Write You a Haskell Stephen Diehl

In all the languages which we will implement the types present during compilation are erased. Although
types are possibly present in the evaluation semantics, the runtime cannot dispatch on types of values at
runtime. Types by definition only exist at compile-time in the static semantics of the language.
Small-Step Semantics
e real quantity we’re interested in formally describing is expressions in programming languages. A
programming language semantics is described by the operational semantics of the language. e operational
semantics can be thought of as a description of an abstract machine which operates over the
abstract terms of the programming language in the same way that a virtual machine might operate over
instructions.
We use a framework called small-step semantics where a derivation shows how individual rewrites compose
to produce a term, which we can evaluate to a value through a sequence of state changes. is is a
framework for modeling aspects of the runtime behavior of the program before running it by describing
the space of possible transitions type and terms may take. Ultimately we’d like the term to transition
and terminate to a value in our language instead of becoming “stuck” as we encountered before.
Recall our little calculator language from before when we constructed our first parser:
data Expr
= Tr
| Fl
| IsZero Expr
| Succ Expr
| Pred Expr
| If Expr Expr Expr
| Zero
e expression syntax is as follows:
e ::= True
False
iszero e
succ e
pred e
if e then e else e
0
e small step evaluation semantics for this little language is uniquely defined by the following 9 rules.
ey describe each step that an expression may take during evaluation which may or may not terminate
and converge on a value.
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