Relative Completeness for Logics of Functional Programs
... is not available in the language of T though primitive recursion is. But this is not a real restriction since all inhabited r.e. sets can be enumerated by a primitive recursive function. This fact will be used subsequently without further mention. As shown in Plotkin’s paper [21] every coherently co ...
... is not available in the language of T though primitive recursion is. But this is not a real restriction since all inhabited r.e. sets can be enumerated by a primitive recursive function. This fact will be used subsequently without further mention. As shown in Plotkin’s paper [21] every coherently co ...
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... that are inherently vacuous by model but are not inherently vacuous by mutation. For example, consider the formula ϕ = p ∨ q. Every deterministic Kripke structure that satisfies ϕ has its (single) initial state labeled either by p or by q or by both, and thus it satisfies ϕ vacuously. On the other h ...
... that are inherently vacuous by model but are not inherently vacuous by mutation. For example, consider the formula ϕ = p ∨ q. Every deterministic Kripke structure that satisfies ϕ has its (single) initial state labeled either by p or by q or by both, and thus it satisfies ϕ vacuously. On the other h ...
Standard ML: A Quick Tutorial
... Since no identifier is given to bind to the value, the interactive system has chosen the identifier it and bound it to the result of 4+6 The semicolon (";") is a marker that indicates to the SML/NJ system that it should perform the interactive top-level loop Hossein Hojjat ...
... Since no identifier is given to bind to the value, the interactive system has chosen the identifier it and bound it to the result of 4+6 The semicolon (";") is a marker that indicates to the SML/NJ system that it should perform the interactive top-level loop Hossein Hojjat ...
Lambda Calculus
... Since no identifier is given to bind to the value, the interactive system has chosen the identifier it and bound it to the result of 4+6 The semicolon (";") is a marker that indicates to the SML/NJ system that it should perform the interactive top-level loop Hossein Hojjat ...
... Since no identifier is given to bind to the value, the interactive system has chosen the identifier it and bound it to the result of 4+6 The semicolon (";") is a marker that indicates to the SML/NJ system that it should perform the interactive top-level loop Hossein Hojjat ...
Curry-Howard Isomorphism - Department of information engineering
... systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed λ-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, etc. The ...
... systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed λ-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, etc. The ...
Lecture Notes on the Lambda Calculus
... exists exactly one y ∈ Y such that (x, y) ∈ f . Two functions f, g : X → Y are considered equal if they yield the same output on each input, i.e., f (x) = g(x) for all x ∈ X. This is called the extensional view of functions, because it specifies that the only thing observable about a function is how ...
... exists exactly one y ∈ Y such that (x, y) ∈ f . Two functions f, g : X → Y are considered equal if they yield the same output on each input, i.e., f (x) = g(x) for all x ∈ X. This is called the extensional view of functions, because it specifies that the only thing observable about a function is how ...
INTEGRATION OF FUNCTIONAL PROGRAMMING AND
... Functional programming is so called because a program consists entirely of functions (Hughes, 1989). The main program itself is written as a function which receives the program’s input as its argument and delivers the program’s output as its result. Features of modern functional languages also inclu ...
... Functional programming is so called because a program consists entirely of functions (Hughes, 1989). The main program itself is written as a function which receives the program’s input as its argument and delivers the program’s output as its result. Features of modern functional languages also inclu ...
Higher-order Logic: Foundations
... • Higher-order logic (HOL) is an expressive foundation for mathematics: analysis, algebra, . . . ...
... • Higher-order logic (HOL) is an expressive foundation for mathematics: analysis, algebra, . . . ...
Beginning with the Haskell Programming Language About the Tutorial
... There are (optionally) two parts to a function definition. The first part (conceptually, not necessarily within a listing) is the type signature of a function. In a function, the type signature defines all the types of the input, and the type of the output. Some analogous C definitions are given in ...
... There are (optionally) two parts to a function definition. The first part (conceptually, not necessarily within a listing) is the type signature of a function. In a function, the type signature defines all the types of the input, and the type of the output. Some analogous C definitions are given in ...
Intuitionistic completeness part I
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
of Folding Domain−Specific Languages: Deep and Shallow
... A shallow embedding supports only compositional interpretations, whereas a deep embedding provides full access to the AST and hence also non-compositional manipulations. Here, ‘compositionality’ of an interpretation means that the interpretation of a whole may be determined solely from the interpret ...
... A shallow embedding supports only compositional interpretations, whereas a deep embedding provides full access to the AST and hence also non-compositional manipulations. Here, ‘compositionality’ of an interpretation means that the interpretation of a whole may be determined solely from the interpret ...
higher-order logic - University of Amsterdam
... etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. EXAMPLE. The notion ‘finiteness of the domain’ is not definable by means of any first-order sentence, or set of such sentences. It will be recalled that the relevant refuta ...
... etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. EXAMPLE. The notion ‘finiteness of the domain’ is not definable by means of any first-order sentence, or set of such sentences. It will be recalled that the relevant refuta ...
View raw file - aaa
... We say (ω ω) doesn’t have a normal form. To solve this problem, we introduce types. ...
... We say (ω ω) doesn’t have a normal form. To solve this problem, we introduce types. ...
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... 1. Type Theory vs. Set Theory 2. Overview of the Nuprl System 3. Proofs of the Integer Square Root Problem ...
... 1. Type Theory vs. Set Theory 2. Overview of the Nuprl System 3. Proofs of the Integer Square Root Problem ...
TR-14-06 - Ynot - Harvard University
... the types of memory locations are invariant. This restriction makes it difficult to model stateful protocols as in the Vault programming language [8], or low-level languages such as TAL [29] and Cyclone [16] where memory management is intended to be coded within the language. The second advantage is ...
... the types of memory locations are invariant. This restriction makes it difficult to model stateful protocols as in the Vault programming language [8], or low-level languages such as TAL [29] and Cyclone [16] where memory management is intended to be coded within the language. The second advantage is ...
Unit 11 — Functional Programming with Haskell
... Lists/1 Haskell also supports lists with the standard square bracket notation ...
... Lists/1 Haskell also supports lists with the standard square bracket notation ...