use ABNF to formally specify the syntax of ABNF. formally specif natural language informally specifies ABNF language syntax semantics

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies semantics syntax formally ABNF language How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification? ACL2

ACL2 The RFCs use natural language to informally specify ABNF.
And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics ACL2 How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

? The RFCs use natural language to informally specify ABNF.
And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics ? How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ? syntax ABNF language semantics How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax semantics ? How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language semantics syn tax ? How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language syntax syntax semantics ? How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

And they use ABNF to formally specify the syntax of ABNF. natural language informally specifies formally specifies ABNF language concrete syntax abstract syntax semantics ? How to formally specify ABNF in ACL2, faithfully to the RFCs, including the meta-circular formal syntax specification?

abstract syntax

Formalize an abstract syntax

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF.

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ...

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ...

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = concatenation *(*c-wsp "/" *c-wsp concatenation)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = concatenation * concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = * concatenation concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = concatenation *concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = *concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... alternation = * concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... = * alternation concatenation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... concatenation repetition (fty::deflist alternation :elt-type concatenation)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) concatenation repetition)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... repetition repeat element (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) repetition repeat element

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element)))

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... element rulename rulename group group alternation (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element)))

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element))) element rulename rulename group alternation

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element))) (fty::deftagsum element (:rulename ((get rulename))) (:group ((get alternation))) ...)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element))) (fty::deftagsum element (:rulename ((get rulename))) (:group ((get alternation))) ...)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element))) (fty::deftagsum element (:rulename ((get rulename))) (:group ((get alternation))) ...) ...

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.: alternation = concatenation *(*c-wsp "/" *c-wsp concatenation) concatenation = repetition *(1*c-wsp repetition) repetition = [repeat] element element = rulename / group / ... group = "(" *c-wsp alternation *c-wsp ")" ... (fty::deftypes alt/conc/rep/elem (fty::deflist alternation :elt-type concatenation) (fty::deflist concatenation :elt-type repetition) (fty::defprod repetition ((range repeat-range) (element element))) (fty::deftagsum element (:rulename ((get rulename))) (:group ((get alternation))) ...)

Formalize an abstract syntax of ABNF in ACL2, based on the ABNF grammar rules that define the concrete syntax of ABNF, e.g.:

ABNF ABNF grammar

The start nonterminal of the ABNF grammar of ABNF is rulelist.

rulelist = 1*( rule / (*c-wsp c-nl) )

rulelist = 1*( rule / (*c-wsp c-nl) ) In the abstract syntax, an ABNF grammar is a value of type rulelist.

rulelist = 1*( rule / (*c-wsp c-nl) ) rule In the abstract syntax, an ABNF grammar is a value of type rulelist.

rulelist = 1*( rule / (*c-wsp c-nl) ) In the abstract syntax, an ABNF grammar is a value of type rulelist. rulelist rule

rulelist = 1*( rule / (*c-wsp c-nl) ) In the abstract syntax, an ABNF grammar is a value of type rulelist. (fty::deflist rulelist :elt-type rule)

rulelist = 1*( rule / (*c-wsp c-nl) ) In the abstract syntax, an ABNF grammar is a value of type rulelist. value (fty::deflist rulelist :elt-type rule)

rulelist = 1*( rule / (*c-wsp c-nl) ) In the abstract syntax, an ABNF grammar is a value of type rulelist. (fty::deflist rulelist :elt-type rule) These values (grammars) can be operated upon in the ACL2 logic, e.g. to check their well-formedness and to compose them.

In the abstract syntax, an ABNF grammar is a value of type rulelist.

abstract syntax

natural language ABNF language concrete syntax abstract syntax
informally specifies formally specifies ABNF language concrete syntax abstract syntax semantics formally specifies

semantics

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities.

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" *y %d17.80

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y %d17.80

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y %d17.80

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" %d17.80 y y y

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y %d17.80

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" %d1-4 y y y (17 80)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) %d1-4

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" %d1-4 y y y (17 80) (2)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) %d1-4

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) (4)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" z z y y y (17 80) (2) (4)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" "a" y y y (17 80) (2) z z (4)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" "a" y y y (17 80) (2) z z (4) (65)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65) "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65) (97)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: match parse tree a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65) (97)

a parse tree that matches x
Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65) (97) a parse tree that matches x

a parse tree that matches x
Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: a grammar x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) branches are organized into lists (for concatenations) of lists (for repetitions) (2) z z (4) a parse tree that matches x (65) (97)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x x = *y %d17.80 y = 2z / %d1-4 z = "a" y y y (17 80) (2) z z (4) (65) (97) branches are organized into lists (for concatenations) of lists (for repetitions)

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a" branches lists lists

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x y (17 80) (2) (4) z (65) (97) branches lists lists

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x y (17 80) (2) (4) z (65) (97) branches tree-list-list

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x y (17 80) (2) (4) z (65) (97) type of parse trees (fty::deftypes trees (fty::deftagsum tree (:leafterm ((get nat-list))) (:leafrule ((get rulename))) (:nonleaf ((rulename? maybe-rulename) (branches tree-list-list)))) (fty::deflist tree-list :elt-type tree) (fty::deflist tree-list-list :elt-type tree-list))

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x (tree-match-element-p tree element rules) x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: matching relation x (tree-match-element-p tree element rules) x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x (tree-match-element-p tree element rules) matching relation x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a"

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x matching relation (tree-match-element-p tree element rules) x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a" 17 80 2 4 65 97

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x matching relation (tree-match-element-p tree element rules) x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a"

string at the leaves of the tree
Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.: x matching relation (tree-match-element-p tree element rules) x y (17 80) (2) (4) z (65) (97) x = *y %d17.80 y = 2z / %d1-4 z = "a" string at the leaves of the tree (equal (tree->string tree) string) ( )

Formalize a semantics of ABNF in terms of matching relations between parse trees and (abstract) syntactic entities, e.g.:

semantics

concrete syntax

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity.

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.: num-val = "%" (bin-val / dec-val / hex-val) group = "(" *c-wsp alternation *c-wsp ")"

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.: num-val = "%" (bin-val / dec-val / hex-val) num-val "%" bin-val / dec-val / hex-val group = "(" *c-wsp alternation *c-wsp ")"

specially crafted and named functions and macros
Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.: num-val = "%" (bin-val / dec-val / hex-val) (def-rule-const *num-val* (/_ "%" (!_ (/_ *bin-val*) (/_ *dec-val*) (/_ *hex-val*)))) specially crafted and named functions and macros group = "(" *c-wsp alternation *c-wsp ")"

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.: num-val = "%" (bin-val / dec-val / hex-val) (def-rule-const *num-val* (/_ "%" (!_ (/_ *bin-val*) (/_ *dec-val*) (/_ *hex-val*)))) specially crafted and named functions and macros group = "(" *c-wsp alternation *c-wsp ")" group "(" * c-wsp alternation * c-wsp ")"

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.: num-val = "%" (bin-val / dec-val / hex-val) (def-rule-const *num-val* (/_ "%" (!_ (/_ *bin-val*) (/_ *dec-val*) (/_ *hex-val*)))) specially crafted and named functions and macros group = "(" *c-wsp alternation *c-wsp ")" (def-rule-const *group* (/_ "(" (*_ *c-wsp*) *alternation* (*_ *c-wsp*) ")"))

Formalize the concrete syntax of ABNF by transcribing the ABNF grammar rules of ABNF “in abstract syntax”, thus breaking the meta-circularity, e.g.:

concrete abstract syntax

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities.

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48)

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) 42 49 50 48

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) 49 42 50 48

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) "1" "*" "2" "0"

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) 1 * 2

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) *

abstraction function for repetition ranges
Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: repeat () (42) DIGIT (49) (50) (48) (:REPEAT 1 (:FINITE 20)) abstraction function for repetition ranges (equal (abstract-repeat tree) range)

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: rulelist rule ...

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: rulelist rule ... rule rule rule ... ... ... ...

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: rulelist rule ... rule ... ...

abstraction function for lists of rules
Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.: rulelist rule ... ((:RULE ...) (:RULE ...) ...) abstraction function for lists of rules (equal (abstract-rulelist tree) rules)

Formalize the relationship between concrete and abstract syntax via abstraction functions from parse trees of ABNF grammars to corresponding abstract syntactic entities, e.g.:

concrete syntax

ABNF language concrete syntax abstract syntax semantics
formally specifies

ABNF language formally specifies

ABNF language ABNF formally specifies

ABNF is used in several Internet syntax specifications, e.g. HTTP.
ABNF language formally specifies

HTTP syntax ABNF language formally specifies

HTTP syntax formally specifies ABNF language formally specifies

syntax HTTP HTTP syntax ABNF language formally specifies

How to formally specify the HTTP syntax in ACL2, faithfully to the RFC?
formally specifies ABNF language formally specifies

ABNF grammar rules of HTTP

Transcribe the ABNF grammar rules of HTTP in abstract (ABNF) syntax, as done with the ABNF grammar rules of ABNF?

Transcribe Transcribe the ABNF grammar rules of HTTP in abstract (ABNF) syntax, as done with the ABNF grammar rules of ABNF?

Transcribe the ABNF grammar rules of HTTP in abstract (ABNF) syntax, as done with the ABNF grammar rules of ABNF? transcribe T

Transcribe the ABNF grammar rules of HTTP in abstract (ABNF) syntax, as done with the ABNF grammar rules of ABNF? a constant of type rulelist, representing an ABNF grammar, which has semantics in ACL2 *http-grammar* transcribe tedious and error-prone

*http-grammar*

Write and use a verified parser of ABNF grammars.
How to formally specify the HTTP syntax in ACL2, faithfully to the RFC? Write and use a verified parser of ABNF grammars. grammar text file *http-grammar* copy & paste

Write and use a verified parser of ABNF grammars. verified parser ABNF
How to formally specify the HTTP syntax in ACL2, faithfully to the RFC? Write and use a verified parser of ABNF grammars. verified parser ABNF grammar grammar text file *http-grammar* copy & paste

Write and use a verified parser of ABNF grammars.
How to formally specify the HTTP syntax in ACL2, faithfully to the RFC? Write and use a verified parser of ABNF grammars. parse tree of the ABNF grammar of HTTP grammar text file rulelist ... *http-grammar* copy & paste top-level syntax abstraction function parse-grammar-from-file abstract-rulelist verified ABNF grammar parser

verified ABNF grammar parser

verified ABNF grammar parser

The verified ABNF grammar parser consists of 85 functions.

The ABNF grammar of ABNF is mostly LL(1), with three LL(2) rules, two LL(*) rules, and one (non-critically) ambiguous rule. The parser is implemented as recursive descent with backtracking, using the Seq macros from the Community Books. The parser correctness proof consists of soundness and completeness. Soundness: if the parser succeeds, the output parse tree matches rulelist and its tree->string is the input string. Completeness: running the parser on the tree->string of a parse tree that matches rulelist and that (necessarily) satisfies certain disambiguating restrictions, succeeds and yields that parse tree. move ABNF grammar parser to next slide The correctness proof consists of 424 theorems, organized into several inter-dependent categories. Completeness is much more laborious to prove than soundness. These proof techniques should be more generally applicable.

ABNF grammar parser

The ABNF grammar parser can be run on the ABNF grammar of ABNF.

parse-grammar-from-file
The ABNF grammar parser can be run on the ABNF grammar of ABNF. The ABNF grammar parser can be run on the ABNF grammar of ABNF. *http-grammar* copy & paste rulelist ... abstract-rulelist parse-grammar-from-file HTTP RFC

The ABNF grammar parser can be run on the ABNF grammar of ABNF. The ABNF grammar parser can be run on the ABNF grammar of ABNF. HTTP RFC rulelist ... *http-grammar* copy & paste parse-grammar-from-file abstract-rulelist

The ABNF grammar parser can be run on the ABNF grammar of ABNF. The ABNF grammar parser can be run on the ABNF grammar of ABNF. ABNFRFCs rulelist ... *abnf-grammar* copy & paste parse-grammar-from-file abstract-rulelist

trascription in the formalization of the ABNF concrete syntax rulelist ... *abnf-grammar* copy & paste parse-grammar-from-file abstract-rulelist

trascription in the formalization of the ABNF concrete syntax formalization ABNF concrete syntax rulelist ... *abnf-grammar* copy & paste parse-grammar-from-file abstract-rulelist

This provides a validation of the ABNF concrete syntax formalization. trascription in the formalization of the ABNF concrete syntax rulelist ... *abnf-grammar* copy & paste parse-grammar-from-file abstract-rulelist

For more information: “ABNF in ACL2”, Technical Report (

For more information:

For much more information:

For much more information:
‘ABNF’ topic in the ACL2+Books manual

ABNF in ACL2 Alessandro Coglio Kestrel Institute Workshop 2017.

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ABNF in ACL2 Alessandro Coglio Kestrel Institute Workshop 2017.

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Presentation on theme: "ABNF in ACL2 Alessandro Coglio Kestrel Institute Workshop 2017."— Presentation transcript:

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