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First-Order Theorem Proving and Vampire
First-Order Theorem Proving and Vampire

... http://www.tptp.org contains a large collection of first-order problems. For representing these problems it uses the TPTP syntax, which is understood by all modern theorem provers, including Vampire. In the TPTP syntax this group theory problem can be written down as follows: %---- 1 * x = 1 fof(lef ...
a-logic - Digital Commons@Wayne State University
a-logic - Digital [email protected] State University

... Whitehead’s great book, Principia Mathematica (1913) of Quine’s Mathematical Logic (1940) and Methods of Logic (4th ed.,1982) and of hundreds of other textbooks and treatises which have the same set of theorems, the same semantical foundations, and use the same concepts of validity and logical truth ...
Announcement as effort on topological spaces
Announcement as effort on topological spaces

code-carrying theory - Computer Science at RPI
code-carrying theory - Computer Science at RPI

... reachable, his door was always open. We held hundreds of meetings, sometimes discussing for hours either in his office or through email. There were times that he even worked harder on this project than I did. He is a good friend, a thoughtful person, and a real problem solver. I will always miss his ...
ppt - CS603
ppt - CS603

Color - Alex Kocurek
Color - Alex Kocurek

2102-282 Digital Electronics - IC Design & Application Research Lab.
2102-282 Digital Electronics - IC Design & Application Research Lab.

... Hold time, thold is the time that the data inputs must remain valid after the clock edge ...
Discrete Mathematics
Discrete Mathematics

PhD Thesis First-Order Logic Investigation of Relativity Theory with
PhD Thesis First-Order Logic Investigation of Relativity Theory with

Incompleteness
Incompleteness

... Definition 1.7. Let A, B be two structures for a first-order language L “ tRi , fi , ci u. A homomorphism π from A to B is a map π : A Ñ B satisfying: RA pa1 , . . . an q iff RB pπpa1 q, . . . πpan qq, πpf A pa1 , . . . , an qq “ f B pπpa1 q, . . . , πpan qq, and πpcA q “ cB for all a1 , . . . , an ...
JUXTAPOSITION - Brown University
JUXTAPOSITION - Brown University

... of propositional logics. The approach to semantics employed here is broadly algebraic. I consider two semantic frameworks. The first involves sets of logical matrices, algebras with an arbitrary set of designated values. The second, more interesting, framework involves sets of unital matrices, algeb ...
Simply Logical: Intelligent Reasoning by Example
Simply Logical: Intelligent Reasoning by Example

... presentation starts with propositional clausal logic, and proceeds via relational clausal logic (without functors) to full clausal logic, and finally arrives at definite clause logic. Since the semantics of clausal logic is defined in its own terms, without reference to the kind of models employed i ...
Calculating Functional Programs - Research School of Computer
Calculating Functional Programs - Research School of Computer

a thesis submitted in partial fulfillment of the requirements for the
a thesis submitted in partial fulfillment of the requirements for the

Independence logic and tuple existence atoms
Independence logic and tuple existence atoms

... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x  ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Artificial Intelligence
Artificial Intelligence

... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...
Standard ML: A Quick Tutorial
Standard ML: A Quick Tutorial

... accomplished by carrying the state around explicitly rather than implicitly  Looping is accomplished via recursion rather than sequencing ...
Lambda Calculus
Lambda Calculus

Hilbert`s Program Then and Now
Hilbert`s Program Then and Now

Measure Quantifier in Monadic Second Order Logic
Measure Quantifier in Monadic Second Order Logic

funprog
funprog

... E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled sep ...
Foundations of Databases - Free University of Bozen
Foundations of Databases - Free University of Bozen

Predicate Logic
Predicate Logic

Introduction to Computational Logic
Introduction to Computational Logic

... and interactive theorem proving with the proof assistant Coq. At Saarland University the course is taught in this format since 2010. Students are expected to be familiar with basic functional programming and the structure of mathematical definitions and proofs. Talented students at Saarland Universi ...
5 model theory of modal logic
5 model theory of modal logic

1 2 3 4 5 ... 69 >

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.
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