| Term | Definition | |------|-------------| | | Tree representation ignoring parentheses and precedence. | | Substitution | ( [e/x]e' ) = replace free occurrences of ( x ) in ( e' ) with ( e ), avoiding capture. | | Canonical Forms | If ( v : \tau_1 \rightarrow \tau_2 ), then ( v ) must be a lambda abstraction. | | Contextual Equivalence | ( e_1 \approx e_2 ) iff for all contexts ( C[,] ), ( C[e_1] \Downarrow v ) iff ( C[e_2] \Downarrow v ). |
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(Deep dive into call-by-value vs. call-by-name) 15312 foundations of programming languages
Furthermore, advanced sections use (a logical framework) to encode programming language definitions as logic programs . In Twelf, you declare rules, and the system checks if your type safety proof is valid. It’s like a proof assistant for language designers.
Computer science relies on programming languages to turn abstract logic into executable reality. At Carnegie Mellon University (CMU), the course serves as a definitive roadmap for understanding how these languages are designed, specified, and implemented. Rather than teaching you how to use a specific language, 15-312 teaches you how to reason about all languages through rigorous mathematical frameworks. | Term | Definition | |------|-------------| | |
How does the program run? You will study two main styles:
To establish a universal framework for analyzing languages, 15-312 relies on several rigorous mathematical tools. These concepts allow computer scientists to strip away superficial syntax and focus on core behavior. 1. Abstract Syntax Trees (ASTs) and Binding | | Contextual Equivalence | ( e_1 \approx
Exploring recursion, functions, and the fundamentals of functional programming. Type Safety: Learning to prove