A fully abstract semantics for a higher
... We can show that the denotational semantics is fully abstract for the operational semantics using a variant of Abramsky (1989) and Ong’s (1988) lazy lambda-calculus and Abramsky’s (1991) domain theory in logical form. This is similar to Ong’s (1993) use of a program logic for the untyped λ-calculus, ...
... We can show that the denotational semantics is fully abstract for the operational semantics using a variant of Abramsky (1989) and Ong’s (1988) lazy lambda-calculus and Abramsky’s (1991) domain theory in logical form. This is similar to Ong’s (1993) use of a program logic for the untyped λ-calculus, ...
Short Introduction to the Lambda
... defined in terms of this one. We shall see this later, when we shall represent this sort of computational step with the beta-reduction rule in the lambda calculus and we shall see that, if one wish, any possible computation can be defined in terms of this beta-rule. When we evaluate an expression th ...
... defined in terms of this one. We shall see this later, when we shall represent this sort of computational step with the beta-reduction rule in the lambda calculus and we shall see that, if one wish, any possible computation can be defined in terms of this beta-rule. When we evaluate an expression th ...
Partiality and recursion in interactive theorem provers: An overview
... One important classification criterion is the distinction between axiomatic and definitional techniques. Following traditional terminology from the higher-order logic community, we call a technique axiomatic if it involves modifications to the rules of the system. This may happen by adding axioms, e ...
... One important classification criterion is the distinction between axiomatic and definitional techniques. Following traditional terminology from the higher-order logic community, we call a technique axiomatic if it involves modifications to the rules of the system. This may happen by adding axioms, e ...
PPT
... (T1,T2,…,Tn) is the type of n-tuples whose ith components have type Ti for any i in 1…n. Lecture 18 – Functional Programming, Spring 2008 ...
... (T1,T2,…,Tn) is the type of n-tuples whose ith components have type Ti for any i in 1…n. Lecture 18 – Functional Programming, Spring 2008 ...
Denotational design with type class morphisms
... Haskell provides a way to organize interfaces via type classes (Wadler and Blott 1989; Jones 1993). Library designers can present parts of a type’s interface as instances of standard type classes, which then provides the library’s users with standard vocabularies, thus making the library more easily ...
... Haskell provides a way to organize interfaces via type classes (Wadler and Blott 1989; Jones 1993). Library designers can present parts of a type’s interface as instances of standard type classes, which then provides the library’s users with standard vocabularies, thus making the library more easily ...
Haskell
... In Haskell, types are collections of related values. Expression's types are automatically calculated at compile time. This is known as type inference. Because the type of an expression is determined at compile time, errors in type are found at compile time. Because the type of every expression is kn ...
... In Haskell, types are collections of related values. Expression's types are automatically calculated at compile time. This is known as type inference. Because the type of an expression is determined at compile time, errors in type are found at compile time. Because the type of every expression is kn ...
Structure of Programming Languages – Lecture 6
... Comments start with ; and go to the end of the line. Strings are enclosed in "double quotes". ...
... Comments start with ; and go to the end of the line. Strings are enclosed in "double quotes". ...
x + 1 - Postech
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
Functional Programming
... For example, functions with multiple arguments or results are possible using lists or tuples: ...
... For example, functions with multiple arguments or results are possible using lists or tuples: ...
A Verified Compiler for Probability Density Functions
... Additionally, standard arithmetical and logical operators exist. All operators are total, meaning that for every input value of their parameter type, they return a single value of their result type. This requires some nonstandard definitions for non-total operations such as division, the logarithm, ...
... Additionally, standard arithmetical and logical operators exist. All operators are total, meaning that for every input value of their parameter type, they return a single value of their result type. This requires some nonstandard definitions for non-total operations such as division, the logarithm, ...
A Verified Compiler for Probability Density Functions
... Additionally, standard arithmetical and logical operators exist. All operators are total, meaning that for every input value of their parameter type, they return a single value of their result type. This requires some nonstandard definitions for non-total operations such as division, the logarithm, ...
... Additionally, standard arithmetical and logical operators exist. All operators are total, meaning that for every input value of their parameter type, they return a single value of their result type. This requires some nonstandard definitions for non-total operations such as division, the logarithm, ...
Proof, Sets, and Logic - Boise State University
... press because it prevents the truncation of the construction of the cumulative hierarchy of isomorphism types of well-founded extensional relations (the world of the usual set theory). Further, it is interesting to note that the von Neumann definition of ordinal numbers is entirely natural if the wo ...
... press because it prevents the truncation of the construction of the cumulative hierarchy of isomorphism types of well-founded extensional relations (the world of the usual set theory). Further, it is interesting to note that the von Neumann definition of ordinal numbers is entirely natural if the wo ...
Proof, Sets, and Logic - Department of Mathematics
... the i operation. It is certainly a valid point which is being made, but I would like to say it neatly. It is nice to get to it before one tries to construct NF(U); thus one does not naturally wander into the NF problem. July 9, 2009: I am editing the text again, much later, with an eye to starting t ...
... the i operation. It is certainly a valid point which is being made, but I would like to say it neatly. It is nice to get to it before one tries to construct NF(U); thus one does not naturally wander into the NF problem. July 9, 2009: I am editing the text again, much later, with an eye to starting t ...
