Notes - Cornell Computer Science
... interesting problems. That language should have a rich type system. Types provide high value in precisely specifying programming tasks and in reasoning about whether a program accomplishes them “according to the spec.” 2.It is characteristic of Cornell CS that the enduring intellectual themes are p ...
... interesting problems. That language should have a rich type system. Types provide high value in precisely specifying programming tasks and in reasoning about whether a program accomplishes them “according to the spec.” 2.It is characteristic of Cornell CS that the enduring intellectual themes are p ...
CS-Intro-AI-LISP - Geometric and Intelligent Computing Laboratory
... • Programmers who are used to other langs sometimes fail to see the point of lambda expressions. Why are they useful? – It's a pain to think up names and to clutter up a program with lots of functions that are only used very locally; – MORE IMPORTANT: We can create new functions at run time ...
... • Programmers who are used to other langs sometimes fail to see the point of lambda expressions. Why are they useful? – It's a pain to think up names and to clutter up a program with lots of functions that are only used very locally; – MORE IMPORTANT: We can create new functions at run time ...
Functional Languages
... – a polymorphic function that has a return type of bool, • assumes only that its two arguments are of the same type and can have the equality operator applied to them. ...
... – a polymorphic function that has a return type of bool, • assumes only that its two arguments are of the same type and can have the equality operator applied to them. ...
Intermediate Logic
... will introduce you to the concepts, results, and methods of formal logic necessary to understand and appreciate these applications as well as the limitations of formal logic. It will be mathematical in that you will be required to master abstract formal concepts and to prove theorems about logic (no ...
... will introduce you to the concepts, results, and methods of formal logic necessary to understand and appreciate these applications as well as the limitations of formal logic. It will be mathematical in that you will be required to master abstract formal concepts and to prove theorems about logic (no ...
The countdown problem - School of Computer Science
... Countdown is a popular quiz programme on British television that includes a numbers game that we shall refer to as the countdown problem. The essence of the problem is as follows: given a sequence of source numbers and a single target number, attempt to construct an arithmetic expression using each ...
... Countdown is a popular quiz programme on British television that includes a numbers game that we shall refer to as the countdown problem. The essence of the problem is as follows: given a sequence of source numbers and a single target number, attempt to construct an arithmetic expression using each ...
YABLO WITHOUT GODEL
... By proving paradoxes from very weak assumption one can hope to reveal what is really needed to arrive at a contradiction and what the source of paradox is. Arithmetic provides us with very strong tools that are not required to arrive at the paradox. In particular, it provides us with the diagonal le ...
... By proving paradoxes from very weak assumption one can hope to reveal what is really needed to arrive at a contradiction and what the source of paradox is. Arithmetic provides us with very strong tools that are not required to arrive at the paradox. In particular, it provides us with the diagonal le ...
Essentials Of Symbolic Logic
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...
Drexel-CS-Intro-AI-LISP
... • Programmers who are used to other langs sometimes fail to see the point of lambda expressions. Why are they useful? – It's a pain to think up names and to clutter up a program with lots of functions that are only used very locally; – MORE IMPORTANT: We can create new functions at run time ...
... • Programmers who are used to other langs sometimes fail to see the point of lambda expressions. Why are they useful? – It's a pain to think up names and to clutter up a program with lots of functions that are only used very locally; – MORE IMPORTANT: We can create new functions at run time ...
functional form
... • “There are quite a few new challenges, most of them are about scale, such as scaling your database, scaling your users sessions etc, but one of the most significant challenges is scaling your algorithm by parallelizing it.” • “The problem is that imperative languages keep state. The state is in th ...
... • “There are quite a few new challenges, most of them are about scale, such as scaling your database, scaling your users sessions etc, but one of the most significant challenges is scaling your algorithm by parallelizing it.” • “The problem is that imperative languages keep state. The state is in th ...
Haskell
... Integer type is integers of arbitrary precision. The Float type which is real floating point numbers with single precision, and the Double type is real floating point numbers with double precision. Lists in Haskell are homogeneous data structures, or sequences of values which all have the same type. ...
... Integer type is integers of arbitrary precision. The Float type which is real floating point numbers with single precision, and the Double type is real floating point numbers with double precision. Lists in Haskell are homogeneous data structures, or sequences of values which all have the same type. ...
Boolean Connectives and Formal Proofs - FB3
... The first rule we use in the above proof is Identity Introd rule allows you to introduce, for any name (or complex term) the proof, the assertion n = n. You are allowed to do this at an proof, and need not cite any earlier step as justification. We w our statement of this rule in the following way: ...
... The first rule we use in the above proof is Identity Introd rule allows you to introduce, for any name (or complex term) the proof, the assertion n = n. You are allowed to do this at an proof, and need not cite any earlier step as justification. We w our statement of this rule in the following way: ...
Supplemental Reading 1
... those elements satisfying condition P . This concept is closely related to the set theory notion written the same way and denoting the \subset" of A satisfying the predicate P . In axiomatic set theory the existence of this set is guaranteed by the separation axiom. The idea is that the predicate P ...
... those elements satisfying condition P . This concept is closely related to the set theory notion written the same way and denoting the \subset" of A satisfying the predicate P . In axiomatic set theory the existence of this set is guaranteed by the separation axiom. The idea is that the predicate P ...
A fully abstract semantics for a higher
... We can show that the denotational semantics is fully abstract for the operational semantics using a variant of Abramsky (1989) and Ong’s (1988) lazy lambda-calculus and Abramsky’s (1991) domain theory in logical form. This is similar to Ong’s (1993) use of a program logic for the untyped λ-calculus, ...
... We can show that the denotational semantics is fully abstract for the operational semantics using a variant of Abramsky (1989) and Ong’s (1988) lazy lambda-calculus and Abramsky’s (1991) domain theory in logical form. This is similar to Ong’s (1993) use of a program logic for the untyped λ-calculus, ...
Intuitionistic Logic - Institute for Logic, Language and Computation
... in this short course. Even though we approach the subject for the most part only formally, it is good to have a general introduction to intuitionism. This we give in section 2 in which also natural deduction is introduced. For more extensive introductions see [35],[17]. After this introduction we st ...
... in this short course. Even though we approach the subject for the most part only formally, it is good to have a general introduction to intuitionism. This we give in section 2 in which also natural deduction is introduced. For more extensive introductions see [35],[17]. After this introduction we st ...
FC §1.1, §1.2 - Mypage at Indiana University
... with which we began this chapter. Logical deduction will be a major topic of this chapter; under the name of proof , it will be the last major topic of this chapter, and a major tool for the rest of this book. ...
... with which we began this chapter. Logical deduction will be a major topic of this chapter; under the name of proof , it will be the last major topic of this chapter, and a major tool for the rest of this book. ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
Sequent Calculus in Natural Deduction Style
... since Gentzen, weakening and contraction have been made into steps independent of the application of these rules. Cut elimination is much more complicated than normalization, with numerous cases of permutation of cut that do not have any correspondence in the normalization process. Moreover, in usua ...
... since Gentzen, weakening and contraction have been made into steps independent of the application of these rules. Cut elimination is much more complicated than normalization, with numerous cases of permutation of cut that do not have any correspondence in the normalization process. Moreover, in usua ...
Formal systems of fuzzy logic and their fragments∗
... L + A we denote the logic resulting from L by adding a set of axioms A to its axiomatic system. A logic L2 in a language L2 is said to be an expansion of L1 in L1 if for each L1 -theory T and each L1 -formula ϕ we have T `L1 ϕ implies T `L2 ϕ. The expansion is conservative if also T `L2 ϕ implies T ...
... L + A we denote the logic resulting from L by adding a set of axioms A to its axiomatic system. A logic L2 in a language L2 is said to be an expansion of L1 in L1 if for each L1 -theory T and each L1 -formula ϕ we have T `L1 ϕ implies T `L2 ϕ. The expansion is conservative if also T `L2 ϕ implies T ...
full text (.pdf)
... Propositional Hoare logic (PHL) consists of atomic proposition and program symbols, the usual propositional connectives, while program constructs, and PCAs built from these. Atomic programs are interpreted as binary relations on a set M and atomic propositions are interpreted as subsets of M. The de ...
... Propositional Hoare logic (PHL) consists of atomic proposition and program symbols, the usual propositional connectives, while program constructs, and PCAs built from these. Atomic programs are interpreted as binary relations on a set M and atomic propositions are interpreted as subsets of M. The de ...
Using linear logic to reason about sequent systems
... that all other linear logic connectives can be defined from these. Proof search using this collection of connectives can be restricted so that simple goal-directed proof search (using the technical device of multiple-conclusion uniform proofs [Mil93]) is complete. Thus, Forum makes it possible to cl ...
... that all other linear logic connectives can be defined from these. Proof search using this collection of connectives can be restricted so that simple goal-directed proof search (using the technical device of multiple-conclusion uniform proofs [Mil93]) is complete. Thus, Forum makes it possible to cl ...
page 139 MINIMIZING AMBIGUITY AND
... we tolerate some logical abnormality (e.g. inconsistency or ambiguity), we should not tolerate more abnormal cases than required in order to safeguard a the theory from triviality. I think it is only natural that we hang on to the minimal abnormality strategy when we are dealing with ambiguity. It i ...
... we tolerate some logical abnormality (e.g. inconsistency or ambiguity), we should not tolerate more abnormal cases than required in order to safeguard a the theory from triviality. I think it is only natural that we hang on to the minimal abnormality strategy when we are dealing with ambiguity. It i ...
Using linear logic to reason about sequent systems ?
... [Mil93]) is complete. Thus, Forum makes it possible to claim that all of linear logic can be seen as an abstract logic programming language [MNPS91]. Forum has been used to specify a number of computation systems, ranging from objectoriented languages [DM95], imperative programming features [Mil96,C ...
... [Mil93]) is complete. Thus, Forum makes it possible to claim that all of linear logic can be seen as an abstract logic programming language [MNPS91]. Forum has been used to specify a number of computation systems, ranging from objectoriented languages [DM95], imperative programming features [Mil96,C ...
Reading 2 - UConn Logic Group
... mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). The Curry-Howard isomorphism transliterates natural derivations in Int to typed !-terms. It is a very important generic functional reading of logica ...
... mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). The Curry-Howard isomorphism transliterates natural derivations in Int to typed !-terms. It is a very important generic functional reading of logica ...