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Syntax Definition
by Eelco Visser
1582 views
Pure and Declarative Syntax Definit...
by Guido Wachsmuth
2946 views
Formal Grammars
by Eelco Visser
2807 views
Software languages
by Eelco Visser
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Programming languages
by Eelco Visser
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Language
by Guido Wachsmuth
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![Term Rewriting
Terms
13
Let(
[ FunDec(
"fact"
, [FArg("n", Tp(Tid("int")))]
, Tp(Tid("int"))
, If(
Lt(Var("n"), Int("1"))
...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-14-2048.jpg?cb=1668514698)
![Term Rewriting
Syntax of Terms
module Terms
sorts Cons Term
lexical syntax
Cons = [a-zA-Z][a-zA-Z0-9]*
context-free syntax...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-15-2048.jpg?cb=1668514698)
![Term Rewriting
Syntax of Terms
module Terms
sorts Cons Term
lexical syntax
Cons = [a-zA-Z][a-zA-Z0-9]*
context-free syntax...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-16-2048.jpg?cb=1668514698)
![Term Rewriting
Syntax of Terms
module ATerms
sorts Cons Term
lexical syntax
Cons = [a-zA-Z][a-zA-Z0-9]*
Cons = String
Int ...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-17-2048.jpg?cb=1668514698)
![Term Rewriting
Syntax of A(nnotated)Terms
module ATerms
sorts Cons Term
lexical syntax
Cons = [a-zA-Z][a-zA-Z0-9]*
// more...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-18-2048.jpg?cb=1668514698)
![context-free syntax
Exp.Uminus = [- [Exp]]
Exp.Power = [[Exp] ** [Exp]]
Exp.Times = [[Exp] * [Exp]]
Exp.Divide = [[Exp] / ...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-20-2048.jpg?cb=1668514698)
![example: map
Term Rewriting
Rules with Parameters
26
[ 1
, 2
, 3
]
[ 2
, 3
, 4
]
map(inc)](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-35-2048.jpg?cb=1668514698)
![example: map
Term Rewriting
Rules with Parameters
26
[ 1
, 2
, 3
]
[ 2
, 3
, 4
]
map(inc)
inc
1
2
3
2
3
4inc
inc](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-36-2048.jpg?cb=1668514698)
![example: map
Term Rewriting
Rules with Parameters
map(s): [] -> []
map(s): [x|xs] -> [<s> x | <map(s)> xs]
26
[ 1
, 2
, 3
...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-37-2048.jpg?cb=1668514698)
![example: zip
Term Rewriting
Rules with Parameters
27
[ 1
, 2
, 3
]
[ (1,4)
, (2,5)
, (3,6)
]
[ 4
, 5
, 6
]
zip](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-38-2048.jpg?cb=1668514698)
![example: zip
Term Rewriting
Rules with Parameters
27
[ 1
, 2
, 3
]
[ (1,4)
, (2,5)
, (3,6)
]
[ 4
, 5
, 6
]
zip
[ 1
, 2
, 3...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-39-2048.jpg?cb=1668514698)
![example: zip
Term Rewriting
Rules with Parameters
27
[ 1
, 2
, 3
]
[ (1,4)
, (2,5)
, (3,6)
]
[ 4
, 5
, 6
]
zip
[ 1
, 2
, 3...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-40-2048.jpg?cb=1668514698)
![example: zip
Term Rewriting
Rules with Parameters
zip(s): ([],[]) -> []
zip(s): ([x|xs],[y|ys]) -> [<s> (x,y) | <zip(s)> (...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-41-2048.jpg?cb=1668514698)
![example: fold
Term Rewriting
Rules with Parameters
28
[1,2,3] foldr(!0,add) 6](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-42-2048.jpg?cb=1668514698)
![example: fold
Term Rewriting
Rules with Parameters
28
[1,2,3] foldr(!0,add) 6
[]
0
[3]
3
[2,3]
56
[1,2,3]](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-43-2048.jpg?cb=1668514698)
![example: fold
Term Rewriting
Rules with Parameters
foldr(s1,s2): [] -> <s1>
foldr(s1,s2): [x|xs] -> <s2> (x,<foldr(s1,s2)>...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-44-2048.jpg?cb=1668514698)
![example: inverse
Term Rewriting
Rules with Parameters
29
[1,2,3] inverse(|[]) [3,2,1]](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-45-2048.jpg?cb=1668514698)
![example: inverse
Term Rewriting
Rules with Parameters
29
[1,2,3] inverse(|[]) [3,2,1]
[2,3]
[1][]
[1,2,3] [3]
[2,1] [3,2,1...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-46-2048.jpg?cb=1668514698)
![example: inverse
Term Rewriting
Rules with Parameters
inverse(|is): [] -> is
inverse(|is): [x|xs] -> <inverse(|[x|is])> xs...](https://image.slidesharecdn.com/termrewriting-170116144519/75/Term-Rewriting-47-2048.jpg?cb=1668514698)
