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A Semantic Analysis of Structural Recursion Andreas Abel
 

Summary: Slide 1
A Semantic Analysis of Structural Recursion
Andreas Abel
May 10, 1999
Slide 2
Example 1: Addition of ordinal numbers in SML
datatype Nat = . . .
datatype Ord = O
| S of Ord
| Lim of Nat ≠> Ord;
fun addord x O = x
| addord x (S y ) = S (addord x y )
| addord x (Lim f) = Lim (fn z => addord x (f z))
WST '99 Andreas Abel 1
Slide 3
Example 2: A pattern matching proof in LEGO
$[leRefl: {T|ClTy}{t|ClTm T}{v:Val T Ts0 t}vLe v v];
[[S,T:ClTy][t:ClTm T][v:Val T Ts0 t][s:ClTm S]
[w:Val S Ts0 s][R:Ty one][r:ClTm (UnfoldRec R)][x:ClV r]
leRefl vUnit ==> leUnit

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen

 

Collections: Computer Technologies and Information Sciences