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Derivation of a parsing algorithm in martin-löf's theory of types

Paul Chisholm
1987 Science of Computer Programming  
Here. a parser for a simple expression language is specified and a program derived from the proof of correctness of its specification using the formalism of Type Theory.  ...  Type Theory was initially developed as a formalizarion of consrructive mathematics but Martin-LGf has pointed out that it can also be viewed as a formal system for the development of provably correct programs  ...  Derivation of a parsing algorithm in a theory of types (b) generalizing the notion of a function.  ... 
doi:10.1016/0167-6423(87)90002-5 fatcat:qrpzowcf5bdzje5hurkpg5p6ta

A formulation of the simple theory of types (for Isabelle) [chapter]

Lawrence C. Paulson
1990 Lecture Notes in Computer Science  
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty.  ...  Descriptions (the η-operator) introduce the Axiom of Choice. Higher-order logic is obtained through reflection between formulae and terms of type bool .  ...  The idea of orders appears today in the universes of Martin-Löf's Type Theory [22] , where propositions are represented by types.  ... 
doi:10.1007/3-540-52335-9_58 fatcat:hhyrxzj6rnbjjcn2zrmp35uqaa

Type checking dependent (record) types and subtyping

GUSTAVO BETARTE
2000 Journal of functional programming  
In this work we put forward an algorithm for the mechanical verification of an extension of Martin-Löf's theory of types with dependent record types and subtyping.  ...  Capsule Review This paper describes a specification and implementation of a proof-checker for an extension of Martin-Löf's theory of types.  ...  Acknowledgements The author is grateful to Cristina Cornes and Alvaro Tasistro who made helpful comments, and to the anonymous referee whose remarks and suggestions helped to improve previous versions of  ... 
doi:10.1017/s0956796899003627 fatcat:fivom7kqpjao5nrk7dfmccrmie

First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory

Jonathan Sterling, Robert Harper
2021 Zenodo  
The implementation and semantics of dependent type theories can be studied in a syntax-independent way: the objective metatheory of dependent type theories exploits the universal properties of their syntactic  ...  question in the syntactic metatheory of cubical type theory: normalization of open terms.  ...  Martin-Löf type theory to a compound judgment classifying type families.What do we mean by Martin-Löf's type theory?  ... 
doi:10.5281/zenodo.5709838 fatcat:3aavpcb3obempcwixl5pbpm7b4

First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory

Jonathan Sterling, Robert Harper
2021 Zenodo  
The implementation and semantics of dependent type theories can be studied in a syntax-independent way: the objective metatheory of dependent type theories exploits the universal properties of their syntactic  ...  question in the syntactic metatheory of cubical type theory: normalization of open terms.  ...  Martin-Löf type theory to a compound judgment classifying type families.What do we mean by Martin-Löf's type theory?  ... 
doi:10.5281/zenodo.6990769 fatcat:jxpqzkagufhrrotxczosgu4pmu

The practice of logical frameworks [chapter]

Frank Pfenning
1996 Lecture Notes in Computer Science  
This is the fundamental idea of higherorder abstract syntax [HHP93, PE88] which goes back to Martin-Löf's system of arities [NPS90] .  ...  In the early 80's the importance of constructive type theories for computer science was being recognized through the pioneering work of Martin-Löf [ML80, ML85a, ML85b] .  ... 
doi:10.1007/3-540-61064-2_33 fatcat:4misu6ivoncvhndnxocin3z6ha

MetaPRL – A Modular Logical Environment [chapter]

Jason Hickey, Aleksey Nogin, Robert L. Constable, Brian E. Aydemir, Eli Barzilay, Yegor Bryukhov, Richard Eaton, Adam Granicz, Alexei Kopylov, Christoph Kreitz, Vladimir N. Krupski, Lori Lorigo (+3 others)
2003 Lecture Notes in Computer Science  
This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.  ...  While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries.  ...  Constructive Set Theory In [2, 3] , Aczel introduced Constructive Zermelo-Fraenkel set theory, CZF, and formulated an embedding of CZF into the Martin-Löf's type theory [41] .  ... 
doi:10.1007/10930755_19 fatcat:nker4ros75gvzpadxblbenbsky

PhD Abstracts

GRAHAM HUTTON
2017 Journal of functional programming  
As a service to the community, the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.  ...  Many students complete PhDs in functional programming each year.  ...  Specifically, we develop a core effectful dependently typed language, eMLTT, based on Martin-Löf's intensional type theory and a clear separation between (effect-free) values and (possibly effectful) computations  ... 
doi:10.1017/s0956796817000181 fatcat:xbdgckkjpnaathslfgakegj3ka

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
As a service to the community, JFP recently launched a new feature, in the form of a regular publication of abstracts from PhD dissertations that were completed during the previous year.  ...  A dissertation is eligible if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed.  ...  -3afdf174bbab Based on a natural unification of logic and computation, Martin-Löf's intuitionistic type theory can be regarded simultaneously as a computationally meaningful higherorder logic system and  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

Natural deduction as higher-order resolution

Lawrence C. Paulson
1986 The Journal of Logic Programming  
Resolution gives both forwards and backwards proof, supporting a large class of logics. Isabelle has been used to prove theorems in Martin-Lofs constructive type theory.  ...  Sets and functions are semantic; formal type theories and Zermelo-Fraenkel set theory are syntactic. The ultimate semanticnotion is truth, faintly approximated by theorems of formal logic.  ...  Isabelle evolved by trial and error from implementations of Martin-Lof's constructive theory of types. I started with ML and the LCF architecture, as described in the next section.  ... 
doi:10.1016/0743-1066(86)90015-4 fatcat:d2jkwnbuyzeo7ko2ymi6qvxvpm

Isabelle: The Next 700 Theorem Provers [article]

Lawrence C. Paulson
2000 arXiv   pre-print
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories.  ...  It gives a thorough history of Isabelle, beginning with its origins in the LCF system. It presents an account of how logics are represented, illustrated using classical logic.  ...  The serc provided a decisive 'efficiency improvement' in the form of workstations (grant GR/E 0355.7). I am grateful to the above people and to anyone mistakenly omitted.  ... 
arXiv:cs/9301106v1 fatcat:l7o4ph2tmzbczgpnhtqlkx6d6u

How to Believe a Machine-Checked Proof

Robert Pollack
1997 BRICS Report Series  
By machine-checked proof I mean a formal derivation in some given formal<br />system; I am talking about derivability, not about truth.  ...  This paper presents a technological<br />approach for reducing the problem of believing a formal proof to the same psychological and philosophical issues as believing a conventional proof in a mathematics  ...  Martin-Löf (1971) gives an algorithm for type synthesis that transforms official derivations to avoid duplication of context validity checking.  ... 
doi:10.7146/brics.v4i18.18945 fatcat:q6qdk5iu5ba63hi4uo4twrcsj4

Type-Theoretical Dynamics [chapter]

Giuseppe Primiero
2011 The Realism-Antirealism Debate in the Age of Alternative Logics  
In the light of the epistemic approaches to logic as agent-based procedures of knowledge, a basic dynamics for type theory is introduced.  ...  The model, restricted to operations of revision, merging and information preference, furnishes interesting hints on a constructive type-theoretical approach to dynamics.  ...  Martin-Löf's type theory is one of the most powerful and natural among the languages based on this approach: it provides a complete methodology of knowledge, by combining syntax and semantics in a unique  ... 
doi:10.1007/978-94-007-1923-1_11 dblp:series/leus/Primiero12 fatcat:coslbvwdtjckvcjmtz3i76qqtq

Computational semantics in type theory

Aarne Ranta
2004 Mathématiques et sciences humaines  
Moreover, a parsing algorithm is derived from the grammar.  ...  GF can be seen as a formal theory of the concrete syntax which in that paper was defined in type theory using all available means.  ...  Then we will introduce dependent types and give a generalization of the classical grammar, together with a model in Martin-Löf's type theory [13] (Section 3).  ... 
doi:10.4000/msh.2925 fatcat:52lgwyfgs5an5dzdintgy7ttpy

From LCF to Isabelle/HOL

Lawrence C. Paulson, Tobias Nipkow, Makarius Wenzel
2019 Formal Aspects of Computing  
But in fact, LCF introduced a broader set of norms that are now taken for granted: a focus on backward proof, the practice of working in a theory hierarchy, and above all, the central role of a functional  ...  Coq and other systems built around constructive type theories represent a distinctive strand of development and fall outside our scope.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s00165-019-00492-1 fatcat:rv5zmo22fjedvjxjz4lm22v6de
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