## A Semantic analysis of control (1998)

Citations: | 32 - 5 self |

### BibTeX

@TECHREPORT{Laird98asemantic,

author = {James David Laird},

title = {A Semantic analysis of control},

institution = {},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Non-local control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for higher-type, sequential computation with access to the flow of control. A simple operational semantics for both call-by-name and call-by-value evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.

### Citations

1361 | A structural Approach to operational semantics
- Plotkin
(Show Context)
Citation Context ...oraPCFredexr,orN=E[µβ.N ′ ]. � Corollary 4.3.3 means that the operational semantics can be given in the following simple format, based on a combination of Plotkin’s ‘Structured Operational Semantics’ =-=[72]-=-, and Felleisen’s use of unique decomposition of programs into a redex and an evaluation context, with one clause for each of the ‘reducible forms’. n ⇓ n µα.[α]n ⇓ n r−→s E[s]⇓n E[r]⇓n µα.M[[α]E ′ [·... |

968 |
Categories for the Working Mathematician
- Lane
- 1971
(Show Context)
Citation Context ...ects: games R(A) for some arena A morphisms from A to B: pre-strategies on R(A ⊸ B), with composition defined using uncovering: σ; τ = {s↾A,B | s ∈ σ�τ ∧ R(s↾A,B)}. In order for this to define a SMCC =-=[51]-=-, it is necessary to make the following further requirements of rules: Copycats: If F : A → B is an isomorphism of arenas, then R(copyF,F−1) : R(A⊸B)={s∈copyF,F−1 | R(s)} is an isomorphism. So, in par... |

762 | Notions of computation and monads
- Moggi
(Show Context)
Citation Context ... by E. Moggi [62] can now be employed to obtain call-by-name and call-by-value semantics from fam(C). As this is a well established notion, only a few facts are recalled here; for further details see =-=[64]-=-. Definition 2.2.6 A strong monad on a category C with cartesian products and ⊥-maps is specified by a quadruple T,η,µ,t(Kleisli triple with tensorial strength t) where: TµA T 3A µTA / / T 2 A µA T 2 ... |

663 | Linear logic
- Girard
- 1987
(Show Context)
Citation Context ...ogic to restore the possibility of performing structural rules, with some measure of restraint. The various translations of classical and intuitionistic types and proofs into linear logic [29], [22], =-=[31]-=- are based upon the ‘decoration’ of linear formulas with sufficient exponentials to permit the translation of all of the structural rules in the proof. Such linear decomposition of the Hyland-Ong game... |

455 | Computational lambda-calculus and monads
- Moggi
- 1989
(Show Context)
Citation Context ...ty of settings — both intellectual and geographical — during 1970-71, and occasionally rediscovered thereafter.” Control was placed in the context of other computational features by the work of Moggi =-=[62]-=-, showing that continuation passing (along with many side effects) could be represented (and reasoned about) as a monad. More recent work by Thielecke [82] and others has further abstracted the notion... |

448 |
Introduction to higher order categorical logic, volume 7 of Camb
- Lambek, Scott
- 1986
(Show Context)
Citation Context ...problems and associated notions are 14sreviewed here, although as cartesian closure, the λ-calculus and the connections between them, are now standard, the reader is referred to e.g. Lambek and Scott =-=[49]-=- for background on semantics, and Barendregt [8] for syntax. The main distinguishing feature of the models of control considered here (as opposed to [39], [79] etc.) is that they include a notion of p... |

405 |
LCF considered as a programming language
- Plotkin
- 1977
(Show Context)
Citation Context ...l for PCF, from which this study borrows much of its motivation, has generated several important insights into the semantics of functional languages, starting from the original observation by Plotkin =-=[71]-=- that full abstraction fails for the Scott continuous functional model of PCF because of the presence of parallel elements. (The problem with the Sitaram and Felleisen model of control [80] is essenti... |

337 |
calculus: An algorithmic interpretation of classical natural deduction
- Parigot
- 1992
(Show Context)
Citation Context ...riffin [32], that Felleisen’s con5strol operator C can be typed as a rule of classical logic, and that its computational rules correspond to normalization of classical proofs. Similarly, Parigot’s λµ =-=[69]-=-, a term-language for classical proofs, can be used as a calculus of control. That is the context in which λµ appears in this thesis, but the possibility of using games as a fully complete semantics f... |

308 | Definitional interpreters for higher-order programming languages
- Reynolds
- 1972
(Show Context)
Citation Context ...c. λµ is syntactically more complicated than either, as it adds a new ‘continuation binding’ operation to the λ-calculus, (this step was already present in Reynolds’ definition of the Escape operator =-=[76]-=- (1972)). This has the advantage of making the control aspect of the calculus more explicit, and separate from the functional part. 4.2.1 The λµ calculus: call-by-name and call-by-value Terms of the λ... |

268 | A revised report on the syntactic theories of sequential control and state, Theoretical Computer Science 103
- Felleisen, Hieb
- 1992
(Show Context)
Citation Context ...to manipulate the flow of control in more subtle and complex 6sways; for instance to write coroutines [37]. Subsequent work on formalizing control operators (for instance, by Felleisen and co-workers =-=[25]-=-), has resulted in a range of ‘idealized’ control constructs. The approach taken here (advocated by Ong and Stewart [67]) is to adopt the λµ-calculus, and a programming language based on it, as a conv... |

250 | A formulae-as-types notion of control
- Griffin
- 1990
(Show Context)
Citation Context ...erators giving programs internal ‘access to the flow of control’. These range from the brutal GOTO, to more elegant exception handling mechanisms. Proofs of classical logic It was observed by Griffin =-=[32]-=-, that Felleisen’s con5strol operator C can be typed as a rule of classical logic, and that its computational rules correspond to normalization of classical proofs. Similarly, Parigot’s λµ [69], a ter... |

214 | Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994 |

210 |
Call-by-name, call-by-value and the λ-calculus
- Plotkin
- 1976
(Show Context)
Citation Context ...l program of type A ⇒ B can be considered as a way of passing control between the ‘argument’ A and the ‘result’ B. Control flow dictates whether this is done in a ‘demand driven’ or ‘data driven’ way =-=[73]-=-. Control operators Purely functional programs have a natural order of evaluation; they exhibit only ‘local control flow’. Only the most recently scheduled task can be completed and so every subproces... |

203 |
The Lambda Calculus: its Syntax and Semantics (revised ed
- Barendregt
- 1984
(Show Context)
Citation Context ...ere, although as cartesian closure, the λ-calculus and the connections between them, are now standard, the reader is referred to e.g. Lambek and Scott [49] for background on semantics, and Barendregt =-=[8]-=- for syntax. The main distinguishing feature of the models of control considered here (as opposed to [39], [79] etc.) is that they include a notion of partiality ab initio, as the intention is to mode... |

173 | An abstract view of programming languages - Moggi - 1990 |

135 | A game semantics for linear logic
- Blass
- 1992
(Show Context)
Citation Context ...[65] which appeared, more-or-less simultaneously, as a solution to the full abstraction problem for PCF. The AJM work used ideas from the Geometry of Interaction [30], and the game semantics of Blass =-=[13]-=-, whilst the Hyland-Ong approach grew from the work of Lorenzen [57] and subsequent researchers, which used games to study the semantics of logic (Felscher’s paper [26] is a useful survey). Subsequent... |

122 |
A fully abstract game semantics for general references
- Abramsky, Honda, et al.
- 1998
(Show Context)
Citation Context ...a are to be found in the rules. (And, more importantly, the ‘projection conditions’ on which his constructions are based simply fail in the games used to model computation with higher-type references =-=[4]-=-.) Instead, games here are simply sets of justified sequences, which are specified (but not uniquely) by an arena, and a set of rules. Thus, for instance, removing the question/answer tagging from an ... |

111 |
Fully abstract models of typed lambda-calculi
- Milner
- 1977
(Show Context)
Citation Context ... but it also contains sequential as well as parallel ‘junk’.) Construction of fully abstract models can be performed solely by syntactic and categorical methods, as shown in the case of PCF by Milner =-=[61]-=-. To move beyond a ‘superficial’ analysis, therefore, additional conditions can be applied, — that the presentation of the model be denotational, or syntax-independent, and (the ‘Jung and Stoughton cr... |

111 | The Discoveries of Continuations
- Reynolds
- 1993
(Show Context)
Citation Context ...time control was given its own semantic representation. In fact (as so often), it was not the result of a single inspiration, but a process of enlightenment. In the conclusion of a survey by Reynolds =-=[77]-=-: “... continuations or closely related concepts were first discovered in 1964 by van Wijngaarden, repeatedly discovered in a wide variety of settings — both intellectual and geographical — during 197... |

109 | A new deconstructive logic: Linear logic
- Danos, Joinet, et al.
- 1997
(Show Context)
Citation Context ...near logic to restore the possibility of performing structural rules, with some measure of restraint. The various translations of classical and intuitionistic types and proofs into linear logic [29], =-=[22]-=-, [31] are based upon the ‘decoration’ of linear formulas with sufficient exponentials to permit the translation of all of the structural rules in the proof. Such linear decomposition of the Hyland-On... |

105 | Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions
- Abramsky, McCusker
- 1997
(Show Context)
Citation Context ...he strategies on dialogue games are constrained by visibility and innocence; although repetitious queries are allowed, Player must make the same response to them every time. The games models of state =-=[2]-=-, [4] are given by succesively dropping innocence and visibility, reflecting a setting where both copying and sharing of data is allowed, to model local binding of imperative variables. One consequenc... |

103 |
Towards a geometry of interaction
- Girard
- 1989
(Show Context)
Citation Context ... [6], Hyland and Ong [43], and Nickau [65] which appeared, more-or-less simultaneously, as a solution to the full abstraction problem for PCF. The AJM work used ideas from the Geometry of Interaction =-=[30]-=-, and the game semantics of Blass [13], whilst the Hyland-Ong approach grew from the work of Lorenzen [57] and subsequent researchers, which used games to study the semantics of logic (Felscher’s pape... |

102 | Premonoidal categories and notions of computation
- Power, Robinson
- 1997
(Show Context)
Citation Context ...resented (and reasoned about) as a monad. More recent work by Thielecke [82] and others has further abstracted the notion of continuation passing, giving it an elegant basis in premonoidal categories =-=[74]-=-. The use of first class continuations as ‘control points’ in functional programs which can be manipulated like ordinary variables can be represented syntactically using the control operator call-with... |

98 | What is a categorical model of intuitionistic linear logic?’, Typed lambda calculi and applications
- Bierman
- 1995
(Show Context)
Citation Context ...and associated ‘linear decomposition’ of a category of games, based on a single rule. The notion of linear decomposition is borrowed from (intuitionistic) linear logic [29] and its categorical models =-=[11]-=-, but the purpose is not to define a full linear type structure. Instead linearity is used to analyze how restricting repetition of moves can define sound and complete models of control (i.e. pointed ... |

95 | Typing First Class Continuations in ML
- Duba, Harper, et al.
- 1993
(Show Context)
Citation Context ...ed that the term of λµ corresponding to a natural deduction proof of Peirce’s law has the same operational behaviour as call/cc [69], and a more formal connection with the callcc of SML of New Jersey =-=[35]-=- is described in [67]. In the other direction, there is the question of whether λµ terms can be written using call/cc. The result proved in [48], that unbracketed games give fully complete model of PC... |

84 | Revised 4 report on the algorithmic language Scheme - Clinger, Rees - 1991 |

83 |
Observable algorithms on concrete data structures
- CURIEN
- 1992
(Show Context)
Citation Context ... fully abstract model of PCF for instance, can be obtained as the extensional collapse of the highly intensional games and strategies model. Berry and Curien’s definition of the sequential algorithms =-=[9]-=- is also in this vein. It developed from an attempt by Kahn and Plotkin [45] to define a notion of sequential function made by structuring domains as concrete data structures (CDS). This allows higher... |

79 | A Curry-Howard foundation for functional computation with control
- Ong, Stewart
- 1997
(Show Context)
Citation Context ...ork on formalizing control operators (for instance, by Felleisen and co-workers [25]), has resulted in a range of ‘idealized’ control constructs. The approach taken here (advocated by Ong and Stewart =-=[67]-=-) is to adopt the λµ-calculus, and a programming language based on it, as a convenient syntax into which other control operators can be translated. Although control is a useful paradigm for understand... |

78 |
Categorical Combinators, Sequential Algorithms and Functional Programming
- Curien
- 1986
(Show Context)
Citation Context ... necessarily somewhat terse, and slanted towards game semantics. A wealth of further material, including relationships with other semantics of for sequential languages is to be found in Curien’s book =-=[18]-=-, and article [19]. Following Cartwright and Felleisen’s discovery that SPCF has a fully abstract semantics in terms of ‘decision trees’, it was observed by Curien that the model could be given an alt... |

72 | Categorical Structure of Continuation Passing Style
- Thielecke
- 1997
(Show Context)
Citation Context ... computational features by the work of Moggi [62], showing that continuation passing (along with many side effects) could be represented (and reasoned about) as a monad. More recent work by Thielecke =-=[82]-=- and others has further abstracted the notion of continuation passing, giving it an elegant basis in premonoidal categories [74]. The use of first class continuations as ‘control points’ in functional... |

69 | Full abstraction for functional languages with control
- Laird
- 1997
(Show Context)
Citation Context ... is analysed here, that access to the flow of control is gained by dropping this condition. It is a possibility which has also been studied by Herbelin [38], as well as in previous work by the author =-=[48]-=-. Here it is developed, and the relationship with continuation passing studied in detail. 1.4 The contents and contributions of the thesis Chapter 2 is a more technical introductory chapter, combining... |

65 | Post-graduate Lecture Notes in Advanced Domain Theory (incorporating the ‘Pisa notes - Plotkin - 1981 |

64 | Call-by-value games
- Abramsky, McCusker
- 1998
(Show Context)
Citation Context ... and subsequent researchers, which used games to study the semantics of logic (Felscher’s paper [26] is a useful survey). Subsequent developments include games for recursive types [59], call-by-value =-=[3]-=-, and games models of state[2], and higher-type references [4]. A connection between games and control is in any case a natural step; both are offered as paradigms for explaining a variety of computat... |

63 | Hereditarily sequential functionals
- Nickau
- 1994
(Show Context)
Citation Context ... semantics together, and building on the basic result for PCF. The intensional hierarchy developed from the models described by Abramsky, Jagadeesan and Malacaria [6], Hyland and Ong [43], and Nickau =-=[65]-=- which appeared, more-or-less simultaneously, as a solution to the full abstraction problem for PCF. The AJM work used ideas from the Geometry of Interaction [30], and the game semantics of Blass [13]... |

62 | A generalization of exceptions and control in ML-like languages
- Gunter, Rémy, et al.
- 1995
(Show Context)
Citation Context ... which create dynamic bindings, such as the exception-handling mechanism of Standard ML. An elegant general treatment of these operators can be found in the work by Gunter, Remy and Riecke on prompts =-=[33]-=-, which have the expressive power of exceptions and call/cc. Unlike the case of call/cc, there are at present no general or denotational models of these features; this leaves real scope for the applic... |

60 | Game-theoretic analysis of call-by-value computation
- Honda, Yoshida
- 1999
(Show Context)
Citation Context ... games and innocent and history-sensitive strategies in [3], and visibility-free strategies in [4], with fully abstract models of call-by-value PCF (an alternative presentation of Honda and Yoshida’s =-=[41]-=-), and function-based languages with references being found as a result. In this thesis, however, it seems appropriate to take a slightly different perspective. In fact, both call-by-name and call-by-... |

51 |
Games and full abstraction for a functional metalanguage with recursive types
- McCusker
- 1996
(Show Context)
Citation Context ...ork of Lorenzen [57] and subsequent researchers, which used games to study the semantics of logic (Felscher’s paper [26] is a useful survey). Subsequent developments include games for recursive types =-=[59]-=-, call-by-value [3], and games models of state[2], and higher-type references [4]. A connection between games and control is in any case a natural step; both are offered as paradigms for explaining a ... |

50 | R.: Fully abstract semantics for observably sequential languages, Information and Computation
- Cartwright, Felleisen
- 1994
(Show Context)
Citation Context ...which extends PCF with control features: errors, and a form of catch operator. Their SPCF semantics was subsequently shown (with Curien) to be equivalent to a presentation using sequential algorithms =-=[16]-=-. Their work is developed here, connecting the sequential algorithms interpreattation of control flow and control operators to the more general notion of continuation-passing, to the less toy-like con... |

50 | Controlling Effects
- Filinski
- 1996
(Show Context)
Citation Context ...ing directly to composition with the natural transformations of lifting (η), and flattening, µ. These maps define an isomorphism between terms of type TA,andvaluesof type T2A, (a ‘monadic reflection’ =-=[27]-=-) which in the case of control defines an ‘idealized’ control operator. The call-by-name interpretation of the simply-typed λ-calculus in the cartesian closed category fam(C) is completely standard. T... |

47 |
Games semantics and abstract machines
- Danos, Herbelin, et al.
- 1996
(Show Context)
Citation Context ...trict strategy on !A ⊸ B, the initial move in the first thread opened in !A appears in every subsequent Player view. (Compare with e.g. Danos, Herbelin and Regnier’s notion of ‘linear head reduction’ =-=[21]-=-.) !A con / / f !A⊗!A id⊗der B oo !A ⊗ A ˆf Figure 3.1: Linearization of head occurrence (f −→ ˆ f ) 3.7.2.5 Uniformity of threads I(!A,(B ⊸ a)) ∼ = I(!A,!(B ⊸ a)). That is, the ‘promotion’ mapping fr... |

40 | Observable sequentiality and full abstraction
- CARTWRIGHT, FELLEISEN
- 1991
(Show Context)
Citation Context ...L1 ...Ln, — in the latter E[·]=µα.IF [·]thenΩ0else Ω0 , to give the required evaluation context. � 142sThe Context Lemma allows a simple proof of the following observation of Cartwright and Felleisen =-=[15]-=-, that adding errors makes all control behaviour observable and hence: Corollary 5.1.7 Observational equivalence in µPCF E is extensional. i.e. M ⊑OBS T N if and only if for all evaluation contexts ET... |

37 | The sequentially realizable functionals
- Longley
- 1998
(Show Context)
Citation Context ...with this one, to yield the result that the extensional collapse of the unbracketed games model is also isomorphic to the strongly stable model (see Figure 5.1, and Corollary 5.4.23). Work by Longley =-=[55]-=-, amongst others, has connected this sequentiality to the formal notion of realizability. 5.2 A sequential algorithms model of control The description of the rich category of sequential algorithms, is... |

33 |
On the symmetry of sequentiality
- CURIEN
- 1993
(Show Context)
Citation Context ...hat terse, and slanted towards game semantics. A wealth of further material, including relationships with other semantics of for sequential languages is to be found in Curien’s book [18], and article =-=[19]-=-. Following Cartwright and Felleisen’s discovery that SPCF has a fully abstract semantics in terms of ‘decision trees’, it was observed by Curien that the model could be given an alternative presentat... |

32 | A Generalization of Jumps and Labels
- LANDIN
- 1965
(Show Context)
Citation Context ...ented syntactically using the control operator call-with-current-continuation, orcall/cc. Thisoriginated in the language Scheme [17], (following other, similar, constructs such as Landin’s J-operator =-=[50]-=-). It can be used both for simple ‘escapes’ from nested computations, and to manipulate the flow of control in more subtle and complex 6sways; for instance to write coroutines [37]. Subsequent work on... |

32 | Reasoning with continuations II: Full abstraction for models of control
- Sitaram, Felleisen
- 1990
(Show Context)
Citation Context ...er (A ⊸ a) ⊸ a must either be ⊥ or the lifting of an element of A. An answer object which includes other possibilities, such as the choice of the flat domain of natural numbers as an answer object in =-=[80]-=- violates this axiom. Lemma 3.7.9 It is equivalent to the following condition from [1]: All maps into the answer object are strict: for any A, IS(A,a)=I(A,a). Proof: For a non-strict map into a to exi... |

31 | A semantic view of classical proofs: Type-theoretic, categorical, and denotational characterizations
- Ong
- 1996
(Show Context)
Citation Context ...=s[E[·]/α] t[E[·]/α] (λx.t)[E[·]/α]=λx.(t[E[·]/α]) (µβ.t)[E[·]/α]=µβ.(t[E[·]/α]) ([β]t)[E[·]/α]=[β](t[E[·]/α]) This is a slight modification to the axiomatizations proposed by Parigot [69] and by Ong =-=[66]-=-, firstly in its presentation via evaluation contexts instead of single applications (but this is a minor change, which is implicit in Ong and Stewart’s paper [67]). There is also a change to the rule... |

28 | Full abstraction for
- Abramsky, Jagadeesan, et al.
- 2000
(Show Context)
Citation Context ...inding syntax and semantics together, and building on the basic result for PCF. The intensional hierarchy developed from the models described by Abramsky, Jagadeesan and Malacaria [6], Hyland and Ong =-=[43]-=-, and Nickau [65] which appeared, more-or-less simultaneously, as a solution to the full abstraction problem for PCF. The AJM work used ideas from the Geometry of Interaction [30], and the game semant... |

27 | Dialogues as a foundation for intuitionistic logic, 115–146 - Felscher - 2002 |

24 |
On the relation between the λµ-calculus and the syntactic theory of sequential control
- Groote
- 1994
(Show Context)
Citation Context ...translation of µPCFn This can be seen as an application to µPCF of previous work on the pure calculus. The novel feature here is the use of infinite lists to model continuations of typenat. de Groote =-=[23]-=- described a wholly syntactic continuation-passing-interpretation of the λµn-calculus which is similar to the one given here. Hofmann and Streicher [40] gave a continuation semantics for λµn, and show... |

23 | Projecting sequential algorithms on strongly stable functions
- Ehrhard
- 1996
(Show Context)
Citation Context ...SSSSextensional SSSSS collapse SS extensional collapse SSSSSSSS SSSSS) ) Strongly stable functions Figure 5.1: Relationship of three models of call-by-name PCF gorithms has been considered by Ehrhard =-=[24]-=-, who proved that the extensional collapse of the sequential algorithms model of PCF is isomorphic to Bucciarelli and Ehrhard’s strongly stable model, or, in other words, that every strongly stable fu... |