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Ari Angga Nugraha
ariangganugraha-funpro2020-lambda
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44f8234a
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44f8234a
authored
8 years ago
by
Sean Gillespie
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8 years ago
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# System F
# Introduction
System F is a typed variant of the Lambda Calculus. It is an extension to
Pure
λ
can easily be extended with a static type system. We explore
another typed
λ
known as the Simply Typed Lambda Calculus. Additionally,
two such systems, the
*Simply Typed Lambda Calculus*
and
*System F*
. The
System F introduces the concept of generic types, also called polymorphic
Simply Typed Lambda Calculus, abbreviated as
λ
<sub>
→
</sub>
is
types [1].
the simplest typed
λ
.
*System F*
is an extension of
λ
<sub>
→
</sub>
that introduces the concept of generic types, also
called polymorphic types [1].
In general, type systems aim to eliminate certain programming errors [3]. A good
In general, type systems aim to eliminate certain programming errors [3]. A good
type system should reject ill-typed programs, while not being too conservative--
type system should reject ill-typed programs, while accepting most valid programs
that is, it accepts most valid programs [2]. Many functional programming
[2]. Many functional programming languages are based on type systems similar
languages are based on type systems similar to System F, including Haskell
to System F, including Haskell (System FC [4]), and ML (Hindley-Milner [5]).
(System FC [4]), and ML (Hindley-Milner [5]).
# Type Context
# Type Context
A typing context is a sequence mapping free variables to their types [2]. Given
A typing context is a sequence mapping free variables to their types [2]. Given
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