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There are essentially two original contributions: (1) Intersection types are used as a new and elegant tool for proving classical properties of pure lambda-calculus. (2) A type assignment system for pure ... Pierce (“Programming with intersection types and bounded polymorphism”, Ph.D. Thesis/Rep. No. ...
The set of lambda theories is naturally equipped with a structure of complete lattice, where the meet of a family of lambda theories is their intersection, and the join is the least lambda theory containing ... We also show that there exists a sublattice of the lattice of lambda theories which satisfies: (i) a restricted form of distributivity, called meet semidistributivity; and (ii) a nontrivial identity in ... It is immediate to verify that ≤ induces an easy intersection type theory according to  . ...doi:10.1093/logcom/14.3.373 fatcat:7pi6axbbonb3zjigqxodc2w4c4
and interpreting the intersection constructor as set-theoretic intersection. ... There are three canonical types of set-theoretical semantics for intersection-types: the inferential semantics, the simple semantics, and the F-semantics. ...
The first is based on intersection types; the second is based on a mixed induction-coinduction principle.” ... (English summary) Typed lambda calculi and applications (Nancy, 1997), 231-247, Lecture Notes in Comput. Sci., 1210, Springer, Berlin, 1997. ...
Principal type schemes). Recursive types (Recursive and infinite types. Semantics). Intersection types (Type assignment systems with intersection types. Basic syntactic properties. ... Recursion theory as a theory of computers. Lambda calculus as a theory of functions. Typed theories. Deductions as computations. The Curry-Howard isomorphism. Automazing mathematics. ...doi:10.1016/0166-218x(92)90240-b fatcat:d4o4kcm5pfe5fkhfngxdt4t6dq
Principal type schemes). Recursive types (Recursive and infinite types. Semantics). Intersection types (Type assignment systems with intersection types. Basic syntactic properties. ... Recursion theory as a theory of computers. Lambda calculus as a theory of functions. Typed theories. Deductions as computations. The Curry-Howard isomorphism. Automazing mathematics. ...doi:10.1016/0166-218x(92)90241-2 fatcat:ytik62gsxvddpcvsqoxm3jfiri
all lambda terms defined by M::= x | Ax.M | MM, where x ranges over a countable set of variables), o is an intersection type (the set 7 of intersection types is generated by the grammar a::=w\y|o +~a|aAa ... Chantal Berline (F-PARIS7-ML; Paris) 2002i:03020 03B40 68N18 Ghilezan, Silvia (YU-NOVIE; Novi Sad Full intersection types and topologies in lambda calculus. (English summary) J. Comput. ...
Summary: “A type theory with infinitary intersection and union types for the lazy /-calculus is introduced. Types are viewed as up- per closed subsets of a Scott domain. ... Intersection and union types constructors are interpreted as the set-theoretic intersection and union, respectively, even when they are not finite. ...
Second, the system of the combinatory logic with intersection types is proven to be sound and complete with respect to the proposed semantics. ... We prove two soundness and completeness results. First, the equational theory of untyped combinatory logic is proven to be sound and complete with respect to the proposed semantics. ... AUTHOR CONTRIBUTIONS Both authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication. ...doi:10.3389/fcomp.2022.792570 fatcat:o6augzgfkjdwrjipe3azolckdy
results for intersection type systems enabling typing invariance of terms w.r.t. various notions of reduction/expansion, like ¬, and a number of relevant restrictions of theirs. ... Being the intersection type systems a general framework for the study of semantic domains for the Lambdacalculus, the present paper provides a characterisation of "meaning invariance" in terms of characterisation ... Intersection types can be also viewed as a restriction of the domain theory in logical form, see  , to the special case of modelling pure Lambda-calculus by means of -algebraic complete lattices. ...doi:10.1016/s1571-0661(04)80843-0 fatcat:ir3idq4yancmndvhaw5r6auuda
Many students complete PhDs in functional programming each year, but there is currently no common location in which to promote and advertise the resulting work. ... The abstracts are made freely available on the JFP website, i.e. not behind any paywall, and do not require any transfer for copyright, merely a license from the author. ... The key is a characterisation of model checking as a problem of intersection type assignment. This dissertation contributes to both the theory and practice of the intersection type approach. ...doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna
Summary: “Intersection types and bounded quantification are complementary extensions of a first-order programming language with subtyping. ... A maximum extension for the theory of £-conversion should then necessarily contain such a union and hence be inconsistent. For the theory of Bn-conversion, the answer depends on the number of types. ...
We show that within the Cedille type theory we can relax functoriality constraints and generically derive an induction principle for Mendler-style lambda-encoded inductive datatypes, which arise as least ... As a result, we can define lambda-encoded natural numbers with an induction principle and a constant-time predecessor function so that the normal form of a numeral requires only linear space. ... We gratefully acknowledge NSF support under award 1524519, and DoD support under award FA9550-16-1-0082 (MURI program). ...arXiv:1803.02473v1 fatcat:wrobkyk5g5htpetv5fbuyn4eju
A simple proof is given of the property that the set of strongly normalizing lambda terms coincides with the set of lambda terms typable in certain intersection type assignment systems. ... The idea that strongly normalizing lambda terms are exactly the terms typable in the intersection type assignment systems without the (ω)-rule first appeared in , Pottinger , and Leivant . ... They are meant to be extensions of Curry's basic functional theory which will provide types for a larger class of lambda terms. ...doi:10.1305/ndjfl/1040067315 dblp:journals/ndjfl/Ghilezan96 fatcat:ac4gutmhxrfnhlnv5kgiw622om
One of the main results here is that, given a theory of the simply typed lambda calculus A~(Z, E), where & is a signature and E is a set of equations, the extension to a theory of the second-order lambda ... A great deal is known about the metatheory of typed lambda calculi, but almost all of it concerns pure type theories. ...
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