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Towards Merging PlatΩ and PGIP
David Aspinall1
Christoph Lüth2
1 University
2 DFKI
3 Saarland
Serge Autexier2
Marc Wagner2,3
of Edinburgh, Scotland
Bremen, Germany
University, Saarbrücken, Germany
8th International Workshop
User Interfaces for Theorem Provers
Montréal, Canada
22. August 2008
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
PGKIT Architecture
Prover Components
Prover 1
IP D
PG
PGI
P
P
Broker
Prover 2
Display Components
Middleware
PP
PGI
PGIPD
PG
IP
D
Graphical User
Interface
Text Editor
Eclipse
File System Theory Store
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
PGKIT Architecture
◮
ACL2, Isabelle, HOL, Lambda-Clam, Lego,
Plastic, Phox, . . .
◮
ASCII Files (Input-only)
◮
Specific parsers
◮
Command-Line oriented
◮
Single focus
◮
Display of proof state
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
PlatΩ Architecture
Prover Components
Prover
PLATOP
Middleware
PLATOD
PlatΩ
OMDoc
Display Components
PL
TEXmacs
URI to Theories in
Text-Editor
Document Format
or OMDoc
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
PlatΩ Architecture
◮
Writing TEXmacs documents assisted by
Ωmega
◮
Ωmega: OMDoc Input/Output
◮
TEXmacs: Specific, flexible proof document
style (PL)
◮
Multiple foci
◮
Bidirectional: proof steps done by the prover
are propagated into the TEXmacs document
◮
XUPDATE/XMLDIFF based
◮
On the fly conversions between OMDoc
and PL
◮
Contect-sensitive menus for assistance
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Comparision
Document format
Document syntax
Change protocol
Operations
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
PlatΩ Display
XML
TEXmacs
XUpdate
Contextdependent
menus
PG Kit Display
Plain text
ASCII
PGIPD
Global menus,
typed
operations
PGIP 2 Display
XML
Generic
XUpdate
Context-dependent
menus, typed
operations
German Research Center
for Artificial Intelligence
Comparision
Document format
Document syntax
PlatΩ Prover
XML
OMDoc
Change protocol
Prover support
XUpdate
Ωmega
Operations
Contextdependent
menus
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
PG Kit Prover
Plain text
Native prover
syntax
PGIPP
Generic (Coq,
Isabelle, etc)
Global menus,
typed
operations
PGIP 2 Prover
XML
Generic
XUpdate
Generic (Coq,
Isabelle, Ωmega,
etc)
Context-dependent
menus, typed
operations
German Research Center
for Artificial Intelligence
Overview of Extensions for PGIP 2
1
Support for Semi Structured Documents
Multiple Foci
XUpdate/Semantic XMLDiff
Protocols
2
Context-Sensitive Service Menus
3
Multiple Editing Displays in Parallel
4
Mutiple Document Formats
Working hypothesis: Do not require any change for current
displays/provers when using the new PGIP 2
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
1
Support for Semi Structured Documents
Multiple Foci
XUpdate/Semantic XMLDiff
Protocols
2
Context-Sensitive Service Menus
3
Multiple Editing Displays in Parallel
4
Mutiple Document Formats
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Unstructured Documents
theory NN
imports Main
begin
text {∗ The datatype of natural numbers\footnote{Not
the real ones!}. ∗}
datatype N = Z | S N
text{∗ Induction is a derived concept: @{thm N.induct}
∗}
add (infixr ”+” 65)
text{∗ We first need two lemmas. ∗}
lemma add Z r: ”x + Z= x”
by (induct x, simp+)
lemma add S: ”S (x+ y)= x+ (S y)”
by (induct x, simp+)
text{∗ Now we can prove commutativity. ∗}
text{∗ We define addition via recursive
equations, and declare its usual syntax. ∗}
fun ”add” :: ”N \<Rightarrow> N \<Rightarrow> N”
where
”add Z x = x”
| ”add (S x) y= S (add x y)”
theorem add commute: ”x+ y= y+ (x::N)”
proof (induct x rule: N.induct)
case Z thus ?case by (simp add: add Z r)
case S thus ?case by (simp add: add S)
qed
end
notation
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Unstructured Documents
Display
User requests
file to be loaded.
Prover
Broker
<loadparsefile>
<parsescript>
<parseresult>
<newcmd>
.
.
.
<newcmd>
Users edits
a text region.
Broker creates new
prover commands.
<editcmd>
<parsescript>
<parseresult>
Old text is
deleted,
<delcmd>
edited text is
inserted.
<newcmd>
User request
command to
be processed.
Text is successfully
parsed.
Text is successfully
parsed.
.
.
.
<setcmdstatus>
prover command
<ready>
<cmdstatus>
.
.
.
<cmdstatus>
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
prover command
.
.
.
Several prover
commands are
successfully
executed.
<ready>
German Research Center
for Artificial Intelligence
Unstructured Documents
<pgip tag = ”Isabelle/Isar” id = ”hume/cxl/27572/1208530140 .785”
destid =
”broker:hume/2658/27571/2008318−144859− Z” class = ”pg” refid =
”broker:hume/2658/27571/2008318−144859− Z” refseq = ”18” seq =
”24”><parseresult>
<opentheory/>
<openblock/>
<theoryitem/>
<opentheory thyname = ”NN” parentnames = ”Main”>theory NN
imports Main
begin</opentheory><openblock objtype = ”theory body”/>
<theoryitem objtype = ”theory declaration”>text {∗ The datatype of
natural numbers\footnote{Not the real ones!}. ∗}</theoryitem
>
<theoryitem objtype = ”theory declaration”>datatype N = Z | S N</
theoryitem>
<theoryitem objtype = ”theory declaration”>text{∗ Induction is a
derived concept: @{thm N.induct} ∗}</theoryitem>
<theoryitem objtype = ”theory declaration”>text{∗ We define addition
via recursive equations,
and declare its syntax as the usual infix operator. ∗}</theoryitem>
<opengoal/>
<openblock/>
<pgip>
<proofstep/>
<closeblock/>
<closegoal/>
<closeblock/>
<closetheory/>
<theoryitem objtype = ”theory declaration”>fun &quot;add&quot; :: &
quot;N \&lt;Rightarrow&gt; N \&lt;Rightarrow&gt; N&quot;
where
&quot;add Z x = x&quot;
| &quot;add (S x) y= S (add x y)&quot;</theoryitem>
Towards
Mergingobjtype
PlatΩ =
and”theory
PGIPdeclaration”>notation
<theoryitem
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Semi Structured Documents
<pgip tag = ”Isabelle/Isar” id = ”hume/cxl/27572/1208530140 .785”
destid =
”broker:hume/2658/27571/2008318−144859− Z” class = ”pg” refid =
”broker:hume/2658/27571/2008318−144859− Z” refseq = ”18” seq =
”24”>
<parseresult>
<document>
<theory thyname=”NN” parentnames=”Main”>theory NN
imports Main
begin
<block objtype=”theory body”>
<theoryitem>text {∗ The datatype of natural numbers\footnote{Not
the real ones!}. ∗}</theoryitem>
<theoryitem type=”adt”>datatype N = Z | S N</theoryitem>
<theoryitem>text{∗ Induction is a derived concept: @{thm N.induct}
∗}</theoryitem>
<theoryitem>text{∗ We define addition via recursive equations,
and declare its syntax as the usual infix operator. ∗}</theoryitem>
<theoryitem objtype=”fundef”>fun &quot;add&quot; :: &quot;N \&lt;
Rightarrow&gt; N \&lt;Rightarrow&gt; N&quot;
where
&quot;add Z x = x&quot;
| &quot;add (S x) y= S (add x y)&quot;</theoryitem>
<theoryitem objtype=”notation”>notation
Towards
PlatΩ and PGIP
addMerging
(infixr &quot;+&quot;
65)</theoryitem>
Aspinall, Autexier, Lüth, Wagner
<pgip>
<document>
<theory>
<block>
<theoryitem/>
<assertion>
<block>
<proofstep/>
<endproof/>
German Research Center
for Artificial Intelligence
Supporting Semi Structured
Documents
◮
New internal PGIP markup (PGML), tree compatible
◮
◮
Use xml:id to flexibilise document structure
Example: theorems and proofs need not occur together physically
Rigid structure computed by the broker for the prover
◮
Provide on-the-fly converters between old and new markup
⇒ provers need not be adapted
◮
Configuration
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Single Focus
Top Level
CloseFile
OpenFile
File Open
OpenTheory
CloseTheory
Theory Open
Closeproof
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OpenProof
Proof Open
German Research Center
for Artificial Intelligence
Single Focus
Top Level
CloseFile
OpenFile
File Open
OpenTheory
CloseTheory
Theory Open
Closeproof
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OpenProof
Proof Open
German Research Center
for Artificial Intelligence
Single Focus
Top Level
CloseFile
OpenFile
File Open
OpenTheory
CloseTheory
Theory Open
Closeproof
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OpenProof
Proof Open
German Research Center
for Artificial Intelligence
Single Focus
Top Level
CloseFile
OpenFile
File Open
OpenTheory
CloseTheory
Theory Open
Closeproof
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OpenProof
Proof Open
German Research Center
for Artificial Intelligence
Single Focus
Top Level
CloseFile
OpenFile
File Open
OpenTheory
CloseTheory
Theory Open
Closeproof
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OpenProof
Proof Open
German Research Center
for Artificial Intelligence
Multiple Foci
<pgip>
Top Level
CloseFile
OpenFile
<document>
File Open
CloseTheory 2
<theory>
OpenTheory 1
OpenTheory
CloseTheory21
<block>
Theory 2 Open
Closeproof T3
OpenProof T3
Proof T3 Open
Theory 1 Open
Closeproof T2
CloseproofOpenProof
T1
T2
Proof T2 Open
OpenProof T1
<theoryitem/>
<assertion>
Proof T1 Open
<block>
<proofstep/>
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
<endproof/>
Supporting Semi Structured
Documents
◮
New internal PGIP markup, tree compatible
◮
Provide on-the-fly converters between old and new markup
⇒ provers need not be adapted
◮
Configuration
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
XUpdates
Old PGIPD protocol (asymmetric):
◮
◮
Display → Broker: <createcmd>,
<editcmd>
Broker → Display: <newcmd>,
<delcmd>, <replacecmd>
New PGIPD protocol:
◮
Rephrase in terms of
Xupdate-modifications
<insert-after>,
<insert-before>, <remove>
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
Display
User requests
file to be loaded.
Broker
<loadparsefile>
<parsescript>
<parseresult>
<newcmd>
.
.
.
<newcmd>
Users edits
a text region.
<editcmd>
Old text is
deleted,
<delcmd>
edited text is
inserted.
<newcmd>
Broker creates new
prover commands.
<parsescript>
<parseresult>
User request
command to
be processed.
.
.
.
<setcmdstatus>
prover command
<ready>
<cmdstatus>
.
.
.
<cmdstatus>
German Research Center
for Artificial Intelligence
prover command
<ready>
.
.
.
Compatibility
◮
XUPDATEs cannot be generated by all displays or provers
◮
Allow components to send only new document version and compute
differences inside the broker
Use semantic XMLDIFF tool inside the broker
◮
◮
◮
◮
◮
Normal tree diff
Configurable to take some “semantics” into account
Configurable level of granularity for modifications
Configuration if component can handle XUPDATES
Broker generates appropriate representation for each component
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Protocol between Prover and Broker
◮
<parsescript> and <parseresult>
◮
Prover commands in native prover
command syntax
◮
prover answers <normalresponse>,
<errorresponse>, <ready>
Unchanged, but contextualized (multiple
foci)
Extension:
◮
<normalresponse> can contain
XUPDATES for document which are
relayed to the display
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Protocols between Display with
Broker
In addition to PGIPD provide
◮
XML-RPC interface and
◮
HTTP in plain REST architecture
HTTP Request
/initsession
/session1/initdocument?CONTENT
/session1/document/1
/session1/document/HEAD
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
HTTP answer
path to new session (/session1)
HTML rendered document after parsing
version 1 of the document
the current version of the document
German Research Center
for Artificial Intelligence
1
Support for Semi Structured Documents
Multiple Foci
XUpdate/Semantic XMLDiff
Protocols
2
Context-Sensitive Service Menus
3
Multiple Editing Displays in Parallel
4
Mutiple Document Formats
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Service Menus
◮
Allow requests of service menus for arbitrary elements in the display
◮
Requests relayed by the broker to the prover
Prover returns menu description (PGML menu format)
◮
◮
◮
Menus contain descriptions and actions
Actions can be
◮
◮
◮
◮
tactic calls (traditional)
requests for axiom/lemma applications (PlatΩ/TEXmacs)
Computing the complete menus is expensive, most of the menu is
discarded
Support lazy menu computation
◮
Menu entries trigger computations which results are modifications of the
menu
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
1
Support for Semi Structured Documents
Multiple Foci
XUpdate/Semantic XMLDiff
Protocols
2
Context-Sensitive Service Menus
3
Multiple Editing Displays in Parallel
4
Mutiple Document Formats
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Multiple Editing Displays
RichTotalOrder
Display Components
Middleware
inst−118
ExtTotalOrder
basic−88
Prover 1
IP D
PG
PGI
P
P
Graphical User
Interface
inst−92
union−63
inst−59
inst−69
Prover 2
PP
PGI
PGIPD
PG
IP
D
inst−57
inst−67
inst−84
Rat
union−61
union−56
union−66
union−83
basic−12
TotalOrder
inst−11
inst−54
union−10
union−53
inst−115
ExtPartialOrder
basic−78
union−86
union−117
inst−81
inst−77
union−75
inst−112
inst−74
union−90
union−76
Int
inst−109
union−73
union−114
union−108
PartialOrder
basic−7
inst−51
inst−6
union−50
union−5
union−58
EquivalenceRelation
union−48
inst−45
union−44
union−30
TransitiveRelation
union−46
inst−31
union−37
union−27
ReflexiveRelation
inst−38
union−32
inst−121
union−35
PartialEquivalenceRelation
inst−47
RichBooleanAlgebra
inst−36
PreOrder
Nat
basic−2
inst−28
union−25
SymmetricRelation
inst−33
inst−26
inst−17
inst−20
basic−42
union−16
union−19
union−41
Eclipse
German Research Center
for Artificial Intelligence
basic−103
inst−102
basic−101
basic−40
basic−100
inst−99
SigOrder
inst−23
Text Editor
inst−111
ExtBooleanAlgebra
SimilarityRelation
basic−80
union−22
File System Theory Store
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
inst−91
union−85
inst−62
Relation
Broker
RichPartialOrder
inst−87
inst−64
union−68
daVinci V2.1
Prover Components
union−97
inst−96
union−120
union−95
inst−107
union−98
BooleanAlgebra
union−110
un
Multiple Editing Displays
RichTotalOrder
Display Components
Middleware
inst−118
ExtTotalOrder
basic−88
Prover 1
IP D
PG
PGI
P
P
Graphical User
Interface
inst−92
union−63
inst−59
inst−69
Prover 2
PP
PGI
PGIPD
PG
IP
D
inst−57
inst−67
inst−84
Rat
union−61
union−56
union−66
union−83
basic−12
TotalOrder
inst−11
inst−54
union−10
union−53
inst−115
ExtPartialOrder
basic−78
union−86
union−117
inst−81
inst−77
union−75
inst−112
inst−74
union−90
union−76
Int
inst−109
union−73
union−114
union−108
PartialOrder
basic−7
inst−51
inst−6
union−50
union−5
union−58
EquivalenceRelation
union−48
inst−45
union−44
union−30
TransitiveRelation
union−46
inst−31
union−37
union−27
ReflexiveRelation
inst−38
union−32
inst−121
union−35
PartialEquivalenceRelation
inst−47
RichBooleanAlgebra
inst−36
PreOrder
Nat
basic−2
inst−28
union−25
SymmetricRelation
inst−33
inst−26
inst−17
inst−20
basic−42
union−16
union−19
union−41
Eclipse
Requires Synchronisation by the Broker
German Research Center
for Artificial Intelligence
basic−103
inst−102
basic−101
basic−40
basic−100
inst−99
SigOrder
inst−23
Text Editor
inst−111
ExtBooleanAlgebra
SimilarityRelation
basic−80
union−22
File System Theory Store
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
inst−91
union−85
inst−62
Relation
Broker
RichPartialOrder
inst−87
inst−64
union−68
daVinci V2.1
Prover Components
union−97
inst−96
union−120
union−95
inst−107
union−98
BooleanAlgebra
union−110
un
Multiple Displays
◮
◮
◮
◮
Simple kind of
version control
inside the broker
Broker stores for
each display the
latest version
communicated
Broker
Display #1
Rev. 47
User changes
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
Rev. 47
Display #2
Latest rev,
Display #2
Head
Rev. 47
Rev. 47
Rev. 47
commit
User changes
Rev. 47’
Uses semantic
XMLMerge (diff3)
Conflicts are
marked in special
markup extending
XUpdate markup.
Latest rev,
Display #1
Rev. 47
Rev. 47’
Rev. 48
New head
!
new revision
ack.
Rev. 48
CT
LI
F
ON
C
Rev. 48
Rev. 48
Rev. 47’’
Conflict resolved
Rev. 47’’
new revision
new revision
ack.
Rev. 49
commit
ack.
Rev. 49
Rev. 49
Rev. 49
Rev. 49
German Research Center
for Artificial Intelligence
1
Support for Semi Structured Documents
Multiple Foci
XUpdate/Semantic XMLDiff
Protocols
2
Context-Sensitive Service Menus
3
Multiple Editing Displays in Parallel
4
Mutiple Document Formats
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Multiple Document Formats
◮
Have: Display D communicates in format A
◮
Have: Prover P communicates in format B
◮
Wanted: Use display D with prover P
TEXmacs
PL
PL ⇋ OMDoc
For instance:
◮
◮
OMDoc
PlatΩ connects TEXmacs with format PL to Ωmega
with format OMDoc
Broker
Now want to use TEXmacs with Isabelle (Isar)
OMDoc
Isar ⇋ OMDoc
Isar
Prover
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Multiple Document Formats
◮
Have: Display D communicates in format A
◮
Have: Prover P communicates in format B
◮
Wanted: Use display D with prover P
TEXmacs
PL
PL ⇋ OMDoc
For instance:
◮
OMDoc
PlatΩ connects TEXmacs with format PL to Ωmega
with format OMDoc
Now want to use TEXmacs with Isabelle (Isar)
Provide autonomous converters from PL to OMDoc and
OMDoc and Isar
Broker
◮
◮
Bidirectional
◮
Conversion of Xupdates
◮
Maintain mappings to relay service requests
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
OMDoc
Isar ⇋ OMDoc
Isar
Prover
German Research Center
for Artificial Intelligence
Related Work
◮
Semi-structured input documents
MathsTiles (structured input to multiple domain reasoners,
unidirectional)
◮
Multiple foci
Ωmega (status management added), Isabelle (multi-foci under the
way)
◮
Multiple displays
Matita (proof script,goal display), LΩui, GeoProof/ Coq
◮
Support modifications to the document from the prover:
Matita (tinycals)
Could be realised by the generic functionality proposed here?
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence
Next Steps
◮
Implementation (any feedback/remarks welcome before we start. . . )
◮
Implement PlatΩ functionality on PGIP 2 basis
◮
Connect other editing displays (Word 2007, OpenOffice, Netbeans)
◮
Multiple foci, changes from prover could serve interaction styles in
other provers (Agda, Mizar, PVS)
Towards Merging PlatΩ and PGIP
Aspinall, Autexier, Lüth, Wagner
German Research Center
for Artificial Intelligence