Formal Models for Programming Languages

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Formal Models for Programming Languages

• FJ and FGJ

Alexandra Stefan
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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)
• Extension
• Generic Java (1.5 beta)
• Featherweight Generic Java (FGJ)
• Some properties compositionality ...
• Related work

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PLs formal models

• First was the computer
• and then the programs
• and then the programs to write programs
• Numerous programming languages
• imperative Ada, Pascal, Perl, Java, all of the
  Cs
• functional Scheme, SML, Prolog, Haskel, OCaml
• How to choose one? What makes one better than the
  other?
• expressive power?
• No.
• friendliness? (readability/ modifiability/
  debugging)
• Yes.

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PLs formal models

• Then questions and needs were raised about
  languages
• How safe is it?
• It passed compilation what next?
• Can I trust it to run well?
• Will it stab me on the back?
• Can it be extended?
• Improved efficiency generic classes
• Increased expressivity XML syntax
• How would I design a new language?

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PLs formal models

• Here we come, the PL people!
• check their properties (e.g. type preservation,
  progress, )
• try to capture the invariants with a type system
• How do we do this?
• using a formal model

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Formal model

• Design choice completeness or compactness?
• more complex is more unwieldy
• too parsimonious is useless
• trade-off

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Formal model

• Examples
• Lambda calculus
• Java FJ, FGJ, Javas (Javase), Javalight,
  ClassicJava,
• C C?

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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)
• Extension
• Generic Java (1.5 beta)
• Featherweight Generic Java (FGJ)
• Some properties compositionality ...
• Related work

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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)

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Case study Featherweight Java (FJ)

• Proposed by Igarashi, Pierce, and Wadler in 1999.
• Models Javas type system.
• Minimal core calculus
• Favors compactness over completeness almost
  obsessively
• (It hardly resembles Java!)
• no assignment -gt functional
• captures the core features of Java typing.
• How close is it to Java?
• FJ purely functional core of Java.
• (every FJ program is literally an executable
  Java program)

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FJ What can be done with it?

• It allows easy proofs for type safety for FJ
• FJs main application is to model extensions
• of Java
• FGJ
• Featherweight Open Java
• Inner classes

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FJ
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FJ

• How does an FJ program look like?
• Pair (class table, expression)
• The class table - fixed
• Sanity conditions for classes
• Object - not part of the class table
• All necessary classes are defined
• No cycles in the subtyping relation
• induced by the class table

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FJ class declaration examples
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FJ expression examples
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FJ syntax subtyping rules
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FJ auxiliary functions
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FJ expression typing
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FJ expression typing
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FJ evaluation rules
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FJ results
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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)
• Extension
• Generic Java (1.5 beta)
• Featherweight Generic Java (FGJ)
• Some properties compositionality ...
• Related work

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Compositional compilation

• Polymorphic Bytecode Compositional Compilation
  for Java-like Languages
• D. Anacona
• S. Drossopoulou
• F. Damiani
• E. Zucca

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Separate compilation motivation

• Why do we want these properties?
• modularity
• safety

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Separate compilation
Used fragments
fragment
compile
link
Used fragments
fragment
compile
fragment
compile
fragment
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Java-like languages clash of philosophy

• Separate compilation -gt byte-code reflects
  compilation environment
• Dynamic linking -gt byte-code does not reflect
  compilation environment
• no (compilation execution) environment
• no (final globally) compiled application
• type-safety through runtime verification
• Example
• E m(B x) return x.f1.f2
• CEnv1 B C f1 C E f2
• -gt mdB1 E m(B x) return xB.f1 CC.f2 E
• CEnv2 B D f1 D F f2 -gt
• -gt mdB2 E m(B x) return xB.f1 DD.f2 F

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Compositionality

• Compositional analysis
• analyze source code fragments separately
• put them together
• finish analysis of the whole without reanalyzing
  the fragments
• Compositional compilation
• typecheck source code fragments separately
• -gt generate corresponding binaries
• link together fragments whose mutual constraints
  are satisfied, without reinspecting the code

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Compositional compilation IDEA

• Compile fragments separately
• Generate
• bytecode with type variables
• constraints gt relate the type variables
• Put the constraints together (particular order)
• Solve the constraints gt substitution
• Put the bytecode together
• Apply the substitution
• Done!

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Compositional compilation

• How good is it?
• We are not sure yet, but it looks promising.
• My work
• Try to apply it for FGJ.

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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)
• Extension
• Generic Java (1.5 beta)
• Featherweight Generic Java (FGJ)
• Some properties compositionality ...
• Related work

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Generic Java

• Version 1.5 beta
• Parametric polymorphism
• Uses the standard JVM
• Backward Forward compatibility with old code.

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FGJ class declaration examples
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FGJ term examples
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Homogeneous vs Heterogeneous polymorphism
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Generic Java (GJ)

• No explicit type arguments to a generic method
• parsing problem
• e.mltA,Bgt(e) ? e.mltA, Bgt(e)
• Performs parameter inference has a least type

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Featherweight Generic Java (FGJ)

• FJ extended with generic classes
• Not a subset of GJ requires type arguments to
  generic methods
• Not concerned with parameter inference

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FGJ syntax subtyping rules
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FGJ auxiliary functions
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FGJ
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FGJ
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FGJ expression typing
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FGJ expression typing
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FGJ evaluation rules
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FGJ results
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Topics of Discussion

• Programming Languages (PLs) and
• Formal Models
• Case study
• Java - Featherweight Java (FJ)
• Extension
• Generic Java (1.5 beta)
• Featherweight Generic Java (FGJ)
• Some properties compositionality ...
• Related work

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Related work

• Types and Programming Languages by B.C.Pierce
• Featherweight Java A Minimal Core Calculus for
  Java and GJ by Atsushi Igarashi, Benjamin C.
  Pierce, Philip Wadler
• GJ Specification by Gilad Bracha, Martin
  Odersky, David Stoutamire, Philid Wadler
• Bringing Genericity to Java by David W. Dunham
• Polymorphic Bytecode Compositional Compilation
  for Java-like Languages by D. Anacona, S.
  Drossopoulou, F. Damiani, E. Zucca