Recent Progress in Field Programmable Gate Arrays
... choices can be made! Primitive element must be classified as a “complete logic family”. • A primitive gate like a NAND gate • A 2/1 mux (this happens to be a complete logic family) • A Lookup table (I.e, 16x1 lookup table can implement any 4 input logic function). ...
... choices can be made! Primitive element must be classified as a “complete logic family”. • A primitive gate like a NAND gate • A 2/1 mux (this happens to be a complete logic family) • A Lookup table (I.e, 16x1 lookup table can implement any 4 input logic function). ...
Compiling Functional Programming Languages (FPLs) λ
... Here’s evaluation of ’FAC 1’ to show the effect of recursion: FAC = Y H FAC 1 = Y H 1 = H (Y H) 1 = λf λn. IF (= n 0) 1 (× n (f (− n 1))) (Y H) 1 = λn. IF (= n 0) 1 (× n (Y H (− n 1))) 1 = IF (= 1 0) 1 (× 1 (Y H (− 1 1))) = × 1 (Y H 0) = × 1 (H (Y H) 0) = × 1 ((λf λn. IF (= n 0) 1 (× n (f (− n 1))) ...
... Here’s evaluation of ’FAC 1’ to show the effect of recursion: FAC = Y H FAC 1 = Y H 1 = H (Y H) 1 = λf λn. IF (= n 0) 1 (× n (f (− n 1))) (Y H) 1 = λn. IF (= n 0) 1 (× n (Y H (− n 1))) 1 = IF (= 1 0) 1 (× 1 (Y H (− 1 1))) = × 1 (Y H 0) = × 1 (H (Y H) 0) = × 1 ((λf λn. IF (= n 0) 1 (× n (f (− n 1))) ...
Proofs in Propositional Logic
... The number of subgoals that remain to be solved decreases only when some tactic application generates 0 new subgoals. The interactive search of a proof is finished when there remain no subgoals to solve. The Qed command makes Coq do the following ...
... The number of subgoals that remain to be solved decreases only when some tactic application generates 0 new subgoals. The interactive search of a proof is finished when there remain no subgoals to solve. The Qed command makes Coq do the following ...
S. P. Odintsov “REDUCTIO AD ABSURDUM” AND LUKASIEWICZ`S
... to finish an investigation of the class of Lj-extensions with an attempt to overcome it. We try to do it by emerging the class of Lj-extensions in a more general class of paraconsistent logics and pointing out some special property distinguishing extensions of minimal logic in the latter class. We su ...
... to finish an investigation of the class of Lj-extensions with an attempt to overcome it. We try to do it by emerging the class of Lj-extensions in a more general class of paraconsistent logics and pointing out some special property distinguishing extensions of minimal logic in the latter class. We su ...
Chapter1_Parts2
... are a computer science major or you are not a freshman.”! One Solution: Let a, c, and f represent respectively “You can access the internet from campus,” “You are a computer science major,” and “You are a freshman.”! a→ (c ∨ ¬ f ) ...
... are a computer science major or you are not a freshman.”! One Solution: Let a, c, and f represent respectively “You can access the internet from campus,” “You are a computer science major,” and “You are a freshman.”! a→ (c ∨ ¬ f ) ...
Logic Programming, Functional Programming, and Inductive
... monotone. However, perhaps the database can be partitioned into several inductive definitions, so that each negation refers to a set that has already been defined (the dependency graph must be acyclic). The database can then be interpreted as an iterated inductive definition (via some treatment of f ...
... monotone. However, perhaps the database can be partitioned into several inductive definitions, so that each negation refers to a set that has already been defined (the dependency graph must be acyclic). The database can then be interpreted as an iterated inductive definition (via some treatment of f ...
Deciding Intuitionistic Propositional Logic via Translation into
... possible worlds, a(v) denotes a being forced at v, w0 denotes some arbitrary “root”-world and A is a conjunction of axiom formulas encoding the logic-specific properties of R (e.g. reflexivity, transitivity, symmetry, etc.). This technique has two major disadvantages: On the one hand the classical t ...
... possible worlds, a(v) denotes a being forced at v, w0 denotes some arbitrary “root”-world and A is a conjunction of axiom formulas encoding the logic-specific properties of R (e.g. reflexivity, transitivity, symmetry, etc.). This technique has two major disadvantages: On the one hand the classical t ...
Aristotle, Boole, and Categories
... The first major effort to bring Aristotle’s syllogistic up to the standards of rigor of 20th century logic was carried out by Lukasiewicz in his book Aristotle’s Syllogistic [7]. Lukasiewicz cast syllogistic deduction in the framework of predicate calculus axiomatized by a Hilbert system, rendering ...
... The first major effort to bring Aristotle’s syllogistic up to the standards of rigor of 20th century logic was carried out by Lukasiewicz in his book Aristotle’s Syllogistic [7]. Lukasiewicz cast syllogistic deduction in the framework of predicate calculus axiomatized by a Hilbert system, rendering ...
Module 4: Propositional Logic Proofs
... Proof strategies • Work backwards from the end • Play with alternate forms of premises • Identify and eliminate irrelevant information • Identify and focus on critical information • Step back from the problem frequently to think about assumptions you might have wrong or other approaches you could t ...
... Proof strategies • Work backwards from the end • Play with alternate forms of premises • Identify and eliminate irrelevant information • Identify and focus on critical information • Step back from the problem frequently to think about assumptions you might have wrong or other approaches you could t ...
Programming with Classical Proofs
... corresponds to a proof of totality of a recursive function. This leads to the area of classical program extraction. There have been several approaches to extracting the computational content of these classical proofs. It was discovered by Griffin in 1989 [20] that inference by contradiction correspo ...
... corresponds to a proof of totality of a recursive function. This leads to the area of classical program extraction. There have been several approaches to extracting the computational content of these classical proofs. It was discovered by Griffin in 1989 [20] that inference by contradiction correspo ...
Is `structure` a clear notion? - University of Illinois at Chicago
... step, singling out the ‘primitive concepts’. Considerable reflection from both mathematical and philosophical standpoints may be involved in the choice. For example, suppose one wants to study ‘Napoleon’s theorem’ that the lines joining the midpoints of any quadrilateral form a parallelogram. At fir ...
... step, singling out the ‘primitive concepts’. Considerable reflection from both mathematical and philosophical standpoints may be involved in the choice. For example, suppose one wants to study ‘Napoleon’s theorem’ that the lines joining the midpoints of any quadrilateral form a parallelogram. At fir ...
proceedings - CERN Indico
... redundancy management to the chip level. Radiation effects on a single FPGA are increasingly likely to have system level consequences, and will need to be addressed in current and future designs. ...
... redundancy management to the chip level. Radiation effects on a single FPGA are increasingly likely to have system level consequences, and will need to be addressed in current and future designs. ...
pdf - at www.arxiv.org.
... problems. Firstly, it does not work well for computations that produce infinite formulas with irrational tree structure, as in this case the derivations do not feature unifiable subgoals. Secondly, CoLP is neither sound nor complete relative to computations at infinity; and thus is not suitable for ...
... problems. Firstly, it does not work well for computations that produce infinite formulas with irrational tree structure, as in this case the derivations do not feature unifiable subgoals. Secondly, CoLP is neither sound nor complete relative to computations at infinity; and thus is not suitable for ...
Document
... methods used to construct valid arguments. An argument is a related sequence of statements to demonstrate the truth of an assertion ...
... methods used to construct valid arguments. An argument is a related sequence of statements to demonstrate the truth of an assertion ...
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.