Lambda Calculus as a Programming Language
... We accept that parameter transfer in λ0 is similar to the call by name (the reduction of λexpressions is left-to-right or, equivalently, the normal-order evaluation is used). Therefore, the functions we will define are non-strict. Moreover, what is subject to evaluation is the function application o ...
... We accept that parameter transfer in λ0 is similar to the call by name (the reduction of λexpressions is left-to-right or, equivalently, the normal-order evaluation is used). Therefore, the functions we will define are non-strict. Moreover, what is subject to evaluation is the function application o ...
Henkin`s Method and the Completeness Theorem
... In addition to formal manipulation of the formulas of this system we shall be concerned with their meaning according to the following interpretation. The propositional constants are to denote one of the truth values, T or F, the symbol “f ” denoting F, and the propositional variables are to have the ...
... In addition to formal manipulation of the formulas of this system we shall be concerned with their meaning according to the following interpretation. The propositional constants are to denote one of the truth values, T or F, the symbol “f ” denoting F, and the propositional variables are to have the ...
Pebble weighted automata and transitive - LSV
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
The Continuity of Monadic Stream Functions
... precise mental steps. A function can consult its sequence argument one element at a time and must algorithmically compute a result in a finite time. It follows that a function can only obtain a finite number of sequence elements in the time it takes it to produce the result. Hence, it must be contin ...
... precise mental steps. A function can consult its sequence argument one element at a time and must algorithmically compute a result in a finite time. It follows that a function can only obtain a finite number of sequence elements in the time it takes it to produce the result. Hence, it must be contin ...
On perturbations of continuous structures - HAL
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
ON PERTURBATIONS OF CONTINUOUS STRUCTURES
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
A Judgmental Reconstruction of Modal Logic
... are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and complete in order to have a satisfactory meaning explanation for the connective. Local sound ...
... are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and complete in order to have a satisfactory meaning explanation for the connective. Local sound ...
Beginning Logic - University of Notre Dame
... We will define what it means for a statement in a propositional or predicate language to be true in an appropriate formal setting. To show that an argument is not valid, we will look for a “counter-example”, a setting in which the premises are all true and the conclusion is false. IV. Analysis of ar ...
... We will define what it means for a statement in a propositional or predicate language to be true in an appropriate formal setting. To show that an argument is not valid, we will look for a “counter-example”, a setting in which the premises are all true and the conclusion is false. IV. Analysis of ar ...
Carnap and Quine on the analytic-synthetic - Philsci
... list of pairs of opposite concepts that have been used by Quine and Carnap, such as analytic/synthetic, logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinctio ...
... list of pairs of opposite concepts that have been used by Quine and Carnap, such as analytic/synthetic, logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinctio ...
Verification of a Cryptographic Primitive: SHA-256 ANDREW W. APPEL
... This paper presents the following result: I have proved functional correctness of the OpenSSL implementation of SHA-256, with respect to a functional specification: a formalization of the FIPS 180-4 Secure Hash Standard [FIPS 2012]. The machinechecked proof is done using the Verifiable C program log ...
... This paper presents the following result: I have proved functional correctness of the OpenSSL implementation of SHA-256, with respect to a functional specification: a formalization of the FIPS 180-4 Secure Hash Standard [FIPS 2012]. The machinechecked proof is done using the Verifiable C program log ...
The Foundations
... Theorem2[substitution theorem]: If A B and C[X] is a proposition containing X as a subproposition, then C[A] and C[B] are logically equivalent, where C[A] is the result of C with X in C replaced by A. ex: (p∨q) (q∨p), C[X] =def ~(p ∧ X) => ~(p∧ (p∨q) )~(p∧ (q∨p)) Transparency No. 1-34 ...
... Theorem2[substitution theorem]: If A B and C[X] is a proposition containing X as a subproposition, then C[A] and C[B] are logically equivalent, where C[A] is the result of C with X in C replaced by A. ex: (p∨q) (q∨p), C[X] =def ~(p ∧ X) => ~(p∧ (p∨q) )~(p∧ (q∨p)) Transparency No. 1-34 ...
Refinement Modal Logic
... equipped with may-transitions and must-transitions. A must-transition is available in every component that implements the modal specification, while a may-transition need not be. This is close to our definition of refinement, as it also is some kind of submodel quantifier, but the two notions are in ...
... equipped with may-transitions and must-transitions. A must-transition is available in every component that implements the modal specification, while a may-transition need not be. This is close to our definition of refinement, as it also is some kind of submodel quantifier, but the two notions are in ...
Structural Proof Theory
... based on axiomatic systems with just one or two rules of inference. Such systems can be useful as formal representations of what is provable, but the actual finding of proofs in axiomatic systems is next to impossible. A proof begins with instances of the axioms, but there is no systematic way of fi ...
... based on axiomatic systems with just one or two rules of inference. Such systems can be useful as formal representations of what is provable, but the actual finding of proofs in axiomatic systems is next to impossible. A proof begins with instances of the axioms, but there is no systematic way of fi ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.