DJ Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as Edinburgh University Computer Science Department Technical Report ECS-LFCS-90-125. Home/Search Document Not in Database Summary Related Articles Check |
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A Framework for Defining Logics - Harper, Honsell, Plotkin (1987) (380 citations) (Correct)
....the AUTOMATH languages. Its proof theoretic strength is quite low (equivalent to that of the simply typed calculus) In fact, the LF type system is chosen to be as weak as possible so as to provide scope for the development of practical unification and matching algorithms for use in applications [44, 16]. The type system has three levels of terms: objects, types (which classify objects) and kinds (which classify families of types) There is also a formal notion of definitional equality, which we take to be fi conversion; all matters relating to encodings of logics are treated up to this ....
.... itself, Martin Lof s type theory, and the Damas Milner type assignment system [22] A natural deduction approach to operational semantics based on the ideas of LF has also been developed [5] A general theory of search, including a unification algorithm for the LF type theory, has been developed [44, 45]. Elliott has also developed a unification algorithm for LF [16] which has been used by Pfenning as the basis for a logic programming language based on the LF type theory [41] An equational variant of LF is introduced, along with the basic model theoretic results, in [21] Three different ....
Pym, D. Proofs, Search and Computation in General Logic. PhD thesis, Edinburgh University, 1990. Available as Edinburgh University Computer Science Department Technical Report ECS--LFCS--90--125.
Kripke Resource Models of a Dependently-Typed, Bunched.. - Ishtiaq, Pym (1999) (2 citations) Self-citation (Pym) (Correct)
....(e.g. a term) X corresponds to X ; each x i corresponds to a place holder for the encoding of J i ; and M is a meta logic term corresponding to the encoding of . The LF logical framework consists of the calculus together with the judgements as types mechanism for representing logics [1, 9, 28]. One consequence of this method of encoding is that encoded systems inherit the structural properties of the meta logic. Now, the structural strength of LF is determined by the structural strength of the calculus which, as it stands in propositionsas types correspondence with the f ; ....
DJ Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as Edinburgh University Computer Science Department Technical Report ECS-LFCS-90-125.
Kripke Resource Models of a Dependently-Typed, Bunched.. - Ishtiaq, Pym (1999) (2 citations) Self-citation (Pym) (Correct)
.... term) Gamma X corresponds to X ; each x i corresponds to a place holder for the encoding of J i ; and M ffi is a meta logic term corresponding to the encoding of ffi. The LF logical framework consists of the Pi calculus together with the judgements as types mechanism for representing logics [1, 9, 25]. One consequence of this method of encoding is that encoded systems inherit the structural properties of the meta logic. Now, the structural strength of LF is determined by the structural strength of the Pi calculus which, as it stands in propositions as types correspondence with the f ; ....
DJ Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as Edinburgh University Computer Science Department Technical Report ECSLFCS -90-125.
A Relevant Analysis of Natural Deduction - Ishtiaq, Pym (1996) (28 citations) Self-citation (Pym) (Correct)
....widely in mathematical [4, 16, 25, 36] philosophical [3, 14, 33] and computational [1, 20, 24, 32, 37] logic. We present a study of a logical framework, RLF, for defining natural deduction presentations of such logics. 1 RLF consists in a language together, in a manner similar to that of LF [5, 18, 28], with a representation mechanism. The language of RLF, the calculus, is a system of first order linear dependent function types which uses a function to describe the degree of sharing of variables between functions and their arguments. The representation mechanism is judgements as types, ....
....a relevant calculus. Finally, in x 6, we consider the further work that arises from our study. 2 Motivation Logical frameworks are formal meta logics which, inter alia, provide languages for describing logics in a manner that is suitable for mechanical implementation. The LF logical framework [5, 18, 28] provides such a metatheory and is suitable for logics which have at least the structural strength of minimal propositional logic. We wish to study a logical framework for describing relevant logics. Now, in order to describe a logical framework one must: 1. Characterize the class of object logics ....
D.J. Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as Edinburgh University Computer Science Department Technical Report ECS-LFCS-90-125.
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