Term Rewriting with Traversal Functions
Thionville
1
Term Rewriting with Traversal Functions Mark van den Brand Paul Klint Jurgen Vinju April 18th, 2001
CWI
Amsterdam
Thionville
2
Overview • Term Rewriting Problems • Solutions • Traversal functions • Limitations • Conclusion & Questions
CWI
Amsterdam
Thionville
3
Term Rewriting Problems
CWI
Amsterdam
Thionville
3-a
Term Rewriting Problems • Term rewriting is expressive, but...
CWI
Amsterdam
Thionville
3-b
Term Rewriting Problems • Term rewriting is expressive, but... • Term traversal is implicit (e.g. innermost) only sort preserving transformations no extra arguments (i.e. context) fixed path
CWI
Amsterdam
Thionville
3-c
Term Rewriting Problems • Term rewriting is expressive, but... • Term traversal is implicit (e.g. innermost) only sort preserving transformations no extra arguments (i.e. context) fixed path • Confluence non-trivial trs’s are not confluent
CWI
Amsterdam
Thionville
4
Solutions
CWI
Amsterdam
Thionville
4-a
Solutions • Encode strategies using functional style
CWI
ASF+SDF
Amsterdam
Thionville
4-b
Solutions • Encode strategies using functional style • Strategy primitives
CWI
ASF+SDF ELAN
Amsterdam
Thionville
4-c
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
CWI
ASF+SDF ELAN Stratego
Amsterdam
Thionville
4-d
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But:
CWI
Amsterdam
Thionville
4-e
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems
CWI
Amsterdam
Thionville
4-f
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal
CWI
Amsterdam
Thionville
4-g
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed
CWI
Amsterdam
Thionville
4-h
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed Strategic Programming is another paradigm
CWI
Amsterdam
Thionville
4-i
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed Strategic Programming is another paradigm • Traversal functions! less powerful fully typed simple CWI
Amsterdam
Thionville
5
Traversal functions
CWI
Amsterdam
Thionville
5-a
Traversal functions • Characteristics:
CWI
Amsterdam
Thionville
5-b
Traversal functions • Characteristics: typed prefix functions
CWI
Amsterdam
Thionville
5-c
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both
CWI
Amsterdam
Thionville
5-d
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop)
CWI
Amsterdam
Thionville
5-e
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation
CWI
Amsterdam
Thionville
5-f
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are:
CWI
Amsterdam
Thionville
5-g
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are: What can we do with them?
CWI
Amsterdam
Thionville
5-h
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are: What can we do with them? What can we not do with them?
CWI
Amsterdam
Thionville
6
PICO module Pico-syntax imports Pico-Identifiers Pico-Integers Pico-Strings Types exports sorts PROGRAM context-free syntax "begin" DECLS {STATEMENT ";"}* "end" -> PROGRAM "declare" {ID-TYPE ","}* ";" -> DECLS PICO-ID ":" TYPE -> ID-TYPE PICO-ID ":=" EXP -> STATEMENT "if" EXP "then" {STATEMENT ";"}* "else" {STATEMENT ";"}* "fi" -> STATEMENT "while" EXP "do" {STATEMENT ";"}* "od" -> STATEMENT PICO-ID -> EXP PICO-NAT-CON -> EXP PICO-STR-CON -> EXP EXP "+" EXP -> EXP {left} EXP "-" EXP -> EXP {left} EXP "*" EXP -> EXP {left}
Figure 1:
CWI
Amsterdam
Thionville
7
Transformer module Pico-Replace imports Pico-syntax exports context-free syntax replace(PROGRAM,ID,ID) -> PROGRAM {traversal(trafo)} equations [] replace(Id1,Id1,Id2) = Id2 Figure 2:
CWI
Amsterdam
Thionville
8
Transformer (cont’d) replace( begin declare input : natural, output : natural; input := 12; output := 1; while input - 1 do output := output * 2; input := input - 1 od end, input, INPUT) Figure 3: CWI
Amsterdam
Thionville
9
Transformer (cont’d) begin declare INPUT : natural, output : natural; INPUT := 12; output := 1; while INPUT - 1 do output := output * 2; INPUT := INPUT - 1 od end Figure 4:
CWI
Amsterdam
Thionville
10
Accumulator module Pico-Count imports Pico-syntax exports context-free syntax count(PROGRAM,NAT) -> NAT {traversal(accu)} equations [] count(Id,Nat) = suc(Nat) Figure 5:
CWI
Amsterdam
Thionville
11
Accumulating Transformer module Pico-ReplaceCount imports Pico-syntax exports context-free syntax replacecount(PROGRAM,NAT,ID,ID) -> PROGRAM # NAT {traversal(accu,trafo)} equations [] replacecount(Id1,Nat,Id1,Id2) = (Id2,suc(Nat)) Figure 6:
CWI
Amsterdam
Thionville
12
Experience • COBOL transformations • CASL transformations • SDF tools: typechecker, statistics • New DSL: Framework for SDF Transformation (FST)
CWI
Amsterdam
Thionville
12-a
Experience • COBOL transformations • CASL transformations • SDF tools: typechecker, statistics • New DSL: Framework for SDF Transformation (FST) • Significant reduction in number of rules • Interpreter efficient enough
CWI
Amsterdam
Thionville
13
Limitations
CWI
Amsterdam
Thionville
13-a
Limitations 1. Types: no arbitrary non-sort-preserving traversals
CWI
Amsterdam
Thionville
13-b
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees
CWI
Amsterdam
Thionville
13-c
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules
CWI
Amsterdam
Thionville
13-d
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes
CWI
Amsterdam
Thionville
13-e
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes 2. Use conditions and default rules to guide the path
CWI
Amsterdam
Thionville
13-f
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes 2. Use conditions and default rules to guide the path 3. Still encode strategies using functions
CWI
Amsterdam
Thionville
14
Conclusions
CWI
Amsterdam
Thionville
14-a
Conclusions • Automated tree traversal
CWI
Amsterdam
Thionville
14-b
Conclusions • Automated tree traversal • Statically typed
CWI
Amsterdam
Thionville
14-c
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting
CWI
Amsterdam
Thionville
14-d
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting • It works (various applications)
CWI
Amsterdam
Thionville
14-e
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting • It works (various applications) • Future work: Efficient compilation
CWI
Amsterdam
Thionville
15
Questions
CWI
Amsterdam
1
Term Rewriting with Traversal Functions Mark van den Brand Paul Klint Jurgen Vinju April 18th, 2001
CWI
Amsterdam
Thionville
2
Overview • Term Rewriting Problems • Solutions • Traversal functions • Limitations • Conclusion & Questions
CWI
Amsterdam
Thionville
3
Term Rewriting Problems
CWI
Amsterdam
Thionville
3-a
Term Rewriting Problems • Term rewriting is expressive, but...
CWI
Amsterdam
Thionville
3-b
Term Rewriting Problems • Term rewriting is expressive, but... • Term traversal is implicit (e.g. innermost) only sort preserving transformations no extra arguments (i.e. context) fixed path
CWI
Amsterdam
Thionville
3-c
Term Rewriting Problems • Term rewriting is expressive, but... • Term traversal is implicit (e.g. innermost) only sort preserving transformations no extra arguments (i.e. context) fixed path • Confluence non-trivial trs’s are not confluent
CWI
Amsterdam
Thionville
4
Solutions
CWI
Amsterdam
Thionville
4-a
Solutions • Encode strategies using functional style
CWI
ASF+SDF
Amsterdam
Thionville
4-b
Solutions • Encode strategies using functional style • Strategy primitives
CWI
ASF+SDF ELAN
Amsterdam
Thionville
4-c
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
CWI
ASF+SDF ELAN Stratego
Amsterdam
Thionville
4-d
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But:
CWI
Amsterdam
Thionville
4-e
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems
CWI
Amsterdam
Thionville
4-f
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal
CWI
Amsterdam
Thionville
4-g
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed
CWI
Amsterdam
Thionville
4-h
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed Strategic Programming is another paradigm
CWI
Amsterdam
Thionville
4-i
Solutions • Encode strategies using functional style • Strategy primitives • Strategy & Traversal primitives
ASF+SDF ELAN Stratego
• Very nice! But: Encoding is boring for large systems ELAN Strategies do not solve term traversal Stratego traversal primitives are not typed Strategic Programming is another paradigm • Traversal functions! less powerful fully typed simple CWI
Amsterdam
Thionville
5
Traversal functions
CWI
Amsterdam
Thionville
5-a
Traversal functions • Characteristics:
CWI
Amsterdam
Thionville
5-b
Traversal functions • Characteristics: typed prefix functions
CWI
Amsterdam
Thionville
5-c
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both
CWI
Amsterdam
Thionville
5-d
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop)
CWI
Amsterdam
Thionville
5-e
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation
CWI
Amsterdam
Thionville
5-f
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are:
CWI
Amsterdam
Thionville
5-g
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are: What can we do with them?
CWI
Amsterdam
Thionville
5-h
Traversal functions • Characteristics: typed prefix functions three generic types: trafo, accu or both two generic strategies: bottom-up (all), top-down (stop) simple semantics, easy implementation • The questions are: What can we do with them? What can we not do with them?
CWI
Amsterdam
Thionville
6
PICO module Pico-syntax imports Pico-Identifiers Pico-Integers Pico-Strings Types exports sorts PROGRAM context-free syntax "begin" DECLS {STATEMENT ";"}* "end" -> PROGRAM "declare" {ID-TYPE ","}* ";" -> DECLS PICO-ID ":" TYPE -> ID-TYPE PICO-ID ":=" EXP -> STATEMENT "if" EXP "then" {STATEMENT ";"}* "else" {STATEMENT ";"}* "fi" -> STATEMENT "while" EXP "do" {STATEMENT ";"}* "od" -> STATEMENT PICO-ID -> EXP PICO-NAT-CON -> EXP PICO-STR-CON -> EXP EXP "+" EXP -> EXP {left} EXP "-" EXP -> EXP {left} EXP "*" EXP -> EXP {left}
Figure 1:
CWI
Amsterdam
Thionville
7
Transformer module Pico-Replace imports Pico-syntax exports context-free syntax replace(PROGRAM,ID,ID) -> PROGRAM {traversal(trafo)} equations [] replace(Id1,Id1,Id2) = Id2 Figure 2:
CWI
Amsterdam
Thionville
8
Transformer (cont’d) replace( begin declare input : natural, output : natural; input := 12; output := 1; while input - 1 do output := output * 2; input := input - 1 od end, input, INPUT) Figure 3: CWI
Amsterdam
Thionville
9
Transformer (cont’d) begin declare INPUT : natural, output : natural; INPUT := 12; output := 1; while INPUT - 1 do output := output * 2; INPUT := INPUT - 1 od end Figure 4:
CWI
Amsterdam
Thionville
10
Accumulator module Pico-Count imports Pico-syntax exports context-free syntax count(PROGRAM,NAT) -> NAT {traversal(accu)} equations [] count(Id,Nat) = suc(Nat) Figure 5:
CWI
Amsterdam
Thionville
11
Accumulating Transformer module Pico-ReplaceCount imports Pico-syntax exports context-free syntax replacecount(PROGRAM,NAT,ID,ID) -> PROGRAM # NAT {traversal(accu,trafo)} equations [] replacecount(Id1,Nat,Id1,Id2) = (Id2,suc(Nat)) Figure 6:
CWI
Amsterdam
Thionville
12
Experience • COBOL transformations • CASL transformations • SDF tools: typechecker, statistics • New DSL: Framework for SDF Transformation (FST)
CWI
Amsterdam
Thionville
12-a
Experience • COBOL transformations • CASL transformations • SDF tools: typechecker, statistics • New DSL: Framework for SDF Transformation (FST) • Significant reduction in number of rules • Interpreter efficient enough
CWI
Amsterdam
Thionville
13
Limitations
CWI
Amsterdam
Thionville
13-a
Limitations 1. Types: no arbitrary non-sort-preserving traversals
CWI
Amsterdam
Thionville
13-b
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees
CWI
Amsterdam
Thionville
13-c
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules
CWI
Amsterdam
Thionville
13-d
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes
CWI
Amsterdam
Thionville
13-e
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes 2. Use conditions and default rules to guide the path
CWI
Amsterdam
Thionville
13-f
Limitations 1. Types: no arbitrary non-sort-preserving traversals 2. Traversals: no arbitrary traversal paths through trees 3. Strategies: still no control over application of rewrite rules 1. Use traversal functions for the unaffected nodes 2. Use conditions and default rules to guide the path 3. Still encode strategies using functions
CWI
Amsterdam
Thionville
14
Conclusions
CWI
Amsterdam
Thionville
14-a
Conclusions • Automated tree traversal
CWI
Amsterdam
Thionville
14-b
Conclusions • Automated tree traversal • Statically typed
CWI
Amsterdam
Thionville
14-c
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting
CWI
Amsterdam
Thionville
14-d
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting • It works (various applications)
CWI
Amsterdam
Thionville
14-e
Conclusions • Automated tree traversal • Statically typed • Simple semantics, first-order term rewriting • It works (various applications) • Future work: Efficient compilation
CWI
Amsterdam
Thionville
15
Questions
CWI
Amsterdam
