PLT: Lecture 2

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PLT Lecture 2

• Compilation and Mathematical Notation

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1st Ever Program
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Semantic TranslationThe Role of the Compiler

• This translation machine (compiler) is feasable
  because its input (program source) has
• A structure which is described in a reference
  manual
• Semantics that can be described in terms of (and
  attached to) that structure.

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Compiler Architecture

• Shows Good Separation of Concerns
• Shows Interpreter Possibility
• For
• High Level Portability
• Much Less Work
• Against
• Slower Execution
• Non Persistent Executable

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Re-engineering tool Architecture

• A Program view may be
• Graphical Representation
• Metrics
• Translated Source Code
• Re-factored Source Code
• Which may in turn by taken as an input to the
  re-engineering tool

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Reengineering Architecture
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Mathematical Notations

• Arithmetic / Algebraic Notations include
• Symbols
• Operator symbols
• Operand symbols
• Literals
• Variables
• Punctuation symbols
• Conventions
• Where symbols should be placed with respect to
  each other
• These allow the building of more complex
  expressions from simpler ones

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Operator Properties

• Arity
• Unary
• Binary
• Ternary
• Variable
• Fixity (conventions)
• Horizontal
• Prefix
• Infix
• Outfix
• Postfix

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Operator Properties Continued

• Fixity (Continued)
• Vertical Elements
• Superfix
• Vertical Infix
• Subfix
• Vertical Outfix
• Invisibilty
• abc
• Exp(2,3) 2 to the power of 3 23
• alta1, a2, a3,.angt. ai implies the selector
  operator (ith element) from that sequence

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More Complex Calculations

• Elementary operations
• More complex operations
• Intermediate naming option
• Delocalizes the original formula
• Introduces many new symbols
• Generalizing operands
• Literal
• Variable
• Result of earlier operation
• Expression
• Sub-Expressions as operands in nesting
  expressions

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Notational Conventions (that enable this nesting)

• Stretchable Operators
• Square root
• Any more?
• Special Delimiters
• Over-lines, Overbraces
• Illustrate for quadratic equations
• Illustrate refined notation
• Expression Trees
• Highly readable (humans and Computers)
• Eliminate delimiters
• Space for annotation
• Extensively used in compilers