Abstract
There are two key parts to any programming language, and these are its syntax and semantics . The syntax is the grammar of the language and a program needs to be syntactically correct with respect to its grammar. The semantics of the language is deeper, and determines the meaning of what has been written by the programmer.
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- 1.
Recall that a monoid (M,*,e) is a structure that is closed and associative under the binary operation ‘*’ and has identity element ‘e’.
- 2.
Chomsky made important contributions to linguistics and the theory of grammars. He is more widely known to-day as a critic of US foreign policy.
- 3.
Backus–Naur Form is named after John Backus and Peter Naur. It was created as part of the design of the Algol 60 programming language, and is used to define the syntax rules of the language.
- 4.
Of course, what the programmer has written may not be what the programmer had intended.
- 5.
There are attribute (or affix) grammars that extend the syntactic description of the language with supplementary elements covering the semantics. The process of adding semantics to the syntactic description is termed decoration.
- 6.
Hoare was influenced by earlier work by Floyd on assigning meanings to programs using flowcharts [Flo:67].
- 7.
Total correctness is expressed using {P}a{Q} and program fragment a is totally correct for precondition P and postcondition Q if and only if whenever a is executed in any state in which P is satisfied then execution terminates, and the resulting state satisfies Q.
- 8.
This virtual stack based machine was originally designed by Peter Landin to evaluate lambda calculus expres-sions, and it has since been used as a targefor several compilers.
- 9.
This is similar to what a compiler does in that if errors are found during the compilation phase, the compiler halts and displays the errors and does not continue with code generation.
- 10.
This essentially expresses that the names of bound variables is unimportant.
- 11.
This essentially expresses the idea of function application.
- 12.
This essentially expresses the idea that two functions are equal if and only if they give the same results for all arguments.
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© 2013 Springer-Verlag London
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O’Regan, G. (2013). Language Theory and Semantics. In: Mathematics in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-4534-9_10
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DOI: https://doi.org/10.1007/978-1-4471-4534-9_10
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