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Is there a universal foundation beneath all programming languages?
This deep link between programming and logic means that writing a correct program is like constructing a proof of a theorem.
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Programs do not always execute linearly. Concepts like exceptions, threads, and early returns disrupt standard evaluation. 15-312 introduces the concept of (the "rest of the program"), often formalized via operators like call/cc , to model complex control flow mathematically. Memory and Mutation 15312 foundations of programming languages
The famous slogan "Well-typed programs do not go wrong."
Each method reveals different truths. Operational semantics is good for implementation. Denotational semantics is good for compositionality. Axiomatic semantics is good for reasoning about correctness.
: A well-typed program is never stuck. It is either already a finished value, or it can take another step of execution. Is there a universal foundation beneath all programming
A student who finishes 15312 sees code differently. A loop is not just a loop—it’s a fixed point. A variable is not just a name—it’s a reference cell in a store. A function call is not just a jump—it’s a β-reduction in lambda calculus.
The "Dynamics" describe how a program steps from one state to the next. Using , you write rules that dictate exactly how an expression evaluates. This is where you learn about:
By the 1960s, the Tower of Babel had been rebuilt—this time with FORTRAN, COBOL, Lisp, ALGOL, and others. No one could agree on what a programming language should be. That’s when a small group of computer scientists began asking a radical question: Concepts like exceptions, threads, and early returns disrupt
The primary tool for proving properties about programs and language systems. The PCF (Programming Computable Functions) Language:
A central pillar of 15-312 is the study of type systems. In this framework, types are not just data tags; they are partial proofs of program correctness.
If you ever want to build your own DSL (Domain Specific Language) or contribute to a major compiler like LLVM or Rust, these foundations are non-negotiable. Recommended Resources
Generic programming and modularity.