What is recorded here?
Milner organized reusable functions that work at different types into a compile-time discipline and Algorithm W, with separate semantic and syntactic soundness theorems for the small applicative language Exp. Let-bound functions may receive fresh instances of their generic type variables while enclosing parameter types retain their constraints. This permits flexible reuse without the specified type violations. The paper connects the construction to the ML checker already used in Edinburgh LCF.
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Scientific scope
The proof concerns Exp under a respecting environment and its defined type-error semantics. It does not prove termination, arbitrary program correctness or full imperative-ML safety. Completeness/most-general inference is conjectured here, not proved; the stateful polymorphic-list example exposes an extension failure. Hindley's principal schemes and Robinson's unification are inherited, and later Damas–Milner results remain separate.
Read the original work
- Robin Milner, A Theory of Type Polymorphism in Programming, Journal of Computer and System Sciences 17(3), 348–375 (1978), DOI 10.1016/0022-0000(78)90014-4
- University of Edinburgh Research Explorer: A theory of type polymorphism in programming
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People and systems
Robin Milner
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English catalogue narrative
Milner: polymorphic typing with a sound inference algorithm
Milner organized reusable functions that work at different types into a compile-time discipline and Algorithm W, with separate semantic and syntactic soundness theorems for the small applicative language Exp.
Let-bound functions may receive fresh instances of their generic type variables while enclosing parameter types retain their constraints. This permits flexible reuse without the specified type violations. The paper connects the construction to the ML checker already used in Edinburgh LCF.
Scientific scope
The proof concerns Exp under a respecting environment and its defined type-error semantics. It does not prove termination, arbitrary program correctness or full imperative-ML safety. Completeness/most-general inference is conjectured here, not proved; the stateful polymorphic-list example exposes an extension failure. Hindley's principal schemes and Robinson's unification are inherited, and later Damas–Milner results remain separate.
People and systems
Robin Milner