Natural Numbers Lists Trees 1 Structural Induction with Haskell Dr. Liam O’Connor University of Edinburgh LFCS UNSW, Term 3 2020 Natural Numbers Lists Trees Recap: Induction Definition Let P(x) be a predicate on natural numbers x ∈ N. To show ∀x ∈ N. P(x), we can use induction: Show P(0) Assuming P(k) (the inductive hypothesis), […]
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Readers and Writers Haskell Issues with Locks Software Transactional Memory Wrap-up Bonus: Semantics for IO 1 Haskell Concurrency and STM Christine Rizkallah CSE, UNSW Term 3 2020 Readers and Writers Haskell Issues with Locks Software Transactional Memory Wrap-up Bonus: Semantics for IO Shared Data Consider the Readers and Writers problem: Problem We have a large
Safety and Liveness Type Safety Exceptions Safety and Liveness; Exceptions Christine Rizkallah CSE, UNSW Term 3; 2020 1 Safety and Liveness Type Safety Exceptions Program Properties Consider a sequence of states, representing the evaluation of a program in a small step semantics (a trace): σ1 →σ2 →σ3 →···→σn Observe that some traces are finite, whereas
1 Safety and Liveness; Exceptions Christine Rizkallah CSE, UNSW Term 3; 2020 Program Properties 2 Consider a sequence of states, representing the evaluation of a program in a small step semantics (a trace): σ1 →σ2 →σ3 →···→σn Observe that some traces are finite, whereas others are infinite. To simplify things, we’ll make all traces infinite
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Natural Numbers Lists Trees 1 Structural Induction with Haskell Dr. Liam O’Connor University of Edinburgh LFCS UNSW, Term 3 2020 Natural Numbers Lists Trees Recap: Induction Definition Let P(x) be a predicate on natural numbers x ∈ N. To show ∀x ∈ N. P(x), we can use induction: Show P(0) Assuming P(k) (the inductive hypothesis),
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Natural Deduction Rule Induction Ambiguity Simultaneous Induction 1 Natural Deduction and Rule Induction Dr. Liam O’Connor University of Edinburgh LFCS UNSW, Term 3 2020 Natural Deduction Rule Induction Ambiguity Simultaneous Induction Formalisation To talk about languages in a mathematical way, we need to formalise them. Formalisation Formalisation is the process of giving a language a
Implicitly Typed MinHS Inference Algorithm Unification Damas-Milner Type Inference Christine Rizkallah CSE, UNSW Term 3 2020 1 Implicitly Typed MinHS Inference Algorithm Unification Implicitly Typed MinHS Explicitly typed languages are awkward to use1. Ideally, we’d like the compiler to determine the types for us. Example What is the type of this function? recfunf x=fstx+1 We
Motivation Polymorphism Implementation Parametricity Polymorphism Christine Rizkallah CSE, UNSW Term 3 2020 1 Motivation Polymorphism Implementation Parametricity Where we’re at Syntax Foundations Concrete/Abstract Syntax, Ambiguity, HOAS, Binding, Variables, Substitution Semantics Foundations Static Semantics, Dynamic Semantics (Small-Step/Big-Step), (Assignment 0) Abstract Machines, Environments (Assignment 1) Features Algebraic Data Types Polymorphism Polymorphic Type Inference (Assignment
Motivation Polymorphism Implementation Parametricity Polymorphism Christine Rizkallah CSE, UNSW Term 3 2020 1 Motivation Polymorphism Implementation Parametricity Where we’re at Syntax Foundations Concrete/Abstract Syntax, Ambiguity, HOAS, Binding, Variables, Substitution Semantics Foundations Static Semantics, Dynamic Semantics (Small-Step/Big-Step), (Assignment 0) Abstract Machines, Environments (Assignment 1) Features Algebraic Data Types Polymorphism Polymorphic Type Inference (Assignment
Abstract Syntax Parsing Bindings First Order Abstract Syntax Higher Order Abstract Syntax 1 Syntax Dr. Liam O’Connor University of Edinburgh LFCS UNSW, Term 3 2020 Abstract Syntax Parsing Bindings First Order Abstract Syntax Higher Order Abstract Syntax Concrete Syntax Arithmetic Expressions i ∈ Z i Atom a Atom a SExp (a) Atom b PExp e