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System F with coercion constraints

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

We present a second-order λ-calculus

doi:10.1145/2603088.2603128
dblp:conf/csl/CretinR14
fatcat:oqyxsxhuffbtzdmxrgnneaq53q
*with**coercion**constraints*that generalizes a previous extension of*System**F**with*parametric*coercion*abstractions by allowing multiple but simultaneous type and*coercion*...*with*parametric*coercion*abstraction, and ML-style subtyping*constraints*. ... Type*systems**with*subtyping*constraints*use two notions, solvability and consistency, that coincide in ML. ...##
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Dynamic typing
[chapter]

1992
*
Lecture Notes in Computer Science
*

We present an extension of a statically typed language

doi:10.1007/3-540-55253-7_14
fatcat:rpbizuxjrvhstcagapgtehwns4
*with*a special type dyn and explicit type tagging and checking operations (*coercions*). ... Programs in run-time typed languages are viewed as incomplete programs that are to be completed to well-typed programs by explicitly inserting*coercions*into them. ... I am also grateful for helpful discussions*with*members of the TOPPS group at DIKU. ...##
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Binding-Time Analysis for Polymorphic Types
[chapter]

2001
*
Lecture Notes in Computer Science
*

*With*this idea, the annotated version of twice becomes twice

*f*x =

*f*@

*f*@ x where implements the

*coercion*2 1 . ... b1b2 2 coerces a function

*with*binding-time b 1 to one

*with*binding-time b 2 , applying

*coercion*1 to the argument and 2 to the result. is the identity

*coercion*. ...

##
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A unified framework for binding-time analysis
[chapter]

1997
*
Lecture Notes in Computer Science
*

It is often specified as a non-standard type

doi:10.1007/bfb0030638
fatcat:5lbo57ecmncvrgxeovbpgo77qa
*system*. Many typebased binding-time analyses are reminiscent of simple type*systems**with*additional features like recursive types. ... We make this connection explicit by expressing binding-time analysis*with*annotated type*systems*that separate the concerns of type inference from those of binding-time annotation. ... Acknowledgements Thanks to Olivier Danvy and Dirk Dussart for discussions on higher-order*coercions*and type-based program analysis. ...##
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Explicit Effect Subtyping
[chapter]

2018
*
Lecture Notes in Computer Science
*

Our typing-directed elaboration comes

doi:10.1007/978-3-319-89884-1_12
fatcat:3oyq4seri5btflslc6whehp7gu
*with*a*constraint*-based inference algorithm that turns an implicitly-typed Eff-like language into our calculus. ... Eff, an ML-like language*with*native support for handlers, has a subtyping-based effect*system*on which an effect-aware optimizing compiler could be built. ... [3] also present a translation of languages*with*inheritance polymorphism into*System**F*, extended*with**coercions*. ...##
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Safe polymorphic type inference for a dynamically typed language

1995
*
Proceedings of the seventh international conference on Functional programming languages and computer architecture - FPCA '95
*

q Consider
a

doi:10.1145/224164.224203
dblp:conf/fpca/HengleinR95
fatcat:ykurclppsvay7ebvvvesdx46sy
*constraint*of the form tc(crl, . . ..an)+tc(pl .*f*?n)*f*?n). There is only one primitive*coercion**with*a signatwe that matches this*constraint*: the identity*coercion*. ... (define*f*(lambda (x) (lambda (y) (if y x (+ x l))))) After annotation*with**coercion*variables of suitable types we get the annotated definition (define*f*[cl, c2, c3, c4, c5, c6, c7, c8] ( [cl] (lambda ... = fn ( 1) ) (map*f*(cdr 1)))))) gets completed without any parameters, but*with*inferred representation shift*coercions*for lists and pairs, val PAIR2LST = fn (x, y) => x: :y val LST2PAIR = fn (x: : ...##
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Explicit Effect Subtyping
[article]

2020
*
arXiv
*
pre-print

Our typing-directed elaboration comes

arXiv:2005.13814v1
fatcat:gaubphgk2vailof4wj5exd5du4
*with*a*constraint*-based inference algorithm that turns an implicitly-typed Eff-like language into our calculus. ... Eff, an ML-like language*with*native support for handlers, has a subtyping-based effect*system*on which an effect-aware optimizing compiler could be built. ... [5] also present a translation of languages*with*inheritance polymorphism into*System**F*, extended*with**coercions*. ...##
###
Equality proofs and deferred type errors

2012
*
SIGPLAN notices
*

The principal difference between

doi:10.1145/2398856.2364554
fatcat:ktmpsoe3gra7pkkhl6iunmwmcu
*System**F*and*System**F*↑ C is that, together*with*type information,*System**F*↑ C carries equality proofs: evidence that type equality*constraints*are satisfied. ... Contrary to the notation used in Section 2.1 and in previous presentations of*System**F*↑ C notice that we use symbol ∼ # instead of ∼ for*coercion*types, and*Constraint*# rather than*Constraint*for their ...##
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Equality proofs and deferred type errors

2012
*
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12
*

The principal difference between

doi:10.1145/2364527.2364554
dblp:conf/icfp/VytiniotisJM12
fatcat:6lyhgwmh4fdvflk4bxryrmd344
*System**F*and*System**F*↑ C is that, together*with*type information,*System**F*↑ C carries equality proofs: evidence that type equality*constraints*are satisfied. ... Contrary to the notation used in Section 2.1 and in previous presentations of*System**F*↑ C notice that we use symbol ∼ # instead of ∼ for*coercion*types, and*Constraint*# rather than*Constraint*for their ...##
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A lean specification for GADTs: system F with first-class equality proofs

2010
*
Higher-Order and Symbolic Computation
*

We present an orthogonal specification for GADTs: the language

doi:10.1007/s10990-011-9065-0
fatcat:hycycv4whzaadixg7vlz247fve
*System**F*∼ , consisting of*System**F*augmented*with*first-class equality proofs. ... Generalized Algebraic Data Types are a generalization of Algebraic Data Types*with*additional type equality*constraints*. ...*System**F*C*System**F*C extends*System**F**with*equality*coercions*. It has a built-in syntax to represent values of the Equal data type mentioned in the Sect. 2.1. ...##
###
Extending Hindley-Milner Type Inference with Coercive Structural Subtyping
[chapter]

2011
*
Lecture Notes in Computer Science
*

We investigate how to add coercive structural subtyping to a type

doi:10.1007/978-3-642-25318-8_10
fatcat:q6yn43kgivh6vkgrbzmowxsjcu
*system*for simply-typed lambda calculus*with*Hindley-Milner polymorphism. ... according to the standard Hindley-Milner*system*(without any subtypes). ... In a*system**with**coercions*, type inference also has to insert*coercions*into the term t in appropriate places, yielding a term u for which θΓ θt u : τ and θΓ u : τ holds. ...##
###
Dynamic typing and subtype inference

1995
*
Proceedings of the seventh international conference on Functional programming languages and computer architecture - FPCA '95
*

This paper shows that dynamic typing at least as powerful as Henglein's

doi:10.1145/224164.224201
dblp:conf/fpca/AikenF95
fatcat:sntgy3e34fhm7oblrvmv7jjc2q
*system*Hen92b] can be expressed using set*constraints*. ... Lemma 3.2 Let ;; S`S e : where the*system*of*constraints*S = S 0*f*g is consistent. Let e 0 = erase(e). Then e is a correct completion of e 0 . ...*Constraint*resolution is the most expensive phase. The rewrite rules work only*with*pairs of subexpressions of the original*constraint**system*. ...##
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Global tagging optimization by type inference

1992
*
ACM SIGPLAN Lisp Pointers
*

(Inequality

doi:10.1145/141478.141542
fatcat:wprmxfry55gfti35lceaka2hza
*constraint*rules) (a) CU{~(')(aI . ..clk) < 7,*f*(k)(pl . ..ok)<y} +cu{*f*(k)(al . ..ak)<y. al =/31,..., ak3k}k} (b) CU{~(k)(a,... ... A solution of a*constraint**system*is a substitu- tion of types for the type variables such that all*constraints*are satisfied. 5.2*Constraint*normalization and minimal solutions The*constraints*...##
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Global tagging optimization by type inference

1992
*
Proceedings of the 1992 ACM conference on LISP and functional programming - LFP '92
*

(Inequality

doi:10.1145/141471.141542
dblp:conf/lfp/Henglein92
fatcat:36byej6fwzcytpm7ll6hinpym4
*constraint*rules) (a) CU{~(')(aI . ..clk) < 7,*f*(k)(pl . ..ok)<y} +cu{*f*(k)(al . ..ak)<y. al =/31,..., ak3k}k} (b) CU{~(k)(a,... ... A solution of a*constraint**system*is a substitu- tion of types for the type variables such that all*constraints*are satisfied. 5.2*Constraint*normalization and minimal solutions The*constraints*...##
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Giving Haskell a promotion

2012
*
Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation - TLDI '12
*

We describe an experiment that enriches Haskell's kind

doi:10.1145/2103786.2103795
dblp:conf/tldi/YorgeyWCJVM12
fatcat:2tkog37jf5dnhlhovyrxuyjh7u
*system**with*two features promoted from its type*system*: data types and polymorphism. ... The new*system*has a very good power-to-weight ratio: it offers a significant improvement in expressiveness, but, by re-using concepts that programmers are already familiar*with*, the*system*is easy to ...*System**F*↑ C overview The expression syntax of*System**F*↑ C is given in Figure 1 ,*with*the differences from*System*FC highlighted. ...
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