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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 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. ...
doi:10.1145/2603088.2603128
dblp:conf/csl/CretinR14
fatcat:oqyxsxhuffbtzdmxrgnneaq53q
Dynamic typing
[chapter]
1992
Lecture Notes in Computer Science
We present an extension of a statically typed language 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. ...
doi:10.1007/3-540-55253-7_14
fatcat:rpbizuxjrvhstcagapgtehwns4
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. ...
doi:10.1007/3-540-45575-2_19
fatcat:c25aam6wcjb7nppgpgaveactzu
A unified framework for binding-time analysis
[chapter]
1997
Lecture Notes in Computer Science
It is often specified as a non-standard type 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. ...
doi:10.1007/bfb0030638
fatcat:5lbo57ecmncvrgxeovbpgo77qa
Explicit Effect Subtyping
[chapter]
2018
Lecture Notes in Computer Science
Our typing-directed elaboration comes 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. ...
doi:10.1007/978-3-319-89884-1_12
fatcat:3oyq4seri5btflslc6whehp7gu
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 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: : ...
doi:10.1145/224164.224203
dblp:conf/fpca/HengleinR95
fatcat:ykurclppsvay7ebvvvesdx46sy
Explicit Effect Subtyping
[article]
2020
arXiv
pre-print
Our typing-directed elaboration comes 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. ...
arXiv:2005.13814v1
fatcat:gaubphgk2vailof4wj5exd5du4
Equality proofs and deferred type errors
2012
SIGPLAN notices
The principal difference between 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 ...
doi:10.1145/2398856.2364554
fatcat:ktmpsoe3gra7pkkhl6iunmwmcu
Equality proofs and deferred type errors
2012
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12
The principal difference between 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 ...
doi:10.1145/2364527.2364554
dblp:conf/icfp/VytiniotisJM12
fatcat:6lyhgwmh4fdvflk4bxryrmd344
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 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. ...
doi:10.1007/s10990-011-9065-0
fatcat:hycycv4whzaadixg7vlz247fve
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 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. ...
doi:10.1007/978-3-642-25318-8_10
fatcat:q6yn43kgivh6vkgrbzmowxsjcu
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 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. ...
doi:10.1145/224164.224201
dblp:conf/fpca/AikenF95
fatcat:sntgy3e34fhm7oblrvmv7jjc2q
Global tagging optimization by type inference
1992
ACM SIGPLAN Lisp Pointers
(Inequality
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 ...
doi:10.1145/141478.141542
fatcat:wprmxfry55gfti35lceaka2hza
Global tagging optimization by type inference
1992
Proceedings of the 1992 ACM conference on LISP and functional programming - LFP '92
(Inequality
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 ...
doi:10.1145/141471.141542
dblp:conf/lfp/Henglein92
fatcat:36byej6fwzcytpm7ll6hinpym4
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 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. ...
doi:10.1145/2103786.2103795
dblp:conf/tldi/YorgeyWCJVM12
fatcat:2tkog37jf5dnhlhovyrxuyjh7u
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