Z. Luo, R. Pollack, P. Taylor. How to Use Lego. Manual, University of Edinburgh, Department of Computer Science, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are generalized ND style systems. The investigation carried out here can have also a significant practical aspect. In fact, Logical Frameworks (LF s) are the logic specification metalanguages of proof development environments (i.e. proof editors or, even better, proof assistants) in the style of [8, 19]. The systems we discuss, ultimately, are specifications (or encodings, or formalizations, or representations, of Modal Logics in the typed metalanguage of LF, and hence readily provide interactive proof assistants tailored to these logics. The main challenge in encoding Modal Logics in ....

....consideration. The specification methodology of LF s, in fact, forces the user to make precise all tacit, or informal, conventions, which always accompany any presentation of a logic. Any interactive proof development environment for the type theoretic metalanguage of an LF (e.g. Coq [8] LEGO [19]) can be readily turned into one for a specific logic. We need only to fix a suitable environment (the signature) i.e. a declaration of typed constants corresponding to the syntactic categories, term constructors, judgements, and rule schemata. Such an LF generated editor allows the user to ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual). Department of Computer Science, University of Edinburgh, Oct. 1989.

....logic specification language, i.e. as a Logical Framework (LF) Thus they can streamline the process of generating interactive proof development environments tailored to the peculiarities of any given logics. In fact, any interactive proof development environment for these type theories (LEGO [16], Coq [14] and ELF [21] can be readily turned into one for a specific logic, as soon as we fix a suitable environment corresponding to the encoding of the logic. Although these editors are not as e#cient as some of those especially designed for a specific logic, nevertheless Logical Frameworks ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual) . Department of Computer Science, University of Edinburgh, Oct. 1989.

....here, x is replaced by x # assuming x # does not occur in any of x, M x) m x) This is achieved by the three discharged rules about in, notin. The full power of LF is exploited: rules are treated just as any other judgment. We can use this encoding with proof editors based on LF, such as LEGO ([13]) and logic programming languages based on LF, such as Elf ( 20] LEGO can be successfully used to develop derivations ( computation traces) and to verify properties about the semantics themselves, e.g. equivalence between constructs. During the phase of operational semantics developing, we can ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual) . Department of Computer Science, University of Edinburgh, Oct. 1989.

....rule applications. In some systems the set of such programs is fixed; in others, users can write their own programs, called tactics, in some high level language, and the system will guarantee that no unsound inferences can be made. The systems LCF [8] Nuprl [4] Coq [5] Isabelle [15] LEGO [13], and HOL [7] although quite different in many respects, all have these two characteristics. This paper addresses the problem of integrating metavariables with tactic based interactive theorem proving systems of this kind. Some of the properties we require of such an integration are the ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (a preliminary user's manual). Technical Report LFCS-TN-27, Department of Computer Science, University of Edinburgh, October 1989.

....proof can be reloaded and used later. There are also basic facilities at the user level to save proofs in a printable format, in both L A T E X and PostScript formats. However these are not well integrated with the system, requiring processing by shell scripts outside of Jape. 3. 15 LEGO LEGO [40, 12, 31] is a meta level theorem prover written in ML. It is a typed system supporting the Calculus of Constructions and other similar logics (including Edinburgh LF) LEGO uses a goal directed proof method which it calls refinement proof. LEGO proofs are represented by terms in the Calculus of ....

....in the Calculus of Constructions, and specifically by their types (under the propositions as types principle) In a propositions as types system, verifying a proof is equivalent to type checking the type of a proof should be the proposition that it claims to prove. Robert Pollack s thesis [40], and some of his subsequent work [42] deals with the verification of a type checking algorithm for a particular form of the LEGO type theory. This work can be seen as the development of a particular instance of a verified proof checker. At the user level LEGO presents a basic commandline ....

R. Pollack. The theory of LEGO. Technical Report LFCS-TR-95-323, Department of Computer Science, University of Edinburgh, Scotland, 1994.

....to our calculus, where subtyping applies uniformly. Other related work includes that of Cardelli [7, 8] who gave basic definitions and ideas about semi decision procedures; Aspinall [2] who describes a system that has subtyping and dependent types but no type variables; Coquand [10] and Luo [14] who each consider forms of subtyping inductive data types in a dependent type theory, and Betarte and Tasistro (Chalmers University) who recently investigated adding dependent records to Martin L f s type theory. We want to continue the work begun here in several ways. The first goal is to find a ....

Z. Luo. Coercive subtyping. Draft paper, Department of Computer Science, University of Durham, 1995.

.... Gamma Gamma Psi Do(PMO) Gamma Gamma Psi R Space of Legitimate Plan Elaborations Figure 7: A Framework of Components in a Planning Scheduling System This approach is taken in systems like O Plan [Currie Tate 91] Tate et al. 94c] rt 1 [D Ambrosio et al. 87] opis [Smith 94] dipart [Pollack 94] tosca [Beck 93] etc. The approach fits well with the concept of treating plans as a set of constraints which can be refined as planning progresses. Some such systems can act in a non monotonic fashion by relaxing constraints in certain ways. Having the implied constraints or agenda as a ....

Pollack, M., DIPART Architecture, Technical Report, Department of Computer Science, University of Pittsburgh, PA 15213, USA, 1994.

....and Natural Deduction proof systems for Modal Logics, Logical Frameworks, Typed calculus, Proof Assistants. Introduction In this paper we address the issue of designing proof development environments (i.e. proof editors or, even better, proof assistants ) for Modal Logics, in the style of [11, 12]. To this end, we explore the possibility of using Logical Frameworks (LF s) based on Type Theory, such as the Edinburgh Logical Framework, the Calculus of Inductive Constructions or Martin Lof predicative Type Theory [7, 4, 22, 16] Logical Frameworks can be viewed as general logic ....

....consideration. The specification methodology of LF s, in fact, forces the user to make precise all tacit, or informal, conventions, which always accompany any presentation of a logic. Any interactive proof development environment for the type theoretic metalanguage of an LF (e.g. Coq [11] LEGO [12]) can be readily turned into one for a specific logic. We need only to fix a suitable environment (the signature) i.e. a declaration of typed constants corresponding to the syntactic categories, term constructors, judgements, and rule schemata. Such an LF generated editor allows the user to ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual). Department of Computer Science, University of Edinburgh, Oct. 1989.

....implementing search strategies [Pau90a] Such extensibility comes at a cost: the description of the theorem proving system must include the programming language. Extensible theorem provers are often comfortable for the experienced user, but bewildering to the novice. Other proof systems[CH85, LPT89] deny the user access to the meta language, allowing only a fixed set of proof commands to be invoked, thus achieving simplicity at the cost of flexibility. In many of our case studies, tacticals were used in the beginning only for building very primitive tactics, and thus might seem superfluous. ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (a preliminary user's manual). Technical Report LFCS-TN-27, Department of Computer Science, Edinburgh University, 1989.

.... be the PTS over terms with variables from V [ C and sorts from S, and the following rules (we choose the name SN because this system will help us in showing that 68 is SN) 4) 2; 4) 2; 4) 2; 2; 4) 4;4) 2; 4;4) 2; 2; 2) 4; 4;4) SN is contained in the system ECC (see [25]) As ECC is fi strongly normalizing, also SN is fi strongly normalizing. We present a translation of 68 contexts to SN contexts: Definition 5.32 Let Delta; Gamma be a legal 68 context. ffl We define j Deltaj by induction on the length of Gamma 1 : j j def = j Delta; b:U j def ....

Z. Luo. ECC and extended Calculus of Constructions. Department of Computer Science, University of Edinburgh.

....to our calculus, where subtyping applies uniformly. Other related work includes that of Cardelli [7, 8] who gave basic de Thetanitions and ideas about semi decision procedures; Aspinall [2] who describes a system that has subtyping and dependent types but no type variables; Coquand [10] and Luo [14] who each consider forms of subtyping inductive data types in a dependent type theory, and Betarte and Tasistro (Chalmers University) who recently investigated adding dependent records to Martin L#f s type theory. We want to continue the work begun here in several ways. The Thetarst goal is to ....

Z. Luo. Coercive subtyping. Draft paper, Department of Computer Science, University of Durham, 1995.

....are generalized ND style systems. The investigation carried out here can have also a significant practical aspect. In fact, Logical Frameworks (LF s) are the logic specification metalanguages of proof development environments (i.e. proof editors or, even better, proof assistants) in the style of [8, 19]. The systems we discuss, ultimately, are specifications (or encodings, or formalizations, or representations, of Modal Logics in the typed metalanguage of LF, and hence readily provide interactive proof assistants tailored to these logics. The main challenge in encoding Modal Logics in ....

....consideration. The specification methodology of LF s, in fact, forces the user to make precise all tacit, or informal, conventions, which always accompany any presentation of a logic. Any interactive proof development environment for the type theoretic metalanguage of an LF (e.g. Coq [8] LEGO [19]) can be readily turned into one for a specific logic. We need only to fix a suitable environment (the signature) i.e. a declaration of typed constants corresponding to the syntactic categories, term constructors, judgements, and rule schemata. Such an LF generated editor allows the user to ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual). Department of Computer Science, University of Edinburgh, Oct. 1989.

....logic specification language, i.e. as a Logical Framework (LF) Thus they can streamline the process of generating interactive proof development environments tailored to the peculiarities of any given logics. In fact, any interactive proof development environment for these type theories (LEGO [16], Coq [14] and ELF [21] can be readily turned into one for a specific logic, as soon as we fix a suitable environment corresponding to the encoding of the logic. Although these editors are not as efficient as some of those especially designed for a specific logic, nevertheless Logical Frameworks ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO (A Preliminary User's Manual) . Department of Computer Science, University of Edinburgh, Oct. 1989.

....produce a list of issues or agenda entries which is then used to drive a processing cycle of choosing a plan modification operator and then executing it to modify the plan state. Figure 7 shows this graphically. This approach is taken in systems like O Plan [8] 34] RT 1 [3] OPIS [25] DIPART [23], TOSCA [5] etc. The approach fits well with the concept of treating plans as a set of constraints which can be refined as planning progresses. Some such systems can act in a non monotonic fashion by relaxing constraints in certain ways. Having the implied constraints or agenda as a formal part ....

Pollack, M., DIPART Architecture, Technical Report, Department of Computer Science, University of Pittsburgh, PA 15213, USA, 1994.

.... The first is the algebraic school, surveyed in [Wir90] The second is the family of type theoretic languages, represented for example by the systems for the non constructive type theories, Hol [Cam89] and Lcf [WGM79, Pau87] and for the constructive type theories, Nuprl [C 86] and Lego [LPT89] Both families have a long tradition which reaches back to the beginning of this century, and all formal methods for specification and development are based on them to some extent. We will discuss their influence on Spectrum more thoroughly in the next section. Spectrum is a language which ....

Z. Luo, R. Pollack, and P. Taylor. How to use LEGO. Department of Computer Science, University of Edinburgh, 1989.

....aspects: first a notion of an algebraic system is proposed, then the monoid is defined by successively adding to theories for groupoids and semigroups. Arity is a variant of the natural numbers, over types rather than propositions. The notation f Delta Delta Deltag, from the Lego implementation [32] of the Calculus of Constructions, denotes a product ( Pi) type. The form: Prophnamei[hcontext Gamma elementsi]hpropositionexpressioni denotes that hnamei when applied to elements of the appropriate type, as specified in hcontext Gamma elementsi will be a Prop with value ....

....the process via the structure it imposes. Chapter 3 Examples of Presentation Construction and Manipulation MF defines a language to manage sequences of statements in a logical framework. For the purposes of the definition of MF we chose the Calculus of Constructions as implemented in LEGO [31] [32], although any logical framework with certain properties will do (see Chapter 1) The goal of this chapter is to give an understanding of the components of MF by introducing some terminology that will be used throughout the description of MF, presenting an example of an MF style derivation, and ....

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Luo, Z., Pollack, R., and Taylor, P. How to use Lego. Tech. Rep. ECSLFCS -92-211, LFCS Report Series, 1992. University of Edinburgh, Department of Computer Science.

....development. For example, the so called proofs as programs paradigm [2, 50, 59] according to which a constructive proof of a speci cation corresponds to a satisfying program, has led to a method of program synthesis from proofs which has been implemented in a number of interactive proof systems [21, 39, 42, 30, 47, 3]. It is the objective of this project to pursue current research on the above mentioned applications of domain theory and proof theory in Computer Science, and to strengthen the existing links between these elds. In domain theory various open problems in connection with the computational and ....

Z. Luo, R. Pollack, P. Taylor. How to Use Lego. Manual, University of Edinburgh, Department of Computer Science, 1989.

....are represented by # terms. As it is well known, Natural Deduction style systems are more suited to the practical usage, since they allow for developing proofs the way mathematicians normally reason. These type theories have been implemented in logic independent systems such as Coq, LEGO and ALF [2, 9, 10]. These systems can be readily turned into interactive proof development environments for a specific logic: we need only to provide the specification of the formal system (the signature) i.e. a declaration of typed constants corresponding to the syntactic categories, term constructors, judgments, ....

Z. Luo, R. Pollack, et al. The LEGO proof assistant. Department of Computer Science, University of Edinburgh. http://www.dcs.ed.ac.uk/home/lego

....are represented by terms. As it is well known, Natural Deduction style systems are more suited to the practical usage, since they allow for developing proofs the way mathematicians normally reason. These type theories have been implemented in logic independent systems such as Coq, LEGO and ALF [2, 9, 10]. These systems can be readily turned into interactive proof development environments for a specific logic: we need only to provide the specification of the formal system (the signature) i.e. a declaration of typed constants corresponding to the syntactic categories, term constructors, judgments, ....

Z. Luo, R. Pollack, et al. The LEGO proof assistant. Department of Computer Science, University of Edinburgh. http://www.dcs.ed.ac.uk/home/lego

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Z. Luo, R. Pollack, and P. Taylor. How to use LEGO. Department of Computer Science, University of Edinburgh, Oct. 1989.

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Z. Luo, R. Pollack, and P. Taylor. How to use LEGO. Department of Computer Science, University of Edinburgh, Oct. 1989.

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