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Predicate logic. Formal and informal proofs
Predicate logic. Formal and informal proofs

unit 8 - WordPress.com
unit 8 - WordPress.com

Thesis Proposal: A Logical Foundation for Session-based
Thesis Proposal: A Logical Foundation for Session-based

... used to give a logically motivated account of parallel evaluation strategies on λ-terms through canonical embeddings of intuitionistic logic in linear logic. One remarkable result is that the resulting embeddings induce a form of sharing (as in futures, relaxing the sequentiality constraints of call ...
On Action Logic
On Action Logic

An introduction to functional programming using Haskell
An introduction to functional programming using Haskell

1992-Ideal Introspective Belief
1992-Ideal Introspective Belief

... This is a simple translation of DL into a minimal AE logic. It is the same as the translation in [5] (except for the use of a A Q instead of a), but there it was necessary to limit the extensions of the AE logic to strongly grounded ones, a syntactic method based on the form of the premises. No such ...
COMP 356 Programming Language Structures Notes for Chapter 15
COMP 356 Programming Language Structures Notes for Chapter 15

ppt - FSU Computer Science
ppt - FSU Computer Science

... Useful features are found in functional languages that are often missing in procedural languages or have been adopted by modern programming languages: • First-class function values: the ability of functions to return newly constructed functions. • Higher-order functions: functions that take other fu ...
Godel`s Incompleteness Theorem
Godel`s Incompleteness Theorem

A Dynamic and Differential CMOS Logic Style to Resist Power and
A Dynamic and Differential CMOS Logic Style to Resist Power and

... Static Complementary CMOS Logic (SC-CMOS), which is the default logic style in standard cell libraries used for security IC's, primarily consumes its energy from the power supply when the output sees a ‘0’ to ‘1’ transition. During the ‘1’ to ‘0’ transition, the energy previously stored in the outpu ...
Judgment and consequence relations
Judgment and consequence relations

... Our standard case is that L is the language of monomodal logic. A (modal) logic is a subset L of L that contains all theorems of PC, the formula p p0 Ñ p1 q Ñ pp0 Ñ p1 q, and is closed under substitution, and Modus Ponens (MP). L is normal if it is also closed under necessitation, that is, if fro ...
Second-Order Logic and Fagin`s Theorem
Second-Order Logic and Fagin`s Theorem

A Note on Bootstrapping Intuitionistic Bounded Arithmetic
A Note on Bootstrapping Intuitionistic Bounded Arithmetic

Belief Revision in non
Belief Revision in non

Dynamic logic of propositional assignments
Dynamic logic of propositional assignments

... the computational complexity of model checking with DL-PA is EXPTIME-complete. In contrast, the complexity of model checking a transition system with PDL is PTIME-complete. As we shall show, the complexity of DL-PA satisfiability checking remains EXPTIME-complete, which is also the complexity of PDL ...
higher-order logic - University of Amsterdam
higher-order logic - University of Amsterdam

Proof analysis beyond geometric theories: from rule systems to
Proof analysis beyond geometric theories: from rule systems to

A Mathematical Introduction to Modal Logic
A Mathematical Introduction to Modal Logic

... research areas show that modal logic is a promising field with many interdisciplinary research opportunities (see my webpage with many small notes discussing variety of modal logics). These lecture notes were prepared for the Turkish Mathematical Society 2009 Summer School. The intended purpose is t ...
Supplemental Reading 1
Supplemental Reading 1

... If we want to indicate the new variables we use in the recursive induction rule we write the rule adding this information: ...
Document
Document

How Does Resolution Works in Propositional Calculus and
How Does Resolution Works in Propositional Calculus and

Arquitectura de una FPGAs de Xilinx
Arquitectura de una FPGAs de Xilinx

... – Local routing provides feedback between slices in the same CLB, and it provides routing to neighboring CLBs – A switch matrix provides access to general routing resources ...
A Simple Tableau System for the Logic of Elsewhere
A Simple Tableau System for the Logic of Elsewhere

Chapter One {Word doc}
Chapter One {Word doc}

... Note: Equivalent to #14 {A student from this class did not watch any Eagles games last season; OR: It is not true that every student watched an Eagles game last ...
Chapter 7 - Dyessick
Chapter 7 - Dyessick

< 1 ... 21 22 23 24 25 26 27 28 29 ... 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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