Semantics of Programming Languages
This directory contains Agda proofs and a literate agda programme designed as a basic course for the sematics of programming. Included are basical operational and denotational semantic approaches.
The terms which prove termination at a value, double as runable evaluation functions!
Structure
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Topic 0: Some basic functional programming in a dependently typed language: Preliminaries.pdf
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Topic 1: Operational semantics for simple arithmetic expressions.
The examples given in the slides are contained in the file: OperationalSemantics.agda
- Topic 2: Induction
A limited number of examples from the slides are present in the file: Induction.agda
Some of the consistency proofs are given in Consistency.agda.
There is a proof that (∀ E → Σ[ n ∈ ℕ ] E ⟶⋆ num n) in SmallStepEval.agda. It makes use of transfinite induction rather than strong mathematical induction. Induction is performed over the size of proofs.
- Topic 3: A (first-order) functional programming language.
Not yet completed: PCF would be a possible choice for implementation.
- Topic 4: The While programming language
The While programming language and progress proof along with a proof of partial correctness is in the file: While.agda
The consistency proofs are in the file WhileConsistency.agda
- Topic 5: Handling Exceptions
Not yet completed
- Topic 6: Functions as data
Not yet completed